#Orthogonalprojection,MathdictionaryOrthogonalprojection,definitionOrthogonalprojection,dictionary#Orthogonalprojection,mathdictionaryOrthogonalsequence,DefinitionmOrthogonalsequence,Dictionarym!Orthogonalsequence,MathDictionarym!Orthogonalsequence,MathdictionarymOrthogonalsequence,definitionmOrthogonalsequence,dictionarym!Orthogonalsequence,mathdictionarymOrthogonalvectors,DefinitionOrthogonalvectors,Dictionary Orthogonalvectors,MathDictionary Orthogonalvectors,MathdictionaryOrthogonalvectors,definitionOrthogonalvectors,dictionary Orthogonalvectors,mathdictionaryOrthographic,Definition/Orthographic,Dictionary/Orthographic,MathDictionary/hdictionary,OrthogonalSequenceMathDictionary,Orthogonal_SequenceMathdictionary,Orthogonal_Sequencemathdictionary,Orthogonal_SequenceMathDictionary,OrthogonalsequenceMathdictionary,Orthogonalsequencemathdictionary,OrthogonalsequenceMathDictionary,Orthogonal_sequenceMathdictionary,Orthogonal_sequencemathdictionary,Orthogonal_sequenceedefinition,Orthogonal_sequenceDictionary,orthogonalsequencedictionary,orthogonalsequenceDictionary,orthogonal_sequencedictionary,orthogonal_sequenceDictionary,OrthogonalSequencedictionary,OrthogonalSequenceDictionary,Orthogonal_Sequencedictionary,Orthogonal_SequenceDictionary,Orthogonalsequencedictionary,OrthogonalsequenceDictionary,Orthogonal_sequencedictionary,Orthogonal_sequenceMathDictionary,orthogonalsequenceMathdictionary,orthogonalsequencemathdictionary,orthogonalsequenceMathDictionary,orthogonal_sequenceMathdictionary,orthogonal_sequencemathdictionary,orthogonal_sequenceMathDictionary,OrthogonalSequenceMathdictionary,OrthogonalSequencemat{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 19 "orthogonal vectors," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 11 " two given " } {HYPERLNK 45 "vectors" 5 "Definition/vector" "" }{TEXT -1 7 " in an " } {HYPERLNK 45 "inner product space" 5 "Definition/innerproductspace" "" }{TEXT -1 48 " are orthogonal if their inner product is zero. " } } } ձ{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 2 "g," } } {PARA 0 "> " 0 "" {TEXT -1 1 "(" } {TEXT 22 9 "Mechanics" } {TEXT -1 2 ") " } {TEXT 22 10 "symbol for" } {TEXT -1 5 " the " } {HYPERLNK 45 "local gravitational constant" 5 "Definition/localgravitationalconstant" "" }{TEXT -1 2 ". " } } } definition,Pdepde definitiondefinition,Pdf=ipdf definition definition,Pepe definitiondefinition,PeanoArithmeticPeano arithmetic definitiondefinition,PeanoAxiomsPeano's axioms definitiondefinition,PeanoCurveJPeano curve definitiondefinition,PeanoGuiseppePeano, Guiseppe definitiondefinition,PeanoSpacePeano space definitiondefinition,Peano_ArithmeticPeano arithmetic definitiondefinition,Peano_AxiomsPeano's axioms definitiondefinition,Peano_CurveJPeano curve definitiondefinition,Peano_GuiseppePeano, Guiseppe definitiondefinition,Peano_SpacePeano space definitiondefinition,Peano_arithmeticPeano arithmetic definitiondefinition,Peano_axiomsPeano's axioms definitiondefinition,Peano_curveJPeano curve definitionOsculatingcircle,Dictionary! "Osculatingcircle,MathDictionary! "Osculatingcircle,Mathdictionary! "Osculatingcircle,definition! "Osculatingcircle,dictionary! "Osculatingcircle,mathdictionary! "Osculatingplane,Definition}Osculatingplane,Dictionary}Osculatingplane,MathDictionary}Osculatingplane,Mathdictionary}Osculatingplane,definition}Osculatingplane,dictionary}Osculatingplane,mathdictionary}!dictionary,Pareto_efficient_point"rPareto optimal point definitiondictionary,Pareto_optimal_point? " 0 "" {TEXT -1 13 "orthographic," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 18 " another word for " } {HYPERLNK 45 "orthogonal" 5 "Definition/orthogonal" "" }{TEXT -1 2 ". " } } } dictionary,Overringover-ring definitiondictionary,Overview)HWMathematics and Engineering Dictionary dictionary,PhSp definition؏P definitiondictionary,P-Elementp-element definitiondictionary,P-Groupp-group definitiondictionary,P-PrimaryModulemp-primary module definitiondictionary,P-Primary_Modulemp-primary module definitiondictionary,P-Subgrouplp-subgroup definitiondictionary,P-Valuep-value definitiondictionary,P-primary_modulemp-primary module definitiondictionary,P-primarymodulemp-primary module definitiondictionary,PElementp-element definitiondictionary,PEqualsNpI9P equals NP definitiondictionary,PGroupp-group definitiondictionary,PPrimaryModulemp-primary module definition"MathDictionary,orthogonalfunctions" orthogonal functions definitionMathDictionary,orthogonalgrouporthogonal group definitionMathDictionary,orthogonalmatrix,orthogonal matrix definition#MathDictionary,orthogonalprojection#orthogonal projection definition!MathDictionary,orthogonalsequence!morthogonal sequence definition MathDictionary,orthogonalvectors orthogonal vectors definitionMathDictionary,orthographic2/orthogonal definitionorthographic definitiondictionary,Orthogonalmatrix,orthogonal matrix definitiondictionary,Orthogonalprojection#orthogonal projection definitiondictionary,Orthogonalsequence!morthogonal sequence definitiondictionary,Orthogonalvectors orthogonal vectors definitiondictionary,Orthographic2/orthogonal definitionorthographic definitiondictionary,Orthonormal4orthonormal definitiondictionary,OrthonormalFunctions#eborthonormal functions definitiondictionary,OrthonormalSequence"orthonormal sequence definitionDefinition,Paired_Vector_Spaces"{paired vector spaces definition Definition,Paired_sample_problem#Mpaired-sample problem definitionDefinition,Paired_vector_spaces"{paired vector spaces definitionDefinition,Pairedsampleproblem#Mpaired-sample problem definitionDefinition,Pairedvectorspaces"{paired vector spaces definitionDefinition,Pairwise$pairwise 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definitionDefinition,Orthogonal_matrix,orthogonal matrix definition Definition,Orthogonal_projection#orthogonal projection definitionDefinition,Orthogonal_sequence!morthogonal sequence definitionDefinition,Orthogonal_vectors orthogonal vectors definitionDefinition,Orthogonalcomplement#=orthogonal complement definitionmathdictionary,orthogonalgrouporthogonal group definitionmathdictionary,orthogonalmatrix,orthogonal matrix definition#mathdictionary,orthogonalprojection#orthogonal projection definition!mathdictionary,orthogonalsequence!morthogonal sequence definition mathdictionary,orthogonalvectors orthogonal vectors definitionmathdictionary,orthographic2/orthogonal definitionorthographic definitionmathdictionary,orthonormal4orthonormal definition$mathdictionary,orthonormal_functions#eborthonormal functions definitionOrthogonalGroup,mathdictionaryOrthogonalMatrix,Definition,OrthogonalMatrix,Dictionary,OrthogonalMatrix,MathDictionary,OrthogonalMatrix,Mathdictionary,OrthogonalMatrix,definition,OrthogonalMatrix,dictionary,OrthogonalMatrix,mathdictionary,OrthogonalProjection,DefinitionOrthogonalProjection,Dictionary#OrthogonalProjection,MathDictionary#OrthogonalProjection,MathdictionaryOrthogonalProjection,definitionDefinition,orthogonalvectorsdefinition,orthogonalvectorsDefinition,orthogonal_vectorsdefinition,orthogonal_vectorsDefinition,OrthogonalVectorsdefinition,OrthogonalVectorsDefinition,Orthogonal_Vectorsdefinition,Orthogonal_VectorsDefinition,Orthogonalvectorsdefinition,OrthogonalvectorsDefinition,Orthogonal_vectorsdefinition,Orthogonal_vectorsDictionary,orthogonalvectorsdictionary,orthogonalvectorsDictionary,orthogonal_vectorsdictionary,orthogonal_vectorsDictionary,OrthogonalVectorsdictionary,OrthogonalVectorsDictionary,Orthogonal_Vectorsdictionary,Orthogonal_VectorsDictionary,Orthogonalvectorsdictionary,OrthogonalvectorsDictionary,Orthogonal_vectorsdictionary,Orthogonal_vectorsMathDictionary,orthogonalvectorsMathdictionary,orthogonalvectorsmathdictionary,orthogonalvectorsMathDictionary,orthogonal_vectorsMathdictionary,orthogonal_vectorsmathdictionary,orthogonal_vectorsMathDictionary,OrthogonalVectorsMathdictionary,OrthogonalVectorsmathdictionary,OrthogonalVectorsMaary,OrthogonalProjectionMathdictionary,OrthogonalProjectionmathdictionary,OrthogonalProjectionMathDictionary,Orthogonal_ProjectionMathdictionary,Orthogonal_Projectionmathdictionary,Orthogonal_ProjectionMathDictionary,OrthogonalprojectionMathdictionary,Orthogonalprojectionmathdictionary,OrthogonalprojectionMathDictionary,Orthogonal_projectionMathdictionary,Orthogonal_projectionmathdictionary,Orthogonal_projectiontiondictionary,orthogonalprojectionDictionary,orthogonal_projectiondictionary,orthogonal_projectionDictionary,OrthogonalProjectiondictionary,OrthogonalProjectionDictionary,Orthogonal_Projectiondictionary,Orthogonal_ProjectionDictionary,Orthogonalprojectiondictionary,OrthogonalprojectionDictionary,Orthogonal_projectiondictionary,Orthogonal_projectionMathDictionary,orthogonalprojectionMathdictionary,orthogonalprojectionmathdictionary,orthogonalprojectionMathDictionary,orthogonal_projectionMathdictionary,orthogonal_projectionmathdictionary,orthogonal_projectionMathDictionm{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 20 "orthogonal sequence," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 3 " a " } {HYPERLNK 45 "sequence" 5 "Definition/sequence" "" }{TEXT -1 14 " of pair-wise " } {HYPERLNK 45 "orthogonal" 5 "Definition/orthogonal" "" }{TEXT -1 1 " " } {HYPERLNK 45 "vectors" 5 "Definition/vector" "" }{TEXT -1 31 ", often functions, such as the " } {HYPERLNK 45 "Legendre polynomials" 5 "Definition/Legendrepolynomials" "" }{TEXT -1 10 ". 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" } } } m=Definition,orthogonalsequenceorthogonal sequence definitionm=Definition,immediateinferenceimmediate inference definitionm2Definition,HilbertDavidHilbert, David definitionmFDefinition,weaklawoflargenumbersweak law of large numbers definitionm7Definition,polyhedralanglepolyhedral angle definitionm.Definition,traversabletraversable definitionm9Definition,rationalfunctionrational function definitionm$Definition,modulemodule definitionm(Definition,multiplemultiple definition%n3Definition,decimalsystemdecimal system definition(n(Definition,disjointdisjoint definition/n0Definition,LeibnizslawLeibniz's law definitionKn>Definition,trisectingtheangletrisecting the angle definitionQn Definition,bytebyte definitiontn$Definition,forestforest definitionnADefinition,Jordan-HoldertheoremJordan-Holder theorem definitionn5Definition,saddlefunctionsaddle function definitionn3Definition,TuringmachineTuring machine definitionn*Definition,supertasksupertask definitionn*Definition,bipartitebipartite definitionn;Definition,unsolvableproblemunsolvable problem definitionn"Definition,metermeter definitionn5Definition,FloquettheoremFloquet theorem definitionn0Definition,displacementdisplacement definitionn1Definition,predualspacepredual space definitionn1Definition,nablasquarednabla squared definitionn7Definition,NeumannJohnvonNeumann, John von definitionn,Definition,LagrangianLagrangian definitiono6Definition,brachistochronebrachistochrone definition&dictionary,pascalmystichexagramtheorem.0Pascal's mystic hexagram theorem definition*dictionary,pascals_mystic_hexagram_theorem.0Pascal's mystic hexagram theorem definitiondictionary,pascals_triangle>Pascal's triangle definition'dictionary,pascalsmystichexagramtheorem.0Pascal's mystic hexagram theorem definitiondictionary,pascalstriangle>Pascal's triangle definitiondictionary,pascaltriangle>Pascal's triangle definitiondictionary,path1Hamiltonian chain definition path definition"MathDictionary,OrthonormalSequence"orthonormal sequence definition$MathDictionary,Orthonormal_Functions#eborthonormal functions definition#MathDictionary,Orthonormal_Sequence"orthonormal sequence definition$MathDictionary,Orthonormal_functions#eborthonormal functions definition#MathDictionary,Orthonormal_sequence"orthonormal sequence definition#MathDictionary,Orthonormalfunctions#eborthonormal functions definition"MathDictionary,Orthonormalsequence"orthonormal sequence definitionu0Definition,osculatedefinition,osculateDefinition,Osculatedefinition,OsculateDictionary,osculatedictionary,osculateDictionary,Osculatedictionary,OsculateMathDictionary,osculateMathdictionary,osculatemathdictionary,osculateMathDictionary,OsculateMathdictionary,Osculatemathdictionary,OsculateDefinition,Pappus_theorem uPappus' theorem definitionDefinition,Pappustheorem uPappus' theorem definitionDefinition,ParJpar. definitionDefinition,ParabolaQ_parabola definitionDefinition,Parabolicparabolic definitionDefinition,ParabolicSpiralYparabolic spiral definitionDefinition,Parabolic_SpiralYparabolic spiral definitionDefinition,Parabolic_spiralYparabolic spiral definitionDefinition,ParabolicspiralYparabolic spiral definition Mathdictionary,pochhammer_symbol Pochhammer symbol definitionMathdictionary,pochhammersymbol Pochhammer symbol definition"Mathdictionary,poincare_conjecture!|Poincare conjecture definition#Mathdictionary,poincare_jules_henri#Poincare, Jules Henri definitionMathdictionary,poincare_lemma>5Poincare's lemma definition!Mathdictionary,poincareconjecture!|Poincare conjecture definition!Mathdictionary,poincarejuleshenri#Poincare, Jules Henri definitionMathdictionary,poincarelemma>5Poincare's lemma definitionDictionary,Ovals_Of_Cassiniovals of Cassini definitionDictionary,Ovals_of_cassiniovals of Cassini definitionDictionary,Ovalsofcassiniovals of Cassini definitionDictionary,Over over definitionDictionary,Over-Ringover-ring definitionDictionary,OverRingover-ring definitionDictionary,Over_Ringover-ring definitionDictionary,Over_ringover-ring definitionDictionary,OverdeterminedPoverdetermined definitionDictionary,Overlap=overlap definitionM{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 22 "axis of perspectivity," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "perspective" 5 "Definition/perspective" "" }{TEXT -1 1 "." } } } in an " } {HYPERLNK 45 "inner product space" 5 "Definition/innerproductspace" "" }{TEXT -1 48 " are orthogonal if their inner product is zero. " } } } ձ{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 2 "g," } } {PARA 0 "> " 0 "" {TEXT -1 1 "(" } {TEXT 22 9 "Mechanics" } {TEXT -1 2 ") " } {TEXT 22 10 "symbol for" } {TEXT -1 5 " the " } {HYPERLNK 45 "local gravitational constant" 5 "Definition/localgravitationalconstant" "" }{TEXT -1 2 ". 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definition>Definition,referencedefinition,referenceDefinition,Referencedefinition,ReferenceDictionary,referencedictionary,referenceDictionary,Referencedictionary,ReferenceMathDictionary,referenceMathdictionary,referencemathdictionary,referenceMathDictionary,ReferenceMathdictionary,Referencemathdictionary,ReferenceMathdictionary,Perfect_numberEperfect number definitionMathdictionary,Perfect_set_perfect set definitionMathdictionary,Perfect_squaret perfect square definitionMathdictionary,Perfectmatchingoperfect matching definitionMathdictionary,PerfectnumberEperfect number definitionMathdictionary,Perfectset_perfect set definitionMathdictionary,Perfectsquaret perfect square definitionMathdictionary,Perigon.Lsround angle definitionoperigon definitionMathdictionary,Perimeterh perimeter definitionDefinition,placevaluenotation"Vplace-value notation definitionDefinition,planar~Bplanar definitionDefinition,planar_pointplanar point definitionDefinition,planarpointplanar point 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definition%dictionary,outer_caratheodory_measure(Gouter Caratheodory measure definitiondictionary,outer_jordan_measure"Nouter Jordan measure definition!dictionary,outer_lebesgue_measure$outer Lebesgue measure definitionoutput_set,dictionary output_set,mathdictionary output_variable,Definitionboutput_variable,Dictionaryboutput_variable,MathDictionaryboutput_variable,Mathdictionaryboutput_variable,definitionboutput_variable,dictionaryboutput_variable,mathdictionaryboutputset,Definition outputset,Dictionary outputset,MathDictionary outputset,Mathdictionary outputset,definition outputset,dictionary %definition,Outer_caratheodory_measure(Gouter Caratheodory measure definitiondefinition,Outer_jordan_measure"Nouter Jordan measure definition!definition,Outer_lebesgue_measure$outer Lebesgue measure definitiondefinition,Outer_measureNouter measure definitiondefinition,Outerautomorphism aouter automorphism definition#definition,Outercaratheodorymeasure(Gouter Caratheodory measure 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4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 21 "orthonormal sequence," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 4 " an " } {HYPERLNK 45 "orthogonal sequence" 5 "Definition/orthogonalsequence" "" }{TEXT -1 4 " of " } {HYPERLNK 45 "vectors" 5 "Definition/vector" "" }{TEXT -1 26 ", often functions, all of " } {HYPERLNK 45 "unit" 5 "Definition/unit" "" }{TEXT -1 1 " " } {HYPERLNK 45 "norm" 5 "Definition/norm" "" }{TEXT -1 56 ". The standard basis in Euclidean space is orthonormal. " } } } Definition,OuterJordanMeasure"Nouter Jordan measure definitionDefinition,OuterLebesgueMeasure$outer Lebesgue measure definitionDefinition,OuterMeasureNouter measure definitionDefinition,Outer_Automorphism aouter automorphism definition%Definition,Outer_Caratheodory_Measure(Gouter Caratheodory measure definitionDefinition,Outer_Jordan_Measure"Nouter Jordan measure definition!Definition,Outer_Lebesgue_Measure$outer Lebesgue measure definitionDefinition,Outer_MeasureNouter measure definitionDefinition,Outer_automorphism aouter automorphism definitionjZj{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 11 "oscillation" } } {PARA 0 "> " 0 "" {TEXT -1 9 "(abbrev. " } {TEXT 39 3 "osc" } {TEXT -1 3 "), " } {TEXT 22 3 "n. " } {TEXT -1 46 "a measure of the spread of a bounded set, the " } {HYPERLNK 45 "supremal" 5 "Definition/supremal" "" }{TEXT -1 77 " difference between pairs of elements, defined as the difference between the " } {HYPERLNK 45 "supremum" 5 "Definition/supremum" "" }{TEXT -1 5 " and " } {HYPERLNK 45 "infimum" 5 "Definition/infimum" "" }{TEXT -1 79 " of the set. The oscillation of a function on an interval is also known as its " } {TEXT 22 7 "saltus." } {TEXT -1 10 " See also " } {HYPERLNK 45 "bounded variation" 5 "Definition/boundedvariation" "" }{TEXT -1 2 ". " } } } Adefinition,One_taileddefinition,Only_ifdefinition,OpenDiskdefinition,Open_coverRdefinition,Opencoverdefinition,Operatedefinition,OppositeRing8definition,OptimalControldefinition,Optimalcontrol>definition,Orbit)definition,Order-Preservingӈdefinition,Order_Completedefinition,Order_idealdefinition,Ordercompletedefinition,Ordered_Geometrydefinition,Orderedgeometryjdefinition,Orderofconvergence{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 17 "Peano arithmetic," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 19 " the theory of the " } {HYPERLNK 45 "natural numbers" 5 "Definition/naturalnumber" "" }{TEXT -1 15 " as defined by " } {HYPERLNK 45 "Peano's axioms" 5 "Definition/Peanosaxioms" "" }{TEXT -1 2 ". " } } } Osbornes_Rule,dictionaryOsbornes_Rule,mathdictionaryOsbornes_rule,DefinitionOsbornes_rule,DictionaryOsbornes_rule,MathDictionaryOsbornes_rule,MathdictionaryOsbornes_rule,definitionOsbornes_rule,dictionaryOsbornes_rule,mathdictionaryOsbornesrule,DefinitionOsbornesrule,DictionaryOsbornesrule,MathDictionaryOsbornesrule,MathdictionaryOsbornesrule,definitionOsbornesrule,dictionaryMathDictionary,OsborneRuleOsborne's rule definitionMathDictionary,Osborne_RuleOsborne's rule definitionMathDictionary,Osborne_ruleOsborne's rule definitionMathDictionary,OsborneruleOsborne's rule definitionMathDictionary,OsbornesRuleOsborne's rule definitionMathDictionary,Osbornes_RuleOsborne's rule definitionMathDictionary,Osbornes_ruleOsborne's rule definitionMathDictionary,OsbornesruleOsborne's rule definitionMathDictionary,Oscosc 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" Osculating_Circle,Mathdictionary! "Osculating_Circle,definition! "Osculating_Circle,dictionary! " Osculating_Circle,mathdictionary! "Osculating_Plane,Definition}Osculating_Plane,Dictionary}Osculating_Plane,MathDictionary}Osculating_Plane,Mathdictionary}Osculating_Plane,definition}Osculating_Plane,dictionary}Osculating_Plane,mathdictionary}Osculating_circle,Definition! "{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 10 "over-ring," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 3 " a " } {HYPERLNK 45 "ring" 5 "Definition/ring" "" }{TEXT -1 12 ", such as a " } {HYPERLNK 45 "quotient ring" 5 "Definition/quotientring" "" }{TEXT -1 41 ", in which a given ring can be embedded. 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" 0 "" {TEXT -1 17 "osculating plane," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 31 " the plane spanned by the unit " } {HYPERLNK 45 "tangent" 5 "Definition/tangent" "" }{TEXT -1 10 " and unit " } {HYPERLNK 45 "principal normal" 5 "Definition/principalnormal" "" }{TEXT -1 108 " vectors to a space curve at a given point; the curvature of the curve is evaluated in this plane. The unit " } {HYPERLNK 45 "binormal" 5 "Definition/binormal" "" }{TEXT -1 47 " is the normal vector to the osculating plane. " } } } RDefinition,oblatespheroiddefinition,oblatespheroidDefinition,oblate_spheroiddefinition,oblate_spheroidDefinition,OblateSpheroiddefinition,OblateSpheroidDefinition,Oblate_Spheroiddefinition,Oblate_SpheroidDefinition,Oblatespheroiddefinition,OblatespheroidDefinition,Oblate_spheroiddefinition,Oblate_spheroidDictionary,oblatespheroiddictionary,oblatespheroidDictionary,oblate_spheroiddictionary,oblate_spheroidDictionary,OblateSpheroiddictionary,OblateSpheroidDictionary,Oblate_Spheroiddictionary,Oblate_SpheroidDictionary,Oblatespheroiddictionary,OblatespheroidDictionary,Oblate_spheroiddictionary,Oblate_spheroidMathDictionary,oblatespheroidMathdictionary,oblatespheroidmathdictionary,oblatespheroidMathDictionary,oblate_spheroidMathdictionary,oblate_spheroidmathdictionary,oblate_spheroidMathDictionary,OblateSpheroidMathdictionary,OblateSpheroidmathdictionary,OblateSpheroidMathDictionary,Oblate_SpheroidMathdictionary,Oblate_Spheroidmathdictionary,Oblate_SpheroidMathDictoblate_spheroid,definitionRoblate_spheroid,dictionaryRoblate_spheroid,mathdictionaryRoblatespheroid,DefinitionRoblatespheroid,DictionaryRoblatespheroid,MathDictionaryRoblatespheroid,MathdictionaryRoblatespheroid,definitionRoblatespheroid,dictionaryRoblatespheroid,mathdictionaryRoblique,Definitionoblique,Dictionaryoblique,MathDictionaryoblique,Mathdictionaryoblique,definitionionary,OblatespheroidMathdictionary,Oblatespheroidmathdictionary,OblatespheroidMathDictionary,Oblate_spheroidMathdictionary,Oblate_spheroidmathdictionary,Oblate_spheroidion,Oblate_Spheroiddefinition,Oblate_SpheroidDefinition,Oblatespheroiddefinition,OblatespheroidDefinition,Oblate_spheroiddefinition,Oblate_spheroidDictionary,oblatespheroiddictionary,oblatespheroidDictionary,oblate_spheroiddictionary,oblate_spheroidDictionary,OblateSpheroiddictionary,OblateSpheroidDictionary,Oblate_Spheroiddictionary,Oblate_SpheroidDictionary,Oblatespheroiddictionary,OblatespheroidDictionary,Oblate_spheroiddictionary,Oblate_spheroidMathDictionary,oblatespheroidMathdictionary,oblatespheroidmathdictionary,oblatespheroidMathDictionary,oblate_spheroidMathdictionary,oblate_spheroidmathdictionary,oblate_spheroidMathDictionary,OblateSpheroidMathdictionary,OblateSpheroidmathdictionary,OblateSpheroidMathDictionary,Oblate_SpheroidMathdictionary,Oblate_Spheroidmathdictionary,Oblate_SpheroidMathDictmathdictionary,orderedstructureordered structure definition!mathdictionary,orderedvectorspace"Kordered vector space definitionmathdictionary,orderideal+order ideal definitionmathdictionary,ordering#ordering definitionmathdictionary,orderintervalAorder interval definitionmathdictionary,ordernotationorder notation definition!mathdictionary,orderofconvergenceCOorder of convergence definition[rate of convergence definitionmathdictionary,orderofmagnitude Sorder of magnitude definitionDictionary,Omegainconsistency!Domega inconsistency definitionDictionary,Oneh_one definitionDictionary,One-Manymone-many definitionDictionary,One-Oneone-one definition$Dictionary,One-PointCompactification("one-point compactification definition%Dictionary,One-Point_Compactification("one-point compactification definitionDictionary,One-Sidedone-sided definitionDictionary,One-Tailedone-tailed definitionDictionary,One-To-One#Oone-to-one definition%Dictionary,One-point_compactification("one-point compactification definitionF{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 7 "octant," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 255 " any of the eight trihedral sections into which the three-space is divided by the Cartesian coordinate axes. The first octant is that bounded by the positive directions of the three axes; the second, third, and fourth are counted anti-clockwise above the " } {TEXT 22 4 "x-y " } {TEXT -1 84 "plane, and the fifth to eighth are respectively below the first to fourth. See also " } {HYPERLNK 45 "orthant" 5 "Definition/orthant" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "quadrant" 5 "Definition/quadrant" "" }{TEXT -1 2 ". " } } } dictionary,Odegode definitiondictionary,OfSetsQsigma-field definitiondictionary,Of_SetsQsigma-field definitiondictionary,Of_setsQsigma-field definitiondictionary,OffDiagonaloff diagonal definitiondictionary,Off_Diagonaloff diagonal definitiondictionary,Off_diagonaloff diagonal definitiondictionary,Offdiagonaloff diagonal definitiondictionary,OfficerProblemofficer problem definitiondictionary,Officer_Problemofficer problem definitiondictionary,Officer_problemofficer problem definitiondictionary,Officerproblemofficer problem definitionMathDictionary,octahedronoctahedron definitionMathDictionary,octaloctal definitionMathDictionary,octantFoctant definitionMathDictionary,oddq odd definitionMathDictionary,odd_part|odd part definitionMathDictionary,oddpart|odd part definitionMathDictionary,odegode definitionMathDictionary,of_setsQsigma-field definitionMathDictionary,off_diagonaloff diagonal definitionMathDictionary,offdiagonaloff diagonal definitionMathDictionary,officer_problemofficer problem definitionoct,mathdictionaryoct-,Definitionoct-,Dictionaryoct-,MathDictionaryoct-,Mathdictionaryoct-,definitionoct-,dictionaryoct-,mathdictionaryoctad,Definition.octad,Dictionary.octad,MathDictionary.octad,Mathdictionary.octad,definition.octad,dictionary.octad,mathdictionary.octagon,Definitiongoctagon,Dictionarygoctagon,MathDictionarygaMDefinition,obliqueangledefinition,obliqueangleDefinition,oblique_angledefinition,oblique_angleDefinition,ObliqueAngledefinition,ObliqueAngleDefinition,Oblique_Angledefinition,Oblique_AngleDefinition,Obliqueangledefinition,ObliqueangleDefinition,Oblique_angledefinition,Oblique_angleDictionary,obliqueangledictionary,obliqueangleDictionary,oblique_angledictionary,oblique_angleDictionary,ObliqueAngledictionary,ObliqueAngleDictionary,Oblique_Angledictionary,Oblique_AngleDictionary,Obliqueangledictionary,ObliqueangleDictionary,Oblique_angledictionary,Oblique_angleMathDictionary,obliqueangleMathdictionary,obliqueanglemathdictionary,obliqueangleMathDictionary,oblique_angleMathdictionary,oblique_anglemathdictionary,oblique_angleMathDictionary,ObliqueAngleMathdictionary,ObliqueAnglemathdictionary,ObliqueAngleMathDictionary,Oblique_AngleMathdictionary,Oblique_Anglemathdictionary,Oblique_AngleMathDictionary,ObliqueangleMathdictionary,Obliqueanglemathdictionary,Obliqueans{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 7 "obtuse," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 1 " " } {TEXT 39 2 "1." } {TEXT -1 39 " (of an angle) strictly greater than a " } {HYPERLNK 45 "right angle" 5 "Definition/rightangle" "" }{TEXT -1 26 " but strictly less than a " } {HYPERLNK 45 "straight angle" 5 "Definition/straightangle" "" }{TEXT -1 2 ". " } {TEXT 39 2 "2." } {TEXT -1 79 " (of a triangle) having one interior angle greater than a right angle. Compare " } {HYPERLNK 45 "acute" 5 "Definition/acute" "" }{TEXT -1 2 ". " } } } oblique,dictionaryoblique,mathdictionaryoblique_angle,Definitionaoblique_angle,Dictionaryaoblique_angle,MathDictionaryaoblique_angle,Mathdictionaryaoblique_angle,definitionaoblique_angle,dictionaryaoblique_angle,mathdictionaryaobliqueangle,Definitionaobliqueangle,Dictionaryaobliqueangle,MathDictionaryaobliqueangle,Mathdictionaryaobliqueangle,definitionaobliqueangle,dictionaryagleMathDictionary,Oblique_angleMathdictionary,Oblique_anglemathdictionary,Oblique_angleon,oblique_angleDefinition,ObliqueAngledefinition,ObliqueAngleDefinition,Oblique_Angledefinition,Oblique_AngleDefinition,Obliqueangledefinition,ObliqueangleDefinition,Oblique_angledefinition,Oblique_angleDictionary,obliqueangledictionary,obliqueangleDictionary,oblique_angledictionary,oblique_angleDictionary,ObliqueAngledictionary,ObliqueAngleDictionary,Oblique_Angledictionary,Oblique_AngleDictionary,Obliqueangledictionary,ObliqueangleDictionary,Oblique_angledictionary,Oblique_angleMathDictionary,obliqueangleMathdictionary,obliqueanglemathdictionary,obliqueangleMathDictionary,oblique_angleMathdictionary,oblique_anglemathdictionary,oblique_angleMathDictionary,ObliqueAngleMathdictionary,ObliqueAnglemathdictionary,ObliqueAngleMathDictionary,Oblique_AngleMathdictionary,Oblique_Anglemathdictionary,Oblique_AngleMathDictionary,ObliqueangleMathdictionary,Obliqueanglemathdictionary,Obliquean2{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 7 "oblong," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 1 " " } {TEXT 39 2 "1." } {TEXT -1 1 " " } {HYPERLNK 45 "rectangular" 5 "Definition/rectangular" "" }{TEXT -1 2 ". " } {TEXT 39 2 "2." } {TEXT -1 1 " " } {TEXT 22 3 "n. " } {TEXT -1 17 "another word for " } {HYPERLNK 45 "rectangle" 5 "Definition/rectangle" "" }{TEXT -1 2 ". " } } } dictionary,Omegainconsistency!Domega inconsistency definitiondictionary,Oneh_one definitiondictionary,One-Manymone-many definitiondictionary,One-Oneone-one definition$dictionary,One-PointCompactification("one-point compactification definition%dictionary,One-Point_Compactification("one-point compactification definitiondictionary,One-Sidedone-sided definitiondictionary,One-Tailedone-tailed definitiondictionary,One-To-One#Oone-to-one definition%dictionary,One-point_compactification("one-point compactification definitiondefinition,octaloctal definitiondefinition,octantFoctant definitiondefinition,oddq odd definitiondefinition,odd_part|odd part definitiondefinition,oddextensionTodd extension definitiondefinition,oddpart|odd part definitiondefinition,odegode definitiondefinition,of_setsQsigma-field definitiondefinition,off_diagonaloff diagonal definitiondefinition,offdiagonaloff diagonal definitiondefinition,officer_problemofficer problem definitiondefinition,officerproblemofficer problem definitionmathdictionary,OrderStatisticorder statistic definitionmathdictionary,Order_Completeorder-complete definitionmathdictionary,Order_Ideal+order ideal definitionmathdictionary,Order_IntervalAorder interval definitionmathdictionary,Order_Notationorder notation definition#mathdictionary,Order_Of_ConvergenceCOorder of convergence definition[rate of convergence definition!mathdictionary,Order_Of_Magnitude Sorder of magnitude definition mathdictionary,Order_Of_Symmetryorder of symmetry definitionmathdictionary,Order_Preservingyorder-preserving definitionDictionary,Octoct- definitionDictionary,Oct-oct- definitionDictionary,Octad.octad definitionDictionary,Octagongoctagon definitionDictionary,Octahedronoctahedron definitionDictionary,Octaloctal definitionDictionary,OctantFoctant definitionDictionary,Oddq odd definitionDictionary,OddPart|odd part definitionDictionary,Odd_Part|odd part definitionDictionary,Odd_part|odd part definitionDictionary,Oddpart|odd part definitionMathdictionary,Octagongoctagon definitionMathdictionary,Octahedronoctahedron definitionMathdictionary,Octaloctal definitionMathdictionary,OctantFoctant definitionMathdictionary,Oddq odd definitionMathdictionary,OddPart|odd part definitionMathdictionary,Odd_Part|odd part definitionMathdictionary,Odd_part|odd part definitionMathdictionary,Oddpart|odd part definitionMathdictionary,Odegode definitionMathdictionary,OfSetsQsigma-field definitionMathdictionary,Of_SetsQsigma-field definitionMathdictionary,Of_setsQsigma-field definitionMathdictionary,OffDiagonaloff diagonal definitionmathdictionary,oblong+2oblong definitionrectangle definitionmathdictionary,observer observer definitionmathdictionary,obtusesobtuse definitionmathdictionary,obverseobverse definitionmathdictionary,octoct- definitionmathdictionary,oct-oct- definitionmathdictionary,octad.octad definitionmathdictionary,octagongoctagon definitionmathdictionary,octahedronoctahedron definitionmathdictionary,octaloctal definitionmathdictionary,octantFoctant definitionMathDictionary,Obliqueangleaoblique angle definitionMathDictionary,Oblong+2oblong definitionrectangle definitionMathDictionary,Observer observer definitionMathDictionary,Obtusesobtuse definitionMathDictionary,Obverseobverse definitionMathDictionary,Octoct- definitionMathDictionary,Oct-oct- definitionMathDictionary,Octad.octad definitionMathDictionary,Octagongoctagon definitionMathDictionary,Octahedronoctahedron definitionMathDictionary,Octaloctal definitionZmathdictionary,nonresiduemathdictionary,nonsymmetricmathdictionary,normal_conemathdictionary,normal_familyDmathdictionary,normalcurve2mathdictionary,normalizeTmathdictionary,normalseriesmathdictionary,normedring,mathdictionary,nowheredifferentiablefunctionmathdictionary,np_hard_problemmathdictionary,null_hypothesis;mathdictionary,nullmeasuremathdictionary,numberfield%mathdictionary,numerical_eccentricity]mathdictionardictionardefinitionhindexparaboloidhyperbolichyperbolicparaboloiddefinit\mathdictionardictionardefinitionmindexderivatpartialmixedmixedpartialderivatdefinitXtrianglallintersectpointmathdictionardictionardefinitionoindexorthocentdefinitprimrelativecosetleftnumbpropertgroupfinitmathdictionardictionardefinitionhindexsubgrouphallhallsubgroupdefinitprecisparticularprinciplmethodmathematiccharacterusingpertainusedmathdictionardictionardefinitionmindexmathematicaldefinit{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 6 "octal," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 55 " (of a number or notation) written in or pertaining to " } {HYPERLNK 45 "place-value notation" 5 "Definition/place-valuenotation" "" }{TEXT -1 6 " with " } {HYPERLNK 45 "base" 5 "Definition/base" "" }{TEXT -1 74 " 8, often used in computing; 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" } } } Definition,nullsequenceMfDefinition,nullsetSDefinition,nullspaceDefinition,nullvectorDefinition,number,Definition,numberfield;Definition,numberlinecDefinition,numbertheoryDefinition,numerableADefinition,numeral6Definition,numerator`Definition,numericalNDefinition,numericalanalysis) Definition,numericaleccentricity uDefinition,numericalidentityDefinition,numericalquadratureAMathdictionary,Picard_Theorems2Picard's theorems definitionMathdictionary,Picard_methodPicard's method definitionMathdictionary,Picard_theorems2Picard's theorems definitionMathdictionary,PicardmethodPicard's method definitionMathdictionary,PicardsMethodPicard's method definitionMathdictionary,PicardsTheorems2Picard's theorems definitionMathdictionary,Picards_MethodPicard's method definitionMathdictionary,Picards_Theorems2Picard's theorems definitionNumberLine,MathDictionary‡Number_Field,definition؇Number_field,DictionaryDNumberfield,dictionaryNumbertheory,mathdictionaryNumerical,Mathdictionary 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Definition,one-pointcompactificationDefinition,onepointcompactificationdefinition,onepointcompactificationDefinition,one_point_compactificationdefinition,one_point_compactificationDefinition,OnePointCompactificationdefinition,OnePointCompactificationDefinition,One_Point_Compactificationdefinition,One_Point_CompactificationDefinition,Onepointcompactificationdefinition,OnepointcompactificationDefinition,One_point_compactificationdefinition,One_point_compactificationDictionary,onepointcompactificationdictionary,onepointcompactificationDictionary,one_point_compactificationdictionary,one_point_compactificationDictionary,OnePointCompactificationdictionary,OnePointCompactificationDictionary,One_Point_Compactificationdictionary,One_Point_CompactificationDictionary,Onepointcompactificationdictionary,OnepointcompactificationDictionary,One_point_compactificationdictionary,One_point_compactificationMathDictionary,onepointcompactificationMathdictionary,onepointcompactificationmathd]Definition,Only_ifskonly if definitionDefinition,Onlyifskonly if definitionDefinition,OnotationȤO notation definitionDefinition,Ontoonto definitionDefinition,Ontologyontology definitionDefinition,Opacityopacity definitionDefinition,Opaqueiopaque definitionDefinition,Openopen definitionDefinition,OpenBall#open ball definitionDefinition,OpenCover open cover definitionDefinition,OpenCovering open cover definitionDefinition,OrderedArrangement:(Mordered arrangement definitionpermutation definitionDefinition,OrderedGeometry=ordered geometry definitionDefinition,OrderedPair#yordered pair definitionDefinition,OrderedSet%ordered set definitionDefinition,OrderedStructureordered structure definitionDefinition,OrderedVectorSpace"Kordered vector space definitionDefinition,Ordered_Arrangement:(Mordered arrangement definitionpermutation definitionDefinition,Ordered_Geometry=ordered geometry definitionMathdictionary,oblong+2oblong definitionrectangle definitionMathdictionary,observer observer definitionMathdictionary,obtusesobtuse definitionMathdictionary,obverseobverse definitionMathdictionary,octoct- definitionMathdictionary,oct-oct- definitionMathdictionary,octad.octad definitionMathdictionary,octagongoctagon definitionMathdictionary,octahedronoctahedron definitionMathdictionary,octaloctal definitionMathdictionary,octantFoctant definitionmathdictionary,Observer observer definitionmathdictionary,Obtusesobtuse definitionmathdictionary,Obverseobverse definitionmathdictionary,Octoct- definitionmathdictionary,Oct-oct- definitionmathdictionary,Octad.octad definitionmathdictionary,Octagongoctagon definitionmathdictionary,Octahedronoctahedron definitionmathdictionary,Octaloctal definitionmathdictionary,OctantFoctant definitionmathdictionary,Oddq odd definitionF{inputresourcgivenobtainabllevelgivingmathdictionardictionardefinitionpindexfunctproductproductionfunctdefinitFspellarchaicderivadjectamsumergocogitophraslatinfamoupropositjustifysinglexpressthinkthereforcannotwhilargumedifichedoubtconceivabanythbeliefsuspensinvolvcertaintachievtherebgeometreuclidmodelaxiomaticevidselfclearonlyrestknowledgallsystematizdesirruledwholworkhismathematicsolvmethodintroducfoundmathematicianphilosophscientistfrenchmathdictionardictionardefinitiondindexrenedescartdescartesrendefinitFalsobelowrespectiveeighthfifthplanabovclockwisanticountfourththirdseconddirectpositboundfirstaxescoordinatcartesiandividspacintosectiontrihedraleightanymathdictionardictionardefinitionoindexoctantdefinitP{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 9 "dominate," } } {PARA 0 "> " 0 "" {TEXT 22 3 "vb." } {TEXT -1 5 " see " } {HYPERLNK 45 "dominated" 5 "Definition/dominated" "" }{TEXT -1 2 ". 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" } } } Definition,Orderedpair#yordered pair definitionDefinition,Orderedset%ordered set definitionDefinition,Orderedstructureordered structure definitionDefinition,Orderedvectorspace"Kordered vector space definitionDefinition,Orderideal+order ideal definitionDefinition,Ordering#ordering definitionDefinition,OrderintervalAorder interval definitionDefinition,Ordernotationorder notation definitionDefinition,OrderofconvergenceCOorder of convergence definition[rate of convergence definitiondefinition,Onlyifskonly if definitiondefinition,OnotationȤO notation definitiondefinition,Ontoonto definitiondefinition,Ontologyontology definitiondefinition,Opacityopacity definitiondefinition,Opaqueiopaque definitiondefinition,Openopen definitiondefinition,OpenBall#open ball definitiondefinition,OpenCover open cover definitiondefinition,OpenCovering open cover definitiondefinition,OpenDisk+open disk 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lemma definition!Mathdictionary,ScientificNotation!Zscientific notation definition"Mathdictionary,Scientific_Notation!Zscientific notation definition"Mathdictionary,Scientific_notation!Zscientific notation definition!Mathdictionary,Scientificnotation!Zscientific notation definitionMathdictionary,Scope}scope definitionMathdictionary,Sd̸sd definitionMathdictionary,SePse definitionMathdictionary,Secsec definitionp<{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 15 "Frechet filter," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "filter" 5 "Definition/filter" "" }{TEXT -1 1 "." } } } rdinarydifferentialequation" "" }{TEXT -1 2 ". " } } } k{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 2 "h," } } {PARA 0 "> " 0 "" {TEXT 22 11 "abbrev. for" } {TEXT -1 1 " " } {HYPERLNK 45 "hecto-" 5 "Definition/hecto-" "" }{TEXT -1 61 ", used in symbols for multiples of the physical units of the " } {HYPERLNK 45 "systeme international" 5 "Definition/systemeinternational" "" }{TEXT -1 1 "." } } } mathdictionary,oddq odd definitionmathdictionary,odd_part|odd part definitionmathdictionary,oddpart|odd part definitionmathdictionary,odegode definitionmathdictionary,of_setsQsigma-field definitionmathdictionary,off_diagonaloff diagonal definitionmathdictionary,offdiagonaloff diagonal definitionmathdictionary,officer_problemofficer problem definitionmathdictionary,officerproblemofficer problem definitionmathdictionary,ofsetsQsigma-field definitionmathdictionary,ogdoad'.octad definitionogdoad definition.Definition,octaddefinition,octadDefinition,Octaddefinition,OctadDictionary,octaddictionary,octadDictionary,Octaddictionary,OctadMathDictionary,octadMathdictionary,octadmathdictionary,octadMathDictionary,OctadMathdictionary,Octadmathdictionary,OctadDefinition,ogdoaddefinition,ogdoadDefinition,Ogdoaddefinition,OgdoadDictionary,ogdoaddictionary,ogdoadDictionary,Ogdoaddictionary,OgdoadMathDictionary,ogdoadMathdictionary,ogdoadmathdictionary,ogdoadMathDictionary,OgdoadMathdictionary,Ogdoadmathdictionary,Ogdoad.`{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 5 "octad" } } {PARA 0 "> " 0 "" {TEXT -1 3 "or " } {TEXT 39 6 "ogdoad" } {TEXT -1 2 ", " } {TEXT 22 2 "n." } {TEXT -1 38 " a set or sequence of eight elements. " } } } dictionary,Ontologyontology definitiondictionary,Opacityopacity definitiondictionary,Opaqueiopaque definitiondictionary,Openopen definitiondictionary,OpenBall#open ball definitiondictionary,OpenCover open cover definitiondictionary,OpenCovering open cover definitiondictionary,OpenDisk+open disk definitiondictionary,OpenIntervalopen interval definitiondictionary,OpenMappingV3open mapping definitiondictionary,OpenMappingTheorem"open mapping theorem definitionPartialproduct,MathDictionaryTPartialproduct,MathdictionaryTPartialproduct,definitionTPartialproduct,dictionaryTPartialproduct,mathdictionaryT#Partialrecursivefunction,Definition#Partialrecursivefunction,Dictionary'Partialrecursivefunction,MathDictionary'Partialrecursivefunction,Mathdictionary#Partialrecursivefunction,definition#Partialrecursivefunction,dictionary'Partialrecursivefunction,mathdictionaryFfunctioncontinuoubutnumberpairorderspacvectorrealexamplwithpossessmathdictionardictionarfinitedimensionaldefinitionfindexdimensionalfinitdefinitFSmathdictionardictionardefinitionfindexpolynomialfejerfejerpolynomialdefinitFEsphermeasurinstrummathdictionardictionarindexspherometdefinitFKmathdictionardictionardefinitiontindexstabltotaltotallystabldefinitFTmathdictionardictionardefinitioncindexfactorcompositcompositionfactordefinitF 2F6FEF:EFRF5FF`.GN`TG`sGGoG8GpG4$G<GLG<G{;GٯGGGSWG8$G͎GiGSG9GΎHǃ.H5ZHI\mOIWI[I/cIdI=hIxIIAI;IIYIWcI$IRI6tJJ_J|J0~JJJe/JoJRJyJ[JhoJ;OJ)VKJrKo"K1KL;5Ki6KCKRtYKK׊KKK K@KaKaLq0LJL;OLRRLhZLmLoL%|L6L#LLN(LI(L2Mw M!MS(M7MT;M#DM&^MaMͿlMMMMjMz}MkMDzMMMMbM:MrMQM NarNrN= *N@N#NNoRONPNN7SNRiNj4mN$NN\NNNONKN?NnNOOiHOZ#O AOMOdOO/O O=OOZOQOnOsO P2*Pu<PPϧPd-PhEXT 39 2 "3." } {TEXT -1 7 " (of a " } {HYPERLNK 45 "permutation" 5 "Definition/permutation" "" }{TEXT -1 53 ") derived from the natural order by an odd number of " } {HYPERLNK 45 "transpositions" 5 "Definition/transposition" "" }{TEXT -1 58 "; thus, the permutation (1, 3, 2) is odd but (3, 1, 2) is " } {HYPERLNK 45 "even" 5 "Definition/even" "" }{TEXT -1 87 ", since it can be achieved by exchanging 1 and 3 and then exchanging 1 and 2. See also " } {HYPERLNK 45 "difference polynomial" 5 "Definition/differencepolynomial" "" }{TEXT -1 11 ". See also " } {HYPERLNK 45 "parity" 5 "Definition/parity" "" }{TEXT -1 10 ". Compare " } {HYPERLNK 45 "even" 5 "Definition/even" "" }{TEXT -1 2 ". " } } } , so that " } {TEXT 22 1 "f" } {TEXT -1 1 "(" } {TEXT 22 1 "x" } {TEXT -1 5 ") = -" } {TEXT 22 1 "f" } {TEXT -1 2 "(-" } {TEXT 22 1 "x" } {TEXT -1 19 "); for example, sin" } {TEXT 22 1 "x" } {TEXT -1 8 " and tan" } {TEXT 22 1 "x" } {TEXT -1 69 " are odd functions. Such a function is symmetrical about the origin. " } {Tdictionary,opaqueiopaque definitiondictionary,openopen definitiondictionary,open_ball#open ball definitiondictionary,open_cover open cover definitiondictionary,open_covering open cover definitiondictionary,open_disk+open disk definitiondictionary,open_intervalopen interval definitiondictionary,open_mappingV3open mapping definitiondictionary,open_mapping_theorem"open mapping theorem definitiondictionary,open_sentenceopen sentence definitiondictionary,open_setTopen set definitiondictionary,open_theory open theory definitiondictionary,openball#open ball definitiondictionary,opencover open cover definitiondictionary,opencovering open cover definitiondictionary,opendisk+open disk definitiondictionary,openintervalopen interval definition!Definition,OrbitStabilizerTheorem&7orbit stabilizer theorem definition#Definition,Orbit_Stabilizer_Theorem&7orbit stabilizer theorem definition#Definition,Orbit_stabilizer_theorem&7orbit stabilizer theorem definition!Definition,Orbitstabilizertheorem&7orbit stabilizer theorem definitionDefinition,Order3Sorder of magnitude definitionjorder definitionDefinition,Order-Completeorder-complete definitionDefinition,Order-Preservingyorder-preserving definitionDefinition,OrderCompleteorder-complete definition MathDictionary,ordered_structureordered structure definition#MathDictionary,ordered_vector_space"Kordered vector space definition!MathDictionary,orderedarrangement:(Mordered arrangement definitionpermutation definitionMathDictionary,orderedgeometry=ordered geometry definitionMathDictionary,orderedpair#yordered pair definitionMathDictionary,orderedset%ordered set definitionMathDictionary,orderedstructureordered structure definition!MathDictionary,orderedvectorspace"Kordered vector space definition`{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 8 "one-one," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 18 " another term for " } {HYPERLNK 45 "one-to-one" 5 "Definition/one-to-one" "" }{TEXT -1 2 ". " } } } definition,Octad.octad definitiondefinition,Octagongoctagon definitiondefinition,Octahedronoctahedron definitiondefinition,Octaloctal definitiondefinition,OctantFoctant definitiondefinition,Oddq odd definitiondefinition,OddPart|odd part definitiondefinition,Odd_Part|odd part definitiondefinition,Odd_part|odd part definitiondefinition,Oddpart|odd part definitiondefinition,Odegode definitiondefinition,OfSetsQsigma-field definitiondefinition,Of_SetsQsigma-field definitiondefinition,Of_setsQsigma-field definitiondefinition,OffDiagonaloff diagonal definitionDefinition,OblatespheroidRoblate spheroid definitionDefinition,Obliqueoblique definitionDefinition,ObliqueAngleaoblique angle definitionDefinition,Oblique_Angleaoblique angle definitionDefinition,Oblique_angleaoblique angle definitionDefinition,Obliqueangleaoblique angle definitionDefinition,Oblong+2oblong definitionrectangle definitionDefinition,Observer observer definitionDefinition,Obtusesobtuse definitionDefinition,Obverseobverse definitionOctant,MathDictionaryFOctant,MathdictionaryFOctant,definitionFOctant,dictionaryFOctant,mathdictionaryFOdd,Definitionq Odd,Dictionaryq Odd,MathDictionaryq Odd,Mathdictionaryq Odd,definitionq Odd,dictionaryq Odd,mathdictionaryq OddExtension,DefinitionTOddPart,Definition|OddPart,Dictionary|OddPart,MathDictionary|OddPart,Mathdictionary|OddPart,definition|onlyif,Dictionaryskonlyif,MathDictionaryskonlyif,Mathdictionaryskonlyif,definitionskonlyif,dictionaryskonlyif,mathdictionaryskonotation,DefinitionȤonotation,DictionaryȤonotation,MathDictionaryȤonotation,MathdictionaryȤonotation,definitionȤonotation,dictionaryȤonotation,mathdictionaryȤonto,Definitiononto,Dictionaryonto,MathDictionaryonto,Mathdictionarydefinition,Order_Ideal+order ideal definitiondefinition,Order_IntervalAorder interval definitiondefinition,Order_Notationorder notation definitiondefinition,Order_Of_ConvergenceCOorder of convergence definition[rate of convergence 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definitiondictionary,onemanymone-many definitiondictionary,oneoneone-one definitionMathdictionary,ogive,ogive definitionMathdictionary,oh_notationoh notation definitionMathdictionary,ohnotationoh notation definitionMathdictionary,omegaomega definition"Mathdictionary,omega_inconsistency!Domega inconsistency definition!Mathdictionary,omegainconsistency!Domega inconsistency definitionMathdictionary,oneh_one definitionMathdictionary,one-manymone-many definitionMathdictionary,one-oneone-one definition)Mathdictionary,one-point_compactification("one-point compactification definition(Mathdictionary,one-pointcompactification("one-point compactification definitionMathdictionary,Ogive,ogive definitionMathdictionary,OhNotationoh notation definitionMathdictionary,Oh_Notationoh notation definitionMathdictionary,Oh_notationoh notation definitionMathdictionary,Ohnotationoh notation definitionMathdictionary,Omegaomega definition!Mathdictionary,OmegaInconsistency!Domega inconsistency definition"Mathdictionary,Omega_Inconsistency!Domega inconsistency definition"Mathdictionary,Omega_inconsistency!Domega inconsistency definitionVHDefinition,probabilitymassfunctionprobability mass function definitioncCDefinition,modularrepresentationmodular representation definition{CDefinition,descriptivestatisticsdescriptive statistics definition-Definition,ohnotationoh notation definition?Definition,EulercharacteristicEuler characteristic definition-Definition,rightangleright angle definitionGDefinition,Cantor-BernsteintheoremCantor-Bernstein theorem definition2Definition,non-symmetricnon-symmetric definition/Definition,DedekindcutDedekind cut definition5Definition,LegendresymbolLegendre symbol definitionmathdictionary,Officer_Problemofficer problem definitionmathdictionary,Officer_problemofficer problem definitionmathdictionary,Officerproblemofficer problem definitionmathdictionary,OfsetsQsigma-field definitionmathdictionary,Ogdoad'.octad definitionogdoad definitionmathdictionary,Ogive,ogive definitionmathdictionary,OhNotationoh notation definitionmathdictionary,Oh_Notationoh notation definitionmathdictionary,Oh_notationoh notation definitionmathdictionary,Ohnotationoh notation definitionI{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 12 "oh notation," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "order notation" 5 "Definition/ordernotation" "" }{TEXT -1 2 ". " } } } mathdictionary,OddPart|odd part definitionmathdictionary,Odd_Part|odd part definitionmathdictionary,Odd_part|odd part definitionmathdictionary,Oddpart|odd part definitionmathdictionary,Odegode definitionmathdictionary,OfSetsQsigma-field definitionmathdictionary,Of_SetsQsigma-field definitionmathdictionary,Of_setsQsigma-field definitionmathdictionary,OffDiagonaloff diagonal definitionmathdictionary,Off_Diagonaloff diagonal definitionmathdictionary,Off_diagonaloff diagonal definitionmathdictionary,Offdiagonaloff diagonal definitionmathdictionary,OfficerProblemofficer problem definitionofficer_problem,Dictionaryofficer_problem,MathDictionaryofficer_problem,Mathdictionaryofficer_problem,definitionofficer_problem,dictionaryofficer_problem,mathdictionaryofficerproblem,Definitionofficerproblem,Dictionaryofficerproblem,MathDictionaryofficerproblem,Mathdictionaryofficerproblem,definitionofficerproblem,dictionaryofficerproblem,mathdictionaryofsets,DefinitionQofsets,DictionaryQofsets,MathDictionaryQofsets,MathdictionaryQofsets,definitionQofsets,dictionaryQofsets,mathdictionaryQogdoad,Definition.Offdiagonal,DictionaryOffdiagonal,MathDictionaryOffdiagonal,MathdictionaryOffdiagonal,definitionOffdiagonal,dictionaryOffdiagonal,mathdictionaryOfficerProblem,DefinitionOfficerProblem,DictionaryOfficerProblem,MathDictionaryOfficerProblem,MathdictionaryOfficerProblem,definitionOfficerProblem,dictionaryOfficerProblem,mathdictionaryOfficer_Problem,DefinitionOfficer_Problem,Dictionarydefinition,Nonempty#"definition,Nonparametricstatisticsdefinition,Nonstandard}definition,Nonzeroring݁definition,NormalDistributiondefinition,NormalSectiondefinition,Normal_Curvature_definition,Normal_Matrix-definition,Normal_curvaturedefinition,Normal_matrixdefinition,Normalclosure7definition,NormalfamilyLdefinition,Normalnumberdefinition,NormedSpacedefinition,Normedspacetdefinition,Nowhere_dense_setކDefinition,Order_intervalAorder interval definitionDefinition,Order_notationorder notation definitionDefinition,Order_of_convergenceCOorder of convergence definition[rate of convergence definitionDefinition,Order_of_magnitude Sorder of magnitude definitionDefinition,Order_of_symmetryorder of symmetry definitionDefinition,Order_preservingyorder-preserving definitionDefinition,Order_statisticorder statistic definitionDefinition,Ordercompleteorder-complete definitionOgive,Mathdictionary,Ogive,definition,Ogive,dictionary,Ogive,mathdictionary,OhNotation,DefinitionOhNotation,DictionaryOhNotation,MathDictionaryOhNotation,MathdictionaryOhNotation,definitionOhNotation,dictionaryOhNotation,mathdictionaryOh_Notation,DefinitionOh_Notation,DictionaryOh_Notation,MathDictionaryOh_Notation,MathdictionaryOh_Notation,definitionOh_Notation,dictionaryOfficer_Problem,MathDictionaryOfficer_Problem,MathdictionaryOfficer_Problem,definitionOfficer_Problem,dictionaryOfficer_Problem,mathdictionaryOfficer_problem,DefinitionOfficer_problem,DictionaryOfficer_problem,MathDictionaryOfficer_problem,MathdictionaryOfficer_problem,definitionOfficer_problem,dictionaryOfficer_problem,mathdictionaryOfficerproblem,DefinitionOfficer_Problem,Dictionaryt salsosuchanothintegnumbsquarenumbmathdictionardictionardefinitionpindexsquarperfectperfectsquardefinitw integeridentitrelatoperateithregardcanfaceclockanalogreferrsometimmodulumultiplintegraldifftheynumberfinitgivenwithdenotsystemanymathdictionardictionardefinitionmindexarithmeticmodularmodulararithmeticdefinitz alsomaintainpossiblsixproducwillnoparameterhaveequivalentcdabdenotbcadbdaccomputlineordersomeliedistinctletfollowobtaincertainproductpointcollinearfourmathdictionardictionardefinitioncindexratiocroscrossratiodefinitT{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 14 "odd extension," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 109 " The odd extension of f(x) from the interval [0, L] to the interval [-L, L] is the piecewise-defined function" } } {PARA 17 "> " 0 "wmitable" {TEXT -1 78 "G(x) = PIECEWISE([-f(-x), `x in [-L, 0]`], [``, ``], [f(x), `x in [0, L]`]) " } } } RQ{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 21 "four-current density," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "Maxwell's laws" 5 "Definition/Maxwellslaws" "" }{TEXT -1 2 ". " } } } iecewise-defined function" } } {PARA 17 "> " 0 "wmitable" {TEXT -1 78 "G(x) = PIECEWISE([-f(-x), `x in [-L, 0]`], [``, ``], [f(x), `x in [0, L]`]) " } } } [z{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 22 "heterological paradox," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 18 " another name for " } {HYPERLNK 45 "Grelling's paradox" 5 "Definition/Grellingsparadox" "" }{TEXT -1 1 "." } } } Definition,omegainconsistency!Domega inconsistency definitionDefinition,oneh_one definitionDefinition,one-manymone-many definitionDefinition,one-norm@one-norm definitionDefinition,one-oneone-one definition%Definition,one-point_compactification("one-point compactification definition$Definition,one-pointcompactification("one-point compactification definitionDefinition,one-sidedone-sided definitionDefinition,one-tailedone-tailed definitionDefinition,one-to-one#Oone-to-one definitionDefinition,one_manymone-many definitiondefinition,OrderCompleteorder-complete definitiondefinition,OrderIdeal+order ideal definitiondefinition,OrderIntervalAorder interval definitiondefinition,OrderNotationorder notation definitiondefinition,OrderOfConvergenceCOorder of convergence definition[rate of convergence definitiondefinition,OrderOfMagnitude Sorder of magnitude definitiondefinition,OrderOfSymmetryorder of symmetry definitiondefinition,OrderPreservingyorder-preserving definitiondefinition,OrderStatisticorder statistic definitiondefinition,Order_Completeorder-complete definitiondictionary,OfsetsQsigma-field definitiondictionary,Ogdoad'.octad definitionogdoad definitiondictionary,Ogive,ogive definitiondictionary,OhNotationoh notation definitiondictionary,Oh_Notationoh notation definitiondictionary,Oh_notationoh notation definitiondictionary,Ohnotationoh notation definitiondictionary,Omegaomega definitiondictionary,OmegaInconsistency!Domega inconsistency definitiondictionary,Omega_Inconsistency!Domega inconsistency definitiondictionary,Omega_inconsistency!Domega inconsistency definitionMathdictionary,oddq odd definitionMathdictionary,odd_part|odd part definitionMathdictionary,oddpart|odd part definitionMathdictionary,odegode definitionMathdictionary,of_setsQsigma-field definitionMathdictionary,off_diagonaloff diagonal definitionMathdictionary,offdiagonaloff diagonal definitionMathdictionary,officer_problemofficer problem definitionMathdictionary,officerproblemofficer problem definitionMathdictionary,ofsetsQsigma-field definitionMathdictionary,ogdoad'.octad definitionogdoad definitionMathDictionary,Oh_notationoh notation definitionMathDictionary,Ohnotationoh notation definitionMathDictionary,Omegaomega definition!MathDictionary,OmegaInconsistency!Domega inconsistency definition"MathDictionary,Omega_Inconsistency!Domega inconsistency definition"MathDictionary,Omega_inconsistency!Domega inconsistency definition!MathDictionary,Omegainconsistency!Domega inconsistency definitionMathDictionary,Oneh_one definitionMathDictionary,One-Manymone-many definition׃dictionary,nonresiduedictionary,nonsymmetricdictionary,normal_curvaturedictionary,normal_matrixdictionary,normalcurvature dictionary,normalizeSdictionary,normalstressQdictionary,normedvectorring dictionary,np-completeproblemdictionary,npcompleteproblemgdictionary,null_sequencedictionary,nullspaceԇdictionary,numerical%dictionary,numericalquadraturedictionary,objectivefunctionxdictionary,obversef,repressymbolreferencwithoutdefinsensapplicatabstractconceptnumberallirrationalwhilintegmayrationaleithsquarwithrealproductequalitselflattsumcomplexeverclassificathierarchicalarrangcanrootextractdivisgivesubtractunderthesextensderivquantitanytwelvdisciplsaysindividualcollectcountusedelementsequencuniqunaturalcallalsomathdictionardictionardefinitionindexnumbdefinit<comparalsoetcdefinsimilarelemminimalsubmodulsetemptnonequivalentallsuchevermemberdistinctnumbfinitmoresupersetnomathdictionardictionardefinitiondindexconditchaindescenddescendingchainconditdefinitMathDictionary,one-oneone-one definition)MathDictionary,one-point_compactification("one-point compactification definition(MathDictionary,one-pointcompactification("one-point compactification definitionMathDictionary,one-sidedone-sided definitionMathDictionary,one-tailedone-tailed definitionMathDictionary,one-to-one#Oone-to-one definitionMathDictionary,one_manymone-many definitionMathDictionary,one_oneone-one definition)MathDictionary,one_point_compactification("one-point compactification definitionMathDictionary,one_sidedone-sided definitionmathdictionary,ogive,ogive definitionmathdictionary,oh_notationoh notation definitionmathdictionary,ohnotationoh notation definitionmathdictionary,omegaomega definition"mathdictionary,omega_inconsistency!Domega inconsistency definition!mathdictionary,omegainconsistency!Domega inconsistency definitionmathdictionary,oneh_one definitionmathdictionary,one-manymone-many definitionmathdictionary,one-oneone-one definition)mathdictionary,one-point_compactification("one-point compactification definition(mathdictionary,one-pointcompactification("one-point compactification definitionmathdictionary,Omegaomega definition!mathdictionary,OmegaInconsistency!Domega inconsistency definition"mathdictionary,Omega_Inconsistency!Domega inconsistency definition"mathdictionary,Omega_inconsistency!Domega inconsistency definition!mathdictionary,Omegainconsistency!Domega inconsistency definitionmathdictionary,Oneh_one definitionmathdictionary,One-Manymone-many definitionmathdictionary,One-Oneone-one definition(mathdictionary,One-PointCompactification("one-point compactification definition;Definition,summabilitytheorysummability theory definition&(Definition,diagonaldiagonal definition'"Definition,focalfocal definition(;Definition,logarithmicserieslogarithmic series definition;"Definition,giga-giga- definitionE?Definition,thermalconductivitythermal conductivity definitionG<Definition,AiryfunctionAiry Ai and Bi function definitionsHCDefinition,primitiverootofunityprimitive root of unity definitionV:Definition,YoungsinequalityYoung's inequality definitionr?Definition,deletedneighborhooddeleted neighborhood definitions4Definition,BuffonsneedleBuffon's needle definitiont,Definition,invariableinvariable definitionu$Definition,bundlebundle definitionDefinition,numericalquantifierDefinition,numericalrange~Definition,objectDefinition,objectiveDefinition,objectivefunctionDefinition,objectlanguageDefinition,oblatespheroidRDefinition,obliqueDefinition,obliqueangleaDefinition,oblong2Definition,observer Definition,obtusesDefinition,obverseDefinition,oct-Definition,octad.Definition,octagongV3{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 13 "open mapping," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 94 " a function that sends open sets in the domain space to open sets in the range space. 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" } } } Definition,officerproblemdefinition,officerproblemDefinition,officer_problemdefinition,officer_problemDefinition,OfficerProblemdefinition,OfficerProblemDefinition,Officer_Problemdefinition,Officer_ProblemDefinition,Officerproblemdefinition,OfficerproblemDefinition,Officer_problemdefinition,Officer_problemDictionary,officerproblemdictionary,officerproblemDictionary,officer_problemdictionary,officer_problemDictionary,OfficerProblemdictionary,OfficerProblemDictionary,Officer_Problemdictionary,Officer_ProblemDictionary,Officerproblemdictionary,OfficerproblemDictionary,Officer_problemdictionary,Officer_problemMathDictionary,officerproblemMathdictionary,officerproblemmathdictionary,officerproblemMathDictionary,officer_problemMathdictionary,officer_problemmathdictionary,officer_problemMathDictionary,OfficerProblemMathdictionary,OfficerProblemmathdictionary,OfficerProblemMathDictionary,Officer_ProblemMathdictionary,Officer_Problemmathdictionary,Officer_ProblemMathDictOffDiagonal,definitionOffDiagonal,dictionaryOffDiagonal,mathdictionaryOff_Diagonal,DefinitionOff_Diagonal,DictionaryOff_Diagonal,MathDictionaryOff_Diagonal,MathdictionaryOff_Diagonal,definitionOff_Diagonal,dictionaryOff_Diagonal,mathdictionaryOff_diagonal,DefinitionOff_diagonal,DictionaryOff_diagonal,MathDictionaryOff_diagonal,MathdictionaryOff_diagonal,definitionOff_diagonal,dictionaryOff_diagonal,mathdictionaryOffdiagonal,Definitionionary,OfficerproblemMathdictionary,Officerproblemmathdictionary,OfficerproblemMathDictionary,Officer_problemMathdictionary,Officer_problemmathdictionary,Officer_problemion,Officer_Problemdefinition,Officer_ProblemDefinition,Officerproblemdefinition,OfficerproblemDefinition,Officer_problemdefinition,Officer_problemDictionary,officerproblemdictionary,officerproblemDictionary,officer_problemdictionary,officer_problemDictionary,OfficerProblemdictionary,OfficerProblemDictionary,Officer_Problemdictionary,Officer_ProblemDictionary,Officerproblemdictionary,OfficerproblemDictionary,Officer_problemdictionary,Officer_problemMathDictionary,officerproblemMathdictionary,officerproblemmathdictionary,officerproblemMathDictionary,officer_problemMathdictionary,officer_problemmathdictionary,officer_problemMathDictionary,OfficerProblemMathdictionary,OfficerProblemmathdictionary,OfficerProblemMathDictionary,Officer_ProblemMathdictionary,Officer_Problemmathdictionary,Officer_ProblemMathDictJ?{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 5 "par.," } } {PARA 0 "> " 0 "" {TEXT 22 12 "abbrev. for " } {HYPERLNK 45 "parallel" 5 "Definition/parallel" "" }{TEXT -1 2 ". 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" } } } 1!Definition,trigtrig. definition2/Definition,setfunctionset function definitionB>Definition,JordancurvetheoremJordan curve theorem definitionJDefinition,parpar. definition$Definition,ogdoadogdoad definition*Definition,referencereference definition4Definition,PeanoGuiseppePeano, Guiseppe definitionADefinition,Newton-RaphsonmethodNewton-Raphson method definition7Definition,countingmeasurecounting measure definition0Definition,metavariablemetavariable definition(Definition,semanticsemantic definition.Definition,meromorphicmeromorphic definition3Definition,needleproblemneedle problem definition(Definition,frontierfrontier definition(Definition,evaluateevaluate definitionz&Definition,bindingbinding definitionz;Definition,instantiationruleinstantiation rule definitionz/Definition,randomerrorrandom error definitionzUDefinition,symmetrygroupofanelasticbodysymmetry group of an elastic body definitionz,Definition,triangulartriangular definitionz)Definition,BorelsetBorel set definitionz,Definition,subtangentsubtangent definitionz;Definition,fundamentalmatrixfundamental matrix definitionz(Definition,quadrantquadrant definition dictionary,or9or definitiondictionary,orbitorbit definition#dictionary,orbit_stabilizer_theorem&7orbit stabilizer theorem definition!dictionary,orbitstabilizertheorem&7orbit stabilizer theorem definitiondictionary,order3Sorder of magnitude definitionjorder definitiondictionary,order-completeorder-complete definitiondictionary,order-preservingyorder-preserving definitiondictionary,order_completeorder-complete definitiondictionary,order_ideal+order ideal definitiondictionary,order_intervalAorder interval definitiondictionary,order_notationorder notation definitiondictionary,order_of_convergenceCOorder of convergence definition[rate of convergence definitiondictionary,order_of_magnitude Sorder of magnitude definitiondictionary,order_of_symmetryorder of symmetry definitiondictionary,order_preservingyorder-preserving definitiondefinition,OhNotationoh notation definitiondefinition,Oh_Notationoh notation definitiondefinition,Oh_notationoh notation definitiondefinition,Ohnotationoh notation definitiondefinition,Omegaomega definitiondefinition,OmegaInconsistency!Domega inconsistency definitiondefinition,Omega_Inconsistency!Domega inconsistency definitiondefinition,Omega_inconsistency!Domega inconsistency definitiondefinition,Omegainconsistency!Domega inconsistency definitionOh_Notation,mathdictionaryOh_notation,DefinitionOh_notation,DictionaryOh_notation,MathDictionaryOh_notation,MathdictionaryOh_notation,definitionOh_notation,dictionaryOh_notation,mathdictionaryOhnotation,DefinitionOhnotation,DictionaryOhnotation,MathDictionaryOhnotation,MathdictionaryOhnotation,definitionOhnotation,dictionaryOhnotation,mathdictionary"Omega_Inconsistency,mathdictionaryDOmega_inconsistency,DefinitionDOmega_inconsistency,DictionaryD"Omega_inconsistency,MathDictionaryD"Omega_inconsistency,MathdictionaryDOmega_inconsistency,definitionDOmega_inconsistency,dictionaryD"Omega_inconsistency,mathdictionaryDOmegainconsistency,DefinitionDOmegainconsistency,DictionaryD!Omegainconsistency,MathDictionaryD!Omegainconsistency,MathdictionaryDOmegainconsistency,definitionDfDefinition,subordinatematrixnormsDefinition,SubordinateMatrixNormsdefinition,subordinatematrixnormsDefinition,omegadefinition,omegaDefinition,Omegadefinition,OmegaDictionary,omegadictionary,omegaDictionary,Omegadictionary,OmegaMathDictionary,omegaMathdictionary,omegamathdictionary,omegaMathDictionary,OmegaMathdictionary,Omegamathdictionary,OmegaDefinition,ohnotationdefinition,ohnotationDefinition,oh_notationdefinition,oh_notationDefinition,OhNotationdefinition,OhNotationDefinition,Oh_Notationdefinition,Oh_NotationDefinition,Ohnotationdefinition,OhnotationDefinition,Oh_notationdefinition,Oh_notationDictionary,ohnotationdictionary,ohnotationDictionary,oh_notationdictionary,oh_notationDictionary,OhNotationdictionary,OhNotationDictionary,Oh_Notationdictionary,Oh_NotationDictionary,Ohnotationdictionary,OhnotationDictionary,Oh_notationdictionary,Oh_notationMathDictionary,ohnotationMathdictionary,ohnotationmathdictionary,ohnotationMathDictionary,oh_notationMathdictionary,oh_notationmathdictionary,oh_notationMathDictionary,OhNotationMathdictionary,OhNotationmathdictionary,OhNotationMathDictionary,Oh_NotationMathdictionary,Oh_Notationmathdictionary,Oh_NotationMathDictionary,OhnotationMathdictionary,Ohnotationmathdictionary,OhnotationMathDictionary,Oh_notationMathdictionary,Oh_notationmathdictionary,Oh_noOmega,DefinitionOmega,DictionaryOmega,MathDictionaryOmega,MathdictionaryOmega,definitionOmega,dictionaryOmega,mathdictionaryOmegaInconsistency,DefinitionDOmegaInconsistency,DictionaryD!OmegaInconsistency,MathDictionaryD!OmegaInconsistency,MathdictionaryDOmegaInconsistency,definitionDOmegaInconsistency,dictionaryD!OmegaInconsistency,mathdictionaryDOmega_Inconsistency,DefinitionDOmega_Inconsistency,DictionaryD"Omega_Inconsistency,MathDictionaryD"Omega_Inconsistency,MathdictionaryDOmega_Inconsistency,definitionDOmega_Inconsistency,dictionaryDtationDefinition,ohnotationdefinition,ohnotationDefinition,oh_notationdefinition,oh_notationDefinition,OhNotationdefinition,OhNotationDefinition,Oh_Notationdefinition,Oh_NotationDefinition,Ohnotationdefinition,OhnotationDefinition,Oh_notationdefinition,Oh_notationDictionary,ohnotationdictionary,ohnotationDictionary,oh_notationdictionary,oh_notationDictionary,OhNotationdictionary,OhNotationDictionary,Oh_Notationdictionary,Oh_NotationDictionary,Ohnotationdictionary,OhnotationDictionary,Oh_notationdictionary,Oh_notationMathDictionary,ohnotationMathdictionary,ohnotationmathdictionary,ohnotationMathDictionary,oh_notationMathdictionary,oh_notationmathdictionary,oh_notationMathDictionary,OhNotationMathdictionary,OhNotationmathdictionary,OhNotationMathDictionary,Oh_NotationMathdictionary,Oh_Notationmathdictionary,Oh_NotationMathDictionary,OhnotationMathdictionary,Ohnotationmathdictionary,OhnotationMathDictionary,Oh_notationMathdictionary,Oh_notationmathdictionary,Oh_no{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 6 "omega," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 23 " the smallest infinite " } {HYPERLNK 45 "ordinal" 5 "Definition/ordinal" "" }{TEXT -1 74 "; the ordinal of the natural order of the natural numbers, written omega. 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interval definitiondefinition,open_mappingV3open mapping definitiondefinition,open_mapping_theorem"open mapping theorem definitiondefinition,open_sentenceopen sentence definitiondefinition,open_setTopen set definitiondefinition,open_theory open theory definitiondefinition,openball#open ball definitiondefinition,opencover open cover definitiondefinition,opencovering open cover definitiondefinition,opendisk+open disk definitiondefinition,openintervalopen interval definitiondefinition,operatornormToperator norm definitiondefinition,ophelmalophelmal definitiondefinition,opposite@!opposite definitiondefinition,opposite_anglesZopposite angles definitiondefinition,opposite_ringopposite ring definitiondefinition,oppositeanglesZopposite angles definitiondefinition,oppositeringopposite ring definitiondefinition,optimaloptimal definition%definition,optimal_assignment_problem(optimal assignment problem definition$Definition,One-pointcompactification("one-point compactification definitionDefinition,OneManymone-many definitionDefinition,OneNorm@one-norm definitionDefinition,OneOneone-one definition%Definition,OneParameterFamilyOfCurves,]one parameter family of curves definition#Definition,OnePointCompactification("one-point compactification definitionDefinition,OneSidedone-sided definitionDefinition,OneTailedone-tailed definitionDefinition,OneToOne#Oone-to-one definitionDefinition,One_Manymone-many definition#dictionary,Onepointcompactification("one-point compactification definitiondictionary,Onesidedone-sided definitiondictionary,Onetailedone-tailed definitiondictionary,Onetoone#Oone-to-one definitiondictionary,OnlyIfskonly if definitiondictionary,Only_Ifskonly if definitiondictionary,Only_ifskonly if definitiondictionary,Onlyifskonly if definitiondictionary,OnotationȤO notation definitiondictionary,Ontoonto definitionMathDictionary,One_to_one#Oone-to-one definitionMathDictionary,Onemanymone-many definitionMathDictionary,Oneoneone-one 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definitiononto,definitiononto,dictionaryonto,mathdictionaryontology,Definitionontology,Dictionaryontology,MathDictionaryontology,Mathdictionaryontology,definitionontology,dictionaryontology,mathdictionaryopacity,Definitionopacity,Dictionaryopacity,MathDictionaryopacity,Mathdictionaryopacity,definitionopacity,dictionaryopacity,mathdictionaryordinalnumber,definition)ordinalnumber,dictionary)ordinalnumber,mathdictionary)ordinalscale,Definitionlordinalscale,Dictionarylordinalscale,MathDictionarylordinalscale,Mathdictionarylordinalscale,definitionlordinalscale,dictionarylordinalscale,mathdictionaryl)ordinary_differential_equation,Definitionݾ)ordinary_differential_equation,Dictionaryݾ-ordinary_differential_equation,MathDictionaryݾtionary,Off_diagonalmathdictionary,Off_diagonalagonalDefinition,off_diagonaldefinition,off_diagonalDefinition,OffDiagonaldefinition,OffDiagonalDefinition,Off_Diagonaldefinition,Off_DiagonalDefinition,Offdiagonaldefinition,OffdiagonalDefinition,Off_diagonaldefinition,Off_diagonalDictionary,offdiagonaldictionary,offdiagonalDictionary,off_diagonaldictionary,off_diagonalDictionary,OffDiagonaldictionary,OffDiagonalDictionary,Off_Diagonaldictionary,Off_DiagonalDictionary,Offdiagonaldictionary,OffdiagonalDictionary,Off_diagonaldictionary,Off_diagonalMathDictionary,offdiagonalMathdictionary,offdiagonalmathdictionary,offdiagonalMathDictionary,off_diagonalMathdictionary,off_diagonalmathdictionary,off_diagonalMathDictionary,OffDiagonalMathdictionary,OffDiagonalmathdictionary,OffDiagonalMathDictionary,Off_DiagonalMathdictionary,Off_Diagonalmathdictionary,Off_DiagonalMathDictionary,OffdiagonalMathdictionary,Offdiagonalmathdictionary,OffdiagonalMathDictionary,Off_diagonalMathdicdefinition,vanderpolequation"`van der Pol equation definition"definition,vanderwaerdenconjecture*wvan der Waerden's conjecture definition#definition,vanderwaerdensconjecture*wvan der Waerden's conjecture definitiondefinition,vanishXvanish definitiondefinition,vanish_at_infinity ovanish at infinity definitiondefinition,vanish_nowhere\vanish nowhere definitiondefinition,vanishatinfinity ovanish at infinity definitiondefinition,vanishnowhere\vanish nowhere definitionC{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 22 "asymptotically stable," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "stable" 5 "Definition/stable" "" }{TEXT -1 1 "." } } } ures) similar with corresponding sides parallel. " } } } {VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 16 "officer problem," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 87 " the problem, due to Euler, of placing 36 officers of six ranks and six regiments in a " } {HYPERLNK 45 "Latin square" 5 "Definition/Latinsquare" "" }{TEXT -1 2 ". 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It is so called since the paradigm case is that of the finite " } {HYPERLNK 45 "ordinal numbers" 5 "Definition/ordinalnumber" "" }{TEXT -1 157 ", each of which has a finite successor while they clearly do not all have a finite successor as the set of finite ordinals is the smallest infinite ordinal, " } {HYPERLNK 45 "omega" 5 "Definition/omega" "" }{TEXT -1 442 ". A philosophical example, due to Russell, is that it is part of the concept of desire that one wants each of one's desires to be satisfied, but amongst those desires is the apparently inconsistent desire to face new challenges, that is, to leave some of one's desires unsatisfied; thus one can satisfy any of one's desires but not all of them. This paradox seems best resolved by observing a change of the scope of the universal quantifier. " } } } of induction" 5 "Definition/principleofinduction" "" }{TEXT -1 197 " fails, that is, when it is not possible to infer from the fact that each element of a domain has a property that all of them have it. It is so called since the paradigm case is that of the finite " } {HYPERLNK 45 "ordinal numbers" 5 "Definition/ordinalnumber" "" }{TEXT -1 157 ", each of which has a finite successor while they clearly do not all have a finite successor as the set of finite ordinals is the smallest infinite ordinal, " } {HYPERLNK 45 "omega" 5 "Definition/omega" "" }{TEXT -1 442 ". 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"{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 26 "one-point compactification" } } {PARA 0 "> " 0 "" {TEXT -1 3 "or " } {TEXT 39 28 "Alexandroff compactification" } {TEXT -1 2 ", " } {TEXT 22 2 "n." } {TEXT -1 3 " a " } {HYPERLNK 45 "compactification" 5 "Definition/compactification" "" }{TEXT -1 53 " that adds a single point, designated infinity, to a " } {HYPERLNK 45 "Hausdorff space" 5 "Definition/Hausdorffspace" "" }{TEXT -1 147 " and adds complements of closed subsets of the original space as neighborhoods of this point. 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" } } } !definition,OrbitStabilizerTheorem&7orbit stabilizer theorem definition#definition,Orbit_Stabilizer_Theorem&7orbit stabilizer theorem definition#definition,Orbit_stabilizer_theorem&7orbit stabilizer theorem definition!definition,Orbitstabilizertheorem&7orbit stabilizer theorem definitiondefinition,Order3Sorder of magnitude definitionjorder definitiondefinition,Order-Completeorder-complete definitiondefinition,Order-Preservingyorder-preserving definitionnumericalanalysi)numericaleccentricit unumericalidentitnumericalquadraturAnumericalquantifi numericalrang~nurnberghnyquistnyquiststabilitycriternystrom nzwoaf oandonotatoath obfobcobeyLM\chobjectK A  0V$).7$8ANIPQUW}X Z__qadeghk prpv{M}c}]ĆÉ-ÕƖ\xDִmrCI 4"1GobjectivefunctobjectiveoptimizatÉ objectlanguagoblatRoblatespheroidRoblig  obligatorinesgBobliqu,Q_'ba obliqueanglaoblong !2obscur >observR *%*0W3=A>FHxIMQKi kzc{ 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definition%One_point_compactification,dictionary")One_point_compactification,mathdictionary"One_sided,DefinitionOne_sided,DictionaryOne_sided,MathDictionaryOne_sided,MathdictionaryOne_sided,definitionOne_sided,dictionaryOne_sided,mathdictionaryOne_tailed,DefinitionOne_tailed,DictionaryOne_tailed,MathDictionaryOne_tailed,MathdictionaryOne_tailed,definitionOne_tailed,dictionaryOne_tailed,mathdictionaryOne_to_one,Definition#OOne_to_one,Dictionary#OOne_to_one,MathDictionary#OOne_to_one,Mathdictionary#OOne_to_one,definition#OOne_to_one,dictionary#OOne_to_one,mathdictionary#OOnemany,DefinitionmOnemany,DictionarymOnemany,MathDictionarymOnetailed,dictionaryOnetailed,mathdictionaryOnetoone,Definition#OOnetoone,Dictionary#OOnetoone,MathDictionary#OOnetoone,Mathdictionary#OOnetoone,definition#OOnetoone,dictionary#OOnetoone,mathdictionary#OOnlyIf,DefinitionskOnlyIf,DictionaryskOnlyIf,MathDictionaryskOnlyIf,MathdictionaryskOnlyIf,definitionskOnlyIf,dictionaryskOnlyIf,mathdictionaryskOnly_If,DefinitionskOnly_If,DictionaryskOnly_If,MathDictionaryskOnly_If,MathdictionaryskOnly_If,definitionsk%one_point_compactification,dictionary")one_point_compactification,mathdictionary"one_sided,Definitionone_sided,Dictionaryone_sided,MathDictionaryone_sided,Mathdictionaryone_sided,definitionone_sided,dictionaryone_sided,mathdictionaryone_tailed,Definitionone_tailed,Dictionaryone_tailed,MathDictionaryone_tailed,Mathdictionaryone_tailed,definitionone_tailed,dictionaryone_tailed,mathdictionaryone_to_one,Definition#Oone_to_one,Dictionary#Oone_to_one,MathDictionary#Oone_to_one,Mathdictionary#Oone_to_one,definition#Oone_to_one,dictionary#Oone_to_one,mathdictionary#Oonemany,Definitionmonemany,Dictionarymonemany,MathDictionarymOne_Sided,DefinitionOne_Sided,DictionaryOne_Sided,MathDictionaryOne_Sided,MathdictionaryOne_Sided,definitionOne_Sided,dictionaryOne_Sided,mathdictionaryOne_Tailed,DefinitionOne_Tailed,DictionaryOne_Tailed,MathDictionaryOne_Tailed,MathdictionaryOne_Tailed,definitionOne_Tailed,dictionaryOne_Tailed,mathdictionaryOne_To_One,Definition#OOne_To_One,Dictionary#OOne_To_One,MathDictionary#OOne_To_One,Mathdictionary#OOne_To_One,definition#OOne_To_One,dictionary#OOne_To_One,mathdictionary#OOne_many,DefinitionmOne_many,DictionarymOne_many,MathDictionarymOne_many,Mathdictionaryme-tailedDefinition,One-Taileddefinition,One-TailedDictionary,one-taileddictionary,one-tailedDictionary,One-Taileddictionary,One-TailedMathDictionary,one-tailedMathdictionary,one-tailedmathdictionary,one-tailedMathDictionary,One-TailedMathdictionary,One-Tailedmathdictionary,One-Tailedary,onetaileddictionary,onetailedDictionary,one_taileddictionary,one_tailedDictionary,OneTaileddictionary,OneTailedDictionary,One_Taileddictionary,One_TailedDictionary,Onetaileddictionary,OnetailedDictionary,One_taileddictionary,One_tailedMathDictionary,onetailedMathdictionary,onetailedmathdictionary,onetailedMathDictionary,one_tailedMathdictionary,one_tailedmathdictionary,one_tailedMathDictionary,OneTailedMathdictionary,OneTailedmathdictionary,OneTailedMathDictionary,One_TailedMathdictionary,One_Tailedmathdictionary,One_TailedMathDictionary,OnetailedMathdictionary,Onetailedmathdictionary,OnetailedMathDictionary,One_tailedMathdictionary,One_tailedmathdictionary,One_taileddefinition,on4#O{VERSION 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" } {TEXT 39 2 "1." } {TEXT -1 156 " (of two sets of individuals) having elements that are able to be paired with one another without remainder, equinumerous. For example, the natural numbers " } {TEXT 22 1 "n" } {TEXT -1 40 " correspond one-to-one with the points <" } {TEXT 22 1 "n" } {TEXT -1 2 ", " } {TEXT 22 1 "n" } {TEXT -1 21 "> on the real plane. " } {TEXT 39 2 "2." } {TEXT -1 13 " also called " } {TEXT 39 9 "bijective" } {TEXT -1 4 " or " } {TEXT 39 15 "into and onto. " } {TEXT -1 310 " (of a mapping) associating a unique member of the codomain with every member of the domain of a function, or a unique first argument with each second argument of a binary rel{ZDefinition,agreedefinition,agreeDefinition,Agreedefinition,AgreeDictionary,agreedictionary,agreeDictionary,Agreedictionary,AgreeMathDictionary,agreeMathdictionary,agreemathdictionary,agreeMathDictionary,AgreeMathdictionary,Agreemathdictionary,Agreenemanydictionary,onemanyDictionary,one_manydictionary,one_manyDictionary,OneManydictionary,OneManyDictionary,One_Manydictionary,One_ManyDictionary,Onemanydictionary,OnemanyDictionary,One_manydictionary,One_manyMathDictionary,onemanyMathdictionary,onemanymathdictionary,onemanyMathDictionary,one_manyMathdictionary,one_manymathdictionary,one_manyMathDictionary,OneManyMathdictionary,OneManymathdictionary,OneManyMathDictionary,One_ManyMathdictionary,One_Manymathdictionary,One_ManyMathDictionary,OnemanyMathdictionary,Onemanymathdictionary,OnemanyMathDictionary,One_manyMathdictionary,One_manymathdictionary,One_manydefinition,one-manyDefinition,One-Manydefinition,One-ManyDictionary,one-manydictionary,one-many"Definition,BooleanDefinition,booleandefinition,booleandefinition,BooleanDictionary,booleandictionary,booleanDictionary,Booleandictionary,BooleanMathDictionary,booleanMathdictionary,booleanmathdictionary,booleanMathDictionary,BooleanMathdictionary,Booleanmathdictionary,Booleanictionary,de_dictomathdictionary,de_dictoMathDictionary,DeDictoMathdictionary,DeDictomathdictionary,DeDictoMathDictionary,De_DictoMathdictionary,De_Dictomathdictionary,De_DictoMathDictionary,DedictoMathdictionary,Dedictomathdictionary,DedictoMathDictionary,De_dictoMathdictionary,De_dictomathdictionary,De_dictoanymathdictionary,One_ManyMathDictionary,OnemanyMathdictionary,Onemanymathdictionary,OnemanyMathDictionary,One_manyMathdictionary,One_manymathdictionary,One_manydefinition,one-manyDefinition,One-Manydefinition,One-ManyDictionary,one-manydictionary,one-many?oza&* L| -V )g/G`J %Rosp qyi;U bbFCbCO]^ 3Iְ);*pqjtukwjYjU;`kW OmQ$hO+E@%A *OTW*XH \cjk){Bν}GJnl`yդ|iSzE:K1@=^Pl[_0B3{[:[L%?g'<$@GYbZ3f\l | |V=-w\ Jz?SKSU|pFvΓy.!}M>%,Lg T@Մ6 9$)4ka6dWeg^uY ~nhl$;=c&D `i']f;EA<t=](>g?/@Om3rT *tDictionary,Optimizationoptimization definitionDictionary,OptimizationTheory!ϻoptimization theory definitionDictionary,Optimization_Theory!ϻoptimization theory definitionDictionary,Optimization_theory!ϻoptimization theory definitionDictionary,Optimizationtheory!ϻoptimization theory definitionDictionary,OptimizeRoptimize definitionDictionary,Optimumoptimum definition Dictionary,Or9or definitionDictionary,Orbitorbit definitiondefinition,nonsymmetrichdefinition,normal_curvaturedefinition,normal_matrixdefinition,normalcurve9definition,normalizer{definition,normalsubgroup͆definition,notdefinition,np-decisionproblemzdefinition,nphardproblemLJdefinition,null_spacedefinition,nullvectordefinition,numericalĄ definition,numericaleccentricitydefinition,oandonotationEdefinition,oblique<definition,octahedrondefinition,officerproblem!definition,Pareto_Efficient_Point"rPareto optimal point definitiondefinition,Pareto_Optimal_Point? " 0 "" {TEXT -1 31 "one parameter family of curves," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 157 " A one-parameter family of curves is a set of curves distinguished from one another by the value of a parameter c in a representation such as y(x) = f(x, c)." } } } Definition,opendisk+open disk definitionDefinition,openintervalopen interval definitionDefinition,openlinesegmentopen interval definitionDefinition,openmappingV3open mapping definitionDefinition,openmappingtheorem"open mapping theorem definitionDefinition,opensentenceopen sentence definitionDefinition,opensetTopen set definitionDefinition,opentheory open theory definitionDefinition,operand$operand definitionDefinition,operateoperate definitionDefinition,operationjoperation definitionDefinition,operatorCoperator definitionDefinition,operator_normToperator norm definitionDefinition,operatornormToperator norm definitionDefinition,ophelmalophelmal definitionDefinition,opposite@!opposite definitionDefinition,opposite_anglesZopposite angles definitionDefinition,opposite_ringopposite ring definitionDefinition,oppositeanglesZopposite angles definitionDefinition,oppositeringopposite ring definitionDefinition,optimaloptimal definition%Definition,optimal_assignment_problem(optimal assignment problem definitionDefinition,optimal_control90control theory definitionFoptimal control definition#Definition,optimalassignmentproblem(optimal assignment problem definitionDefinition,optimalcontrol90control theory definitionFoptimal control definition{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 5 "onto," } } {PARA 0 "> " 0 "" {TEXT 22 5 "prep." } {TEXT -1 1 " " } {TEXT 39 3 "1. " } {TEXT -1 66 "(of a mapping) to the whole of (the stated set); having the whole " } {HYPERLNK 45 "codomain" 5 "Definition/codomain" "" }{TEXT -1 8 " as its " } {HYPERLNK 45 "range" 5 "Definition/range" "" }{TEXT -1 2 ". " } {TEXT 39 2 "2." } {TEXT -1 2 " (" } {TEXT 22 7 "as adj." } {TEXT -1 19 ") another term for " } {HYPERLNK 45 "surjective" 5 "Definition/surjective" "" }{TEXT -1 2 ". " } } } Optimizationtheory,definitionϻOptimizationtheory,dictionaryϻ!Optimizationtheory,mathdictionaryϻOptimize,DefinitionROptimize,DictionaryROptimize,MathDictionaryROptimize,MathdictionaryROptimize,definitionROptimize,dictionaryROptimize,mathdictionaryROptimum,DefinitionOptimum,DictionaryOptimum,MathDictionaryOptimum,MathdictionaryOptimum,definitionOptimum,dictionaryoptimum,mathdictionary or,Definition9 or,Dictionary9or,MathDictionary9or,Mathdictionary9 or,definition9 or,dictionary9or,mathdictionary9orbit,Definitionorbit,Dictionaryorbit,MathDictionaryorbit,Mathdictionaryorbit,definitionorbit,dictionaryorbit,mathdictionary#orbit_stabilizer_theorem,Definition7#orbit_stabilizer_theorem,Dictionary7'orbit_stabilizer_theorem,MathDictionary7#"{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 10 "open ball," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 2 " (" } {TEXT 22 8 "Topology" } {TEXT -1 13 ") an epsilon-" } {HYPERLNK 45 "neighborhood" 5 "Definition/neighborhood" "" }{TEXT -1 4 " or " } {HYPERLNK 45 "open set" 5 "Definition/openset" "" }{TEXT -1 6 " in a " } {HYPERLNK 45 "metric space" 5 "Definition/metricspace" "" }{TEXT -1 2 ". " } } } Definition,Open_covering open cover definitionDefinition,Open_disk+open disk definitionDefinition,Open_intervalopen interval definitionDefinition,Open_mappingV3open mapping definitionDefinition,Open_mapping_theorem"open mapping theorem definitionDefinition,Open_sentenceopen sentence definitionDefinition,Open_setTopen set definitionDefinition,Open_theory open theory definitionDefinition,Openball#open ball definitionDefinition,Opencover open cover definitiondefinition,Open_covering open cover definitiondefinition,Open_disk+open disk definitiondefinition,Open_intervalopen interval definitiondefinition,Open_mappingV3open mapping definitiondefinition,Open_mapping_theorem"open mapping theorem definitiondefinition,Open_sentenceopen sentence definitiondefinition,Open_setTopen set definitiondefinition,Open_theory open theory definitiondefinition,Openball#open ball definitiondefinition,Opencover open cover definitionOpenMapping,mathdictionaryV3OpenMappingTheorem,DefinitionOpenMappingTheorem,Dictionary!OpenMappingTheorem,MathDictionary!OpenMappingTheorem,MathdictionaryOpenMappingTheorem,definitionOpenMappingTheorem,dictionary!OpenMappingTheorem,mathdictionaryOpenSentence,DefinitionOpenSentence,DictionaryOpenSentence,MathDictionaryOpenSentence,MathdictionaryOpenSentence,definitionOpenSentence,dictionaryjMathdictionary,non_atomic^Mathdictionary,non_empty_word<(Mathdictionary,non_parametric_statistics'Mathdictionary,non_standard_real_numberPMathdictionary,nondenumerable#Mathdictionary,noneuclideangeometryMathdictionary,nonresidueMathdictionary,nonsymmetric>Mathdictionary,normal_coneMathdictionary,normal_familyCMathdictionary,normalcurveMathdictionary,normalizeMathdictionary,normalseriesMathdictionary,normedringA#MathDictionary,Orthogonal_Functions" orthogonal functions definitionMathDictionary,Orthogonal_Grouporthogonal group definition MathDictionary,Orthogonal_Matrix,orthogonal matrix 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definitionone_many,dictionarymone_many,mathdictionarymone_one,Definitionone_one,Dictionaryone_one,MathDictionaryone_one,Mathdictionaryone_one,definitionone_one,dictionaryone_one,mathdictionary%one_point_compactification,Definition"%one_point_compactification,Dictionary")one_point_compactification,MathDictionary")one_point_compactification,Mathdictionary"%one_point_compactification,definition"onemany,Mathdictionarymonemany,definitionmonemany,dictionarymonemany,mathdictionarymoneone,Definitiononeone,Dictionaryoneone,MathDictionaryoneone,Mathdictionaryoneone,definitiononeone,dictionaryoneone,mathdictionary%oneparameterfamilyofcurves,Definition]%oneparameterfamilyofcurves,definition]#onepointcompactification,Definition"#onepointcompactification,Dictionary"'onepointcompactification,MathDictionary"'onepointcompactification,Mathdictionary" 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OpenDisk,Definition+OpenDisk,Dictionary+OpenDisk,MathDictionary+OpenDisk,Mathdictionary+OpenDisk,definition+OtermexpresscansatisfwillminimizscalarsetvectordistancapproximatbestdescribmathdictionardictionardefinitionindexequationnormalnormalequatdefinitOblowhammsuchshortsystemmechanicalapplimomentumlinearchangtotalparticlsetactinginttimebetweenforcintegralmathdictionardictionardefinitioniindeximpulsdefinit#OcomparcoincidrangcasereservoftentermthesevenintegerteamrugbmemberbetweencorrespondencversavicerelatbinarsecondeachargumfirstfunctdomainevercodomainmembuniquassociatmappontointobijectcallalsoplanrealpointcorrespondnumbernaturalexamplequinumerouremaindwithoutanothwithpairableelementhavingindividualsetsmathdictionardictionaronetoondefinitionoindexdefinitDefinition,one-sidedDefinition,onesideddefinition,onesidedDefinition,one_sideddefinition,one_sidedDefinition,OneSideddefinition,OneSidedDefinition,One_Sideddefinition,One_SidedDefinition,Onesideddefinition,OnesidedDefinition,One_sideddefinition,One_sidedDictionary,onesideddictionary,onesidedDictionary,one_sideddictionary,one_sidedDictionary,OneSideddictionary,OneSidedDictionary,One_Sideddictionary,One_SidedDictionary,Onesideddictionary,OnesidedDictionary,One_sideddictionary,One_sidedMathDictionary,onesidedMathdictionary,onesidedmathdictionary,onesidedMathDictionary,one_sidedMathdictionary,one_sidedmathdictionary,one_sidedMathDictionary,OneSidedMathdictionary,OneSidedmathdictionary,OneSidedMathDictionary,One_SidedMathdictionary,One_Sidedmathdictionary,One_SidedMathDictionary,OnesidedMathdictionary,Onesidedmathdictionary,OnesidedMathDictionary,One_sidedMathdictionary,One_sidedmathdictionary,One_sideddefinition,one-sidedDefinition,One-Sideddefinition,Oneictionary,onepointcompactificationMathDictionary,one_point_compactificationMathdictionary,one_point_compactificationmathdictionary,one_point_compactificationMathDictionary,OnePointCompactificationMathdictionary,OnePointCompactificationmathdictionary,OnePointCompactificationMathDictionary,One_Point_CompactificationMathdictionary,One_Point_Compactificationmathdictionary,One_Point_CompactificationMathDictionary,OnepointcompactificationMathdictionary,Onepointcompactificationmathdictionary,OnepointcompactificationMathDictionary,One_point_compactificationMathdictionary,One_point_compactificationmathdictionary,One_point_compactificationdefinition,one-pointcompactificationDefinition,one-point_compactificationdefinition,one-point_compactificationDefinition,One-PointCompactificationdefinition,One-PointCompactificationDefinition,One-Point_Compactificationdefinition,One-Point_CompactificationDefinition,One-pointcompactificationdefinition,One-pointcompactificationDefinition,One-point_compactif^icationdefinition,One-point_compactificationDictionary,one-pointcompactificationdictionary,one-pointcompactificationDictionary,one-point_compactificationdictionary,one-point_compactificationDictionary,One-PointCompactificationdictionary,One-PointCompactificationDictionary,One-Point_Compactificationdictionary,One-Point_CompactificationDictionary,One-pointcompactificationdictionary,One-pointcompactificationDictionary,One-point_compactificationdictionary,One-point_compactificationMathDictionary,one-pointcompactificationMathdictionary,one-pointcompactificationmathdictionary,one-pointcompactificationMathDictionary,one-point_compactificationMathdictionary,one-point_compactificationmathdictionary,one-point_compactificationMathDictionary,One-PointCompactificationMathdictionary,One-PointCompactificationmathdictionary,One-PointCompactificationMathDictionary,One-Point_CompactificationMathdictionary,One-Point_Compactificationmathdictionary,One-Point_CompactificationMathDictionary,One-pointco_mpactificationMathdictionary,One-pointcompactificationmathdictionary,One-pointcompactificationMathDictionary,One-point_compactificationMathdictionary,One-point_compactificationmathdictionary,One-point_compactificationificationdictionary,One-PointCompactificationDictionary,One-Point_Compactificationdictionary,One-Point_CompactificationDictionary,One-pointcompactificationdictionary,One-pointcompactificationDictionary,One-point_compactificationdictionary,One-point_compactificationMathDictionary,one-pointcompactificationMathdictionary,one-pointcompactificationmathdictionary,one-pointcompactificationMathDictionary,one-point_compactificationMathdictionary,one-point_compactificationmathdictionary,one-point_compactificationMathDictionary,One-PointCompactificationMathdictionary,One-PointCompactificationmathdictionary,One-PointCompactificationMathDictionary,One-Point_CompactificationMathdictionary,One-Point_Compactificationmathdictionary,One-Point_CompactificationMathDictionary,One-pointco_{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 10 "one-sided," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 1 " " } {TEXT 39 2 "1." } {TEXT -1 100 " (of a surface) having the property that any two points can be joined without crossing an edge. See " } {HYPERLNK 45 "Mobius strip" 5 "Definition/Mobiusstrip" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "Klein bottle" 5 "Definition/Kleinbottle" "" }{TEXT -1 2 ". " } {TEXT 39 2 "2." } {TEXT -1 9 " (of the " } {HYPERLNK 45 "limit" 5 "Definition/limit" "" }{TEXT -1 53 " of a function of a single real variable at a point, " } {TEXT 22 1 "p" } {TEXT -1 95 ") the limit as computed when the function is viewed as restricted to the half-line ]-infinity, " } {TEXT 22 2 "p " } {TEXT -1 23 "[ or to the half-line ]" } {TEXT 22 1 "p" } {TEXT -1 32 ", infinity[. The function has a " } {HYPERLNK 45 "discontinuity" 5 "Definition/discontainuity" "" }{TEXT -1 4 " at " } {TEXT 22 2 "p " } {TEXT -1 76 "if the one-sided limits do not exist or are not equal, and is continuous at " } {TEXT 22 2 "p " } {TEXT -1 62 "if they are finite and equal, in which case that value is the " } {TEXT 22 9 "two-sided" } {TEXT -1 10 " limit at " } {TEXT 22 2 "p." } {TEXT -1 37 " For example, the one-sided limit of " } {TEXT 22 1 "x" } {TEXT -1 2 "/|" } {TEXT 22 1 "x" } {TEXT -1 78 "| at zero from above is +1 and the one-sided limit from below is -1. See also " } {HYPERLNK 45 "left-hand limit" 5 "Definition/left-handlimit" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "right-hand limit" 5 "Definition/right-handlimit" "" }{TEXT -1 2 ". " } } } le real variable at a point, " } {TEXT 22 1 "p" } {TEXT -1 95 ") the limit as computed when the function is viewed as restricted to the half-line ]-infinity, " } {TEXT 22 2 "p " } {TEXT -1 23 "[ or to the half-line ]" } {TEXT 22 1 "p" } {TEXT -1 32 ", infinity[. The function has a " } {HYPERLNK 45 "discontinuity" 5 "Definition/discontaomathdictionary,Orbit mathdictionary,Order-Preserving-mathdictionary,OrderPreservingmathdictionary,Order_Preserving/mathdictionary,Order_preserving"mathdictionary,Ordered_Arrangement!mathdictionary,Orderedarrangementmathdictionary,Ordernotation>mathdictionary,OrdinallySimilarZ-mathdictionary,Ordinary_Differential_Equationmathdictionary,Ordinarypoint #mathdictionary,OrthogonalComplement$mathdictionary,Orthogonal_Complement #mathdictionary,Open_mapping_theorem"open mapping theorem definitionmathdictionary,Open_sentenceopen sentence definitionmathdictionary,Open_setTopen set definitionmathdictionary,Open_theory open theory definitionmathdictionary,Openball#open ball definitionmathdictionary,Opencover open cover definitionmathdictionary,Opencovering open cover definitionmathdictionary,Opendisk+open disk definitionmathdictionary,Openintervalopen interval definitiondictionary,OperatorNormToperator norm definitiondictionary,Operator_NormToperator norm definitiondictionary,Operator_normToperator norm definitiondictionary,OperatornormToperator norm definitiondictionary,Ophelmalophelmal definitiondictionary,Opposite@!opposite definitiondictionary,OppositeAnglesZopposite angles definitiondictionary,OppositeRingopposite ring definitiondictionary,Opposite_AnglesZopposite angles definitionwkB{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 18 "exchange property," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "matroid" 5 "Definition/matroid" "" }{TEXT -1 2 ". " } } } mathdictionary,Opaqueiopaque definitionmathdictionary,Openopen definitionmathdictionary,OpenBall#open ball definitionmathdictionary,OpenCover open cover definitionmathdictionary,OpenCovering open cover definitionmathdictionary,OpenDisk+open disk definitionmathdictionary,OpenIntervalopen interval definitionmathdictionary,OpenMappingV3open mapping definition!mathdictionary,OpenMappingTheorem"open mapping theorem definitionmathdictionary,OpenSentenceopen sentence definitionmathdictionary,OpenSetTopen set definitionmathdictionary,OpenTheory open theory definitionmathdictionary,Open_Ball#open ball definitionmathdictionary,Open_Cover open cover definitionmathdictionary,Open_Covering open cover definitionmathdictionary,Open_Disk+open disk definitionOntology,definitionOntology,dictionaryOntology,mathdictionaryOpacity,DefinitionOpacity,DictionaryOpacity,MathDictionaryOpacity,MathdictionaryOpacity,definitionOpacity,dictionaryOpacity,mathdictionaryOpaque,DefinitioniOpaque,DictionaryiOpaque,MathDictionaryiOpaque,MathdictionaryiOpaque,definitioniOpaque,dictionaryiOpaque,mathdictionaryi Definition,opencoverdefinition,opencoverDefinition,open_coverdefinition,open_coverDefinition,OpenCoverdefinition,OpenCoverDefinition,Open_Coverdefinition,Open_CoverDefinition,Opencoverdefinition,OpencoverDefinition,Open_coverdefinition,Open_coverDictionary,opencoverdictionary,opencoverDictionary,open_coverdictionary,open_coverDictionary,OpenCoverdictionary,OpenCoverDictionary,Open_Coverdictionary,Open_CoverDictionary,Opencoverdictionary,OpencoverDictionary,Open_coverdictionary,Open_coverMathDictionary,opencoverMathdictionary,opencovermathdictionary,opencoverMathDictionary,open_coverMathdictionary,open_covermathdictionary,open_coverMathDictionary,OpenCoverMathdictionary,OpenCovermathdictionary,OpenCoverMathDictionary,Open_CoverMathdictionary,Open_Covermathdictionary,Open_CoverMathDictionary,OpencoverMathdictionary,Opencovermathdictionary,OpencoverMathDictionary,Open_coverMathdictionary,Open_covermathdictionary,Open_coverDefinition,opencoveringdefinition,ʉi@{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 7 "opaque," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 7 " (of a " } {HYPERLNK 45 "modal" 5 "Definition/modal" "" }{TEXT -1 59 " context) not permitting variables within the scope of the " } {HYPERLNK 45 "modal" 5 "Definition/modal" "" }{TEXT -1 25 " operator to be bound by " } {HYPERLNK 45 "quantifiers" 5 "Definition/quantifier" "" }{TEXT -1 35 " of wider scope. For example, from " } } {PARA 0 "> " 0 "" {TEXT 22 32 "John believes someone robbed him" } {TEXT -1 1 " " } } {PARA 0 "> " 0 "" {TEXT -1 17 "one cannot infer " } } {PARA 0 "> " 0 "" {TEXT 22 46 "There is someone whom John believes robbed him" } {TEXT -1 1 "," } } {PARA 0 "> " 0 "" {TEXT -1 63 "since he may have no idea who the culprit might be. Similarly, " } } {PARA 0 "> " 0 "" {TEXT 22 24 "He ought to do something" } {TEXT -1 1 " " } } {PARA 0 "> j" 0 "" {TEXT -1 21 "is not equivalent to " } } {PARA 0 "> " 0 "" {TEXT 22 34 "There is something he ought to do." } {TEXT -1 1 " " } } {PARA 0 "> " 0 "" {TEXT -1 28 " Likewise, the principle of " } {HYPERLNK 45 "substitutivity" 5 "Definition/substitutivity" "" }{TEXT -1 77 " fails in opaque contexts. Opacity is responsible for the difference between " } {HYPERLNK 45 "de re" 5 "Definition/dere" "" }{TEXT -1 5 " and " } {HYPERLNK 45 "de dicto" 5 "Definition/dedicto" "" }{TEXT -1 19 " modality. 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" } {TEXT -1 13 "the smallest " } {HYPERLNK 45 "natural number" 5 "Definition/naturalnumber" "" }{TEXT -1 21 "; the first non-null " } {HYPERLNK 45 "cardinal number" 5 "Definition/cardinalnumber" "" }{TEXT -1 22 "; the second smallest " } {HYPERLNK 45 "natural number" 5 "Definition/naturalnumber" "" }{TEXT -1 28 " in the construction of the " } {HYPERLNK 45 "ordinals" 5 "Definition/ordinal" "" }{TEXT -1 72 "; the number of members of a set that has all of its members identical; " } {HYPERLNK 45 "unity" 5 "Definition/unity" "" }{TEXT -1 2 ". 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For example, any punctured neighborhood in the reals is disconnected, as is the cut interval (-1,1) \\ {0}. " } } } ȤH{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 11 "O notation," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "order notation" 5 "Definition/ordernotation" "" }{TEXT -1 2 ". " } } } ؤo{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 16 "Cartesian space," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 18 " another term for " } {HYPERLNK 45 "Euclidean space" 5 "Definition/Euclideanspace" "" }{TEXT -1 1 "." } } } ample, any punctured neighborhood in the reals is disconnected, as is the cut interval (-1,1) \\ {0}. " } } } ȤH{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 11 "O notation," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "order notation" 5 "Definition/ordernotation" "" }{TEXT -1 2 ". 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For example, there is a 1-1 correspondence between the members of a rugby team and the natural numbers 1 to 15; " } {TEXT 22 1 "x" } {TEXT -1 5 " -> 2" } {TEXT 22 1 "x" } {TEXT -1 148 " is a 1-1 mapping from the integers to the even integers. These terms are often reserved for the case when the codomain and range coincide. Compare " } {HYPERLNK 45 "surjective" 5 "Definition/surjective" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "injective" 5 "Definition/injective" "" }{TEXT -1 2 ". " } } } ample, the natural numbers " } {TEXT 22 1 "n" } {TEXT -1 40 " correspond one-to-one with the points <" } {TEXT 22 1 "n" } {TEXT -1 2 ", " } {TEXT 22 1 "n" } {TEXT -1 21 "> on the real plane. " } {TEXT 39 2 "2." } {TEXT -1 13 " also called " } {TEXT 39 9 "bijective" } {TEXT -1 4 " or " } {TEXT 39 15 "into and onto. " } {TEXT -1 310 " (of a mapping) associating a unique member of the codomain with every member of the domain of a function, or a unique first argument with each second argument of a binary rel{Dictionary,Opposite_Ringopposite ring definitionDictionary,Opposite_anglesZopposite angles definitionDictionary,Opposite_ringopposite ring definitionDictionary,OppositeanglesZopposite angles definitionDictionary,Oppositeringopposite ring definitionDictionary,Optimaloptimal definition#Dictionary,OptimalAssignmentProblem(optimal assignment problem definitionDictionary,OptimalControl90control theory definitionFoptimal control definitionmathdictionary,Opposite_Ringopposite ring definitionmathdictionary,Opposite_anglesZopposite angles definitionmathdictionary,Opposite_ringopposite ring definitionmathdictionary,OppositeanglesZopposite angles definitionmathdictionary,Oppositeringopposite ring definitionmathdictionary,Optimaloptimal definition'mathdictionary,OptimalAssignmentProblem(optimal assignment problem definitionmathdictionary,OptimalControl90control theory definitionFoptimal control definitionDictionary,Ordinary_Point,ordinary point definition"Dictionary,Ordinary_Representation%ordinary representation definition)Dictionary,Ordinary_differential_equation,ݾordinary differential equation definitionDictionary,Ordinary_point,ordinary point definition"Dictionary,Ordinary_representation%ordinary representation definition'Dictionary,Ordinarydifferentialequation,ݾordinary differential equation definitionDictionary,Ordinarypoint,ordinary point definition"Definition,opacitydefinition,opacityDefinition,Opacitydefinition,OpacityDictionary,opacitydictionary,opacityDictionary,Opacitydictionary,OpacityMathDictionary,opacityMathdictionary,opacitymathdictionary,opacityMathDictionary,OpacityMathdictionary,Opacitymathdictionary,Opacity{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 9 "ontology," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 95 " the (set of) entities whose existence is implicit in any given theory; the set over which its " } {HYPERLNK 45 "quantifiers" 5 "Definition/quantifier" "" }{TEXT -1 37 " can range. 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" } } } "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 4 "one," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 1 " " } {TEXT 39 3 "1. " } {TEXT -1 13 "the smallest " } {HYPERLNK 45 "natural number" 5 "Definition/naturalnumber" "" }{TEXT -1 21 "; the first non-null " } {HYPERLNK 45 "cardinal number" 5 "Definition/cardinalnumber" "" }{TEXT -1 22 "; the second smallest " } {HYPERLNK 45 "natural number" 5 "Definition/naturalnumber" "" }{TEXT -1 28 " in the construction of the " } {HYPERLNK 45 "ordinals" 5 "Definition/ordinal" "" }{TEXT -1 72 "; the number of members of a set that has all of its members identical; " } {HYPERLNK 45 "unity" 5 "Definition/unity" "" }{TEXT -1 2 ". " } {TEXT 39 2 "2." } {TEXT -1 5 " the " } {HYPERLNK 45 "identity element" 5 "Definition/identityelement" "" }{TEXT -1 27 " under multiplication in a " } {HYPERLNK 45 "ring" 5 "Definition/ring" "" }{Mathdictionary,openmappingV3open mapping definition!Mathdictionary,openmappingtheorem"open mapping theorem definitionMathdictionary,opensentenceopen sentence definitionMathdictionary,opensetTopen set definitionMathdictionary,opentheory open theory definitionMathdictionary,operand$operand definitionMathdictionary,operateoperate definitionMathdictionary,operationjoperation definitionMathdictionary,operatorCoperator definition)dictionary,ordinary_differential_equation,ݾordinary differential equation definitiondictionary,ordinary_point,ordinary point definition"dictionary,ordinary_representation%ordinary representation definition'dictionary,ordinarydifferentialequation,ݾordinary differential equation definitiondictionary,ordinarypoint,ordinary point definition!dictionary,ordinaryrepresentation%ordinary representation definitiondictionary,ordinate " 0 "" {TEXT -1 8 "opacity," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 26 " the property of being an " } {HYPERLNK 45 "opaque" 5 "Definition/opaque" "" }{TEXT -1 10 " context. " } } } manipulat+OI4l^ mann+L"HTiC{4mannwhitneytestmantissa]manual> manuscript>manyM -k!!X"&$%)E+<-Z-/0(3L5;7>BREGHJ'0L M?QUSJUUCZb^ggi7lmnoww~{{|0ex%Oɔ םMN;w0U=7~XHm*NE_%XmanyonJmanyvaluedlogicUmapK8mJ-4[a8yQ~=XB\mathdictionary,ontologyontology definitionmathdictionary,opacityopacity definitionmathdictionary,opaqueiopaque definitionmathdictionary,openopen definitionmathdictionary,open_ball#open ball definitionmathdictionary,open_cover open cover definitionmathdictionary,open_covering open cover definitionmathdictionary,open_disk+open disk definitionmathdictionary,open_intervalopen interval definitionmathdictionary,open_mappingV3open mapping definitionOpencovering,definition Opencovering,dictionary Opencovering,mathdictionary 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open cover definitiondictionary,Opencovering open cover definitiondictionary,Opendisk+open disk definitionMathdictionary,Opaqueiopaque definitionMathdictionary,Openopen definitionMathdictionary,OpenBall#open ball definitionMathdictionary,OpenCover open cover definitionMathdictionary,OpenCovering open cover definitionMathdictionary,OpenDisk+open disk definitionMathdictionary,OpenIntervalopen interval definitionMathdictionary,OpenMappingV3open mapping definition!Mathdictionary,OpenMappingTheorem"open mapping theorem definitionmathdictionary,Open_Intervalopen interval definitionmathdictionary,Open_MappingV3open mapping definition#mathdictionary,Open_Mapping_Theorem"open mapping theorem definitionmathdictionary,Open_Sentenceopen sentence definitionmathdictionary,Open_SetTopen set definitionmathdictionary,Open_Theory open theory definitionmathdictionary,Open_ball#open ball definitionmathdictionary,Open_cover open cover definitionmathdictionary,Open_covering open cover definitionmathdictionary,Open_disk+open disk definitionmathdictionary,Open_intervalopen interval definitionmathdictionary,Open_mappingV3open mapping definitionopen_ball,definition#open_ball,dictionary#open_ball,mathdictionary#open_cover,Definition open_cover,Dictionary open_cover,MathDictionary open_cover,Mathdictionary open_cover,definition open_cover,dictionary open_cover,mathdictionary open_covering,Definition open_covering,Dictionary open_covering,MathDictionary open_covering,Mathdictionary open_covering,definition !Openmappingtheorem,mathdictionaryOpensentence,DefinitionOpensentence,DictionaryOpensentence,MathDictionaryOpensentence,MathdictionaryOpensentence,definitionOpensentence,dictionaryOpensentence,mathdictionaryOpenset,DefinitionTOpenset,DictionaryTOpenset,MathDictionaryTOpenset,MathdictionaryTOpenset,definitionTOpenset,dictionaryTOpenset,mathdictionaryTOpentheory,Definition Secretary_problem,Dictionary1= Secretary_problem,MathDictionary1= 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Open_covering,mathdictionary Open_disk,Definition+Open_disk,Dictionary+Open_disk,MathDictionary+Open_disk,Mathdictionary+Open_disk,definition+Open_disk,dictionary+Open_disk,mathdictionary+Open_interval,DefinitionOpen_interval,DictionaryOpen_interval,MathDictionaryOpen_interval,MathdictionaryOpen_interval,definitionOpen_interval,dictionaryOpenDisk,dictionary+OpenDisk,mathdictionary+OpenInterval,DefinitionOpenInterval,DictionaryOpenInterval,MathDictionaryOpenInterval,MathdictionaryOpenInterval,definitionOpenInterval,dictionaryOpenInterval,mathdictionaryOpenMapping,DefinitionV3OpenMapping,DictionaryV3OpenMapping,MathDictionaryV3OpenMapping,MathdictionaryV3OpenMapping,definitionV3OpenMapping,dictionaryV3alsothereondomaingivenconstantnonfunctanalyticspacbanachbetweenlinearsurjectcontinuouassertconditgivingmathdictionardictionardefinitionoindextheoremmappopenopenmappingtheoremdefinitopencovering,mathdictionary opendisk,Definition+opendisk,Dictionary+opendisk,MathDictionary+opendisk,Mathdictionary+opendisk,definition+opendisk,dictionary+opendisk,mathdictionary+openinterval,Definitionopeninterval,Dictionaryopeninterval,MathDictionaryopeninterval,Mathdictionaryopeninterval,definitionopeninterval,dictionaryopeninterval,mathdictionaryopenlinesegment,DefinitionvalMathDictionary,Open_intervalMathdictionary,Open_intervalmathdictionary,Open_intervalDefinition,openlinesegment,OpenIntervaldefinition,OpenIntervalDefinition,Open_Intervaldefinition,Open_IntervalDefinition,Openintervaldefinition,OpenintervalDefinition,Open_intervaldefinition,Open_intervalDictionary,openintervaldictionary,openintervalDictionary,open_intervaldictionary,open_intervalDictionary,OpenIntervaldictionary,OpenIntervalDictionary,Open_Intervaldictionary,Open_IntervalDictionary,Openintervaldictionary,OpenintervalDictionary,Open_intervaldictionary,Open_intervalMathDictionary,openintervalMathdictionary,openintervalmathdictionary,openintervalMathDictionary,open_intervalMathdictionary,open_intervalmathdictionary,open_intervalMathDictionary,OpenIntervalMathdictionary,OpenIntervalmathdictionary,OpenIntervalMathDictionary,Open_IntervalMathdictionary,Open_Intervalmathdictionary,Open_IntervalMathDictionary,OpenintervalMathdictionary,Openintervalmathdictionary,OpeninterZDefinition,contractiondefinition,contractionDefinition,Contractiondefinition,ContractionDictionary,contractiondictionary,contractionDictionary,Contractiondictionary,ContractionMathDictionary,contractionMathdictionary,contractionmathdictionary,contractionMathDictionary,ContractionMathdictionary,Contractionmathdictionary,Contractionry,open_intervaldictionary,open_intervalDictionary,OpenIntervaldictionary,OpenIntervalDictionary,Open_Intervaldictionary,Open_IntervalDictionary,Openintervaldictionary,OpenintervalDictionary,Open_intervaldictionary,Open_intervalMathDictionary,openintervalMathdictionary,openintervalmathdictionary,openintervalMathDictionary,open_intervalMathdictionary,open_intervalmathdictionary,open_intervalMathDictionary,OpenIntervalMathdictionary,OpenIntervalmathdictionary,OpenIntervalMathDictionary,Open_IntervalMathdictionary,Open_Intervalmathdictionary,Open_IntervalMathDictionary,OpenintervalMathdictionary,Openintervalmathdictionary,OpeninterC>Definition,ancestraldefinition,ancestralDefinition,Ancestraldefinition,AncestralDictionary,ancestraldictionary,ancestralDictionary,Ancestraldictionary,AncestralMathDictionary,ancestralMathdictionary,ancestralmathdictionary,ancestralMathDictionary,AncestralMathdictionary,Ancestralmathdictionary,Ancestral,openintervalMathDictionary,open_intervalMathdictionary,open_intervalmathdictionary,open_intervalMathDictionary,OpenIntervalMathdictionary,OpenIntervalmathdictionary,OpenIntervalMathDictionary,Open_IntervalMathdictionary,Open_Intervalmathdictionary,Open_IntervalMathDictionary,OpenintervalMathdictionary,Openintervalmathdictionary,OpeninterT{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 21 "open mapping theorem," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 52 " a theorem giving conditions for a mapping to be an " } {HYPERLNK 45 "open mapping" 5 "Definition/openmapping" "" }{TEXT -1 6 ". The " } {TEXT 22 41 "open mapping theorem for linear operators" } {TEXT -1 88 " asserts that a continuous surjective linear mapping between Banach spaces is open. The " } {TEXT 22 44 "open mapping theorem for analytic functions " } {TEXT -1 99 "asserts that an analytic function that is non-constant on a given domain is open thereon. See also " } {HYPERLNK 45 "invariance of domain theorem" 5 "Definition/invarianceofdomaintheorem" "" }{TEXT -1 2 ". " } } } !Dictionary,ordinaryrepresentation%ordinary representation definitionDictionary,ordinate " 0 "" {TEXT -1 10 "open cover" } } {PARA 0 "> " 0 "" {TEXT -1 3 "or " } {TEXT 39 13 "open covering" } {TEXT -1 2 ", " } {TEXT 22 2 "n." } {TEXT -1 3 " a " } {HYPERLNK 45 "cover" 5 "Definition/cover" "" }{TEXT -1 16 " of a set using " } {HYPERLNK 45 "open" 5 "Definition/open" "" }{TEXT -1 10 " subsets. " } } } #<[++HWЕ['`Z$Gϸ{6{H{ ,TOfeuj!+ u802ξޅ*j  d lE  0 M d  cP ~  d;  C=    9  @  ( m 8 PA E ڻO Z X` 9 i Pl 7 H  ߪ K>  l   Q p & 84 J nP n Q _T h q t h yl 2  q qK % ; 8[        չ g e' \B $H    މ  5 U nY )! gK! qD V pa ђ  " G   S  9 o gQ p  G   D5J?bAAF[GP=U8o\6w>y*]i@h,v&}^a,-0 8_2:߬<H(X)mHj~')J4JQ openball,definition#openball,dictionary#openball,mathdictionary#opencover,Definition opencover,Dictionary opencover,MathDictionary opencover,Mathdictionary opencover,definition opencover,dictionary opencover,mathdictionary opencovering,Definition opencovering,Dictionary opencovering,MathDictionary opencovering,Mathdictionary opencovering,definition opencovering,dictionary +Definition,opendiskdefinition,opendiskDefinition,open_diskdefinition,open_diskDefinition,OpenDiskdefinition,OpenDiskDefinition,Open_Diskdefinition,Open_DiskDefinition,Opendiskdefinition,OpendiskDefinition,Open_diskdefinition,Open_diskDictionary,opendiskdictionary,opendiskDictionary,open_diskdictionary,open_diskDictionary,OpenDiskdictionary,OpenDiskDictionary,Open_Diskdictionary,Open_DiskDictionary,Opendiskdictionary,OpendiskDictionary,Open_diskdictionary,Open_diskMathDictionary,opendiskMathdictionary,opendiskmathdictionary,opendiskMathDictionary,open_diskMathdictionary,open_diskmathdictionary,open_diskMathDictionary,OpenDiskMathdictionary,OpenDiskmathdictionary,OpenDiskMathDictionary,Open_DiskMathdictionary,Open_Diskmathdictionary,Open_DiskMathDictionary,OpendiskMathdictionary,Opendiskmathdictionary,OpendiskMathDictionary,Open_diskMathdictionary,Open_diskmathdictionary,Open_diskOddPart,definitionOddpart,Definition3OfSets,definitioniOffDiagonal,MathdictionaryOffdiagonal,DefinitionɈOfficer_Problem,Dictionary͈Officerproblem,DefinitionʆOgive,MathDictionarÿOh_Notation,dictionaryOhnotation,mathdictionaryOmega_Inconsistency,dictionaryOmegainconsistency,definitionOne-One,mathdictionary %One-Point_Compactification,dictionaryOne-Tailed,mathdictionaryF)One-point_compactification,mathdictionaryDefinition,Optimizationoptimization definitionDefinition,OptimizationTheory!ϻoptimization theory definitionDefinition,Optimization_Theory!ϻoptimization theory definitionDefinition,Optimization_theory!ϻoptimization theory definitionDefinition,Optimizationtheory!ϻoptimization theory definitionDefinition,OptimizeRoptimize definitionDefinition,Optimumoptimum definition Definition,Or9or definitionDefinition,Orbitorbit definitionc{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 14 "open interval," } } {PARA 0 "> " 0 "" {TEXT 22 3 "n. " } {TEXT -1 74 "a set of real numbers lying between but excluding its endpoints, written ]" } {TEXT 22 1 "x" } {TEXT -1 2 ", " } {TEXT 22 1 "y" } {TEXT -1 6 "[ or (" } {TEXT 22 1 "x" } {TEXT -1 2 ", " } {TEXT 22 1 "y" } {TEXT -1 8 ") where " } {TEXT 22 1 "x" } {TEXT -1 5 " and " } {TEXT 22 1 "y" } {TEXT -1 24 " are the endpoints; the " } {HYPERLNK 45 "half-open" 5 "Definition/half-open" "" }{TEXT -1 1 " " } {HYPERLNK 45 "intervals" 5 "Definition/interval" "" }{TEXT -1 2 " ]" } {TEXT 22 1 "x" } {TEXT -1 2 ", " } {TEXT 22 1 "y" } {TEXT -1 7 "] and [" } {TEXT 22 1 "x" } {TEXT -1 2 ", " } {TEXT 22 1 "y" } {TEXT -1 10 "[ are not " } {HYPERLNK 45 "open sets" 5 "Definition/openset" "" }{TEXT -1 77 " as they do not contain neighborhoods of one endpoint. All the foregoing are " } {HYPERLNK 45 "bounded" 5 "Definition/bounded" "" }{TEXT -1 7 ", with " } {HYPERLNK 45 "minimum" 5 "Definition/minimum" "" }{TEXT -1 1 " " } {TEXT 22 1 "x" } {TEXT -1 5 " and " } {HYPERLNK 45 "supremum" 5 "Definition/supremum" "" }{TEXT -1 1 " " } {TEXT 22 1 "y" } {TEXT -1 12 ", but only [" } {TEXT 22 1 "x" } {TEXT -1 2 ", " } {TEXT 22 1 "y" } {TEXT -1 8 "[ has a " } {HYPERLNK 45 "minimum" 5 "Definition/minimum" "" }{TEXT -1 11 " and only ]" } {TEXT 22 1 "x" } {TEXT -1 2 ", " } {TEXT 22 1 "y" } {TEXT -1 8 "] has a " } {HYPERLNK 45 "maximum" 5 "Definition/maximum" "" }{TEXT -1 3 "; ]" } {TEXT 22 1 "x" } {TEXT -1 75 ",infinity[ is open and unbounded, and R is also an open interval. See also " } {HYPERLNK 45 "interval" 5 "Definition/interval" "" }{TEXT -1 10 ". Compare " } {HYPERLNK 45 "closed interval" 5 "Definition/closedinterval" "" }{TEXT -1 2 ". " } } } t " } {HYPERLNK 45 "open sets" 5 "Definition/openset" "" }{TEXT -1 77 " as they do not contain neighborhoods of one endpoint. All the foregDictionary,Order_statisticorder statistic definitionDictionary,Ordercompleteorder-complete definitionDictionary,OrderedArrangement:(Mordered arrangement definitionpermutation definitionDictionary,OrderedGeometry=ordered geometry definitionDictionary,OrderedPair#yordered pair definitionDictionary,OrderedSet%ordered set definitionDictionary,OrderedStructureordered structure definitionDictionary,OrderedVectorSpace"Kordered vector space definitionDictionary,Ordered_Arrangement:(Mordered arrangement definitionpermutation definitionmathdictionary,openmappingV3open mapping definition!mathdictionary,openmappingtheorem"open mapping theorem definitionmathdictionary,opensentenceopen sentence definitionmathdictionary,opensetTopen set definitionmathdictionary,opentheory open theory definitionmathdictionary,operand$operand definitionmathdictionary,operateoperate definitionmathdictionary,operationjoperation definitionmathdictionary,operatorCoperator definitionopposite_angles,MathdictionaryZopposite_angles,definitionZopposite_angles,dictionaryZopposite_angles,mathdictionaryZopposite_ring,Definitionopposite_ring,Dictionaryopposite_ring,MathDictionaryopposite_ring,Mathdictionaryopposite_ring,definitionopposite_ring,dictionaryopposite_ring,mathdictionaryoppositeangles,DefinitionZoppositeangles,DictionaryZoppositeangles,MathDictionaryZ#open_mapping_theorem,mathdictionaryopen_sentence,Definitionopen_sentence,Dictionaryopen_sentence,MathDictionaryopen_sentence,Mathdictionaryopen_sentence,definitionopen_sentence,dictionaryopen_sentence,mathdictionaryopen_set,DefinitionTopen_set,DictionaryTopen_set,MathDictionaryTopen_set,MathdictionaryTopen_set,definitionTopen_set,dictionaryTopen_set,mathdictionaryTopen_theory,Definition open_theory,Dictionary open_theory,MathDictionary open_theory,Mathdictionary open_theory,definition open_theory,dictionary open_theory,mathdictionary openball,Definition#openball,Dictionary#openball,MathDictionary#openball,Mathdictionary#`{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 27 "optimal assignment problem," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "assignment problem" 5 "Definition/assignmentproblem" "" }{TEXT -1 2 ". " } } } parallelepip Y parallelism parallelogramG(6/;|Jjڗ?{f parallelogramlawparallelogramofforcfparallelogramofperiod parallelogramrulf parallelopip !Yparallelpostulat2 parallelsecttparametD O e`%67DSF_I1KPQeTZ ]h`cgqtaS:- /]) parametero4z e$)(T= " 0 "" {TEXT -1 9 "operator," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 1 " " } {TEXT 39 4 "1a. " } {TEXT -1 31 "any symbol used to indicate an " } {HYPERLNK 45 "operation" 5 "Definition/operation" "" }{TEXT -1 77 ", such as the integration operator Int, and the differential operator Delta. " } } {PARA 0 "> " 0 "" {TEXT 39 2 "b." } {TEXT -1 47 " the function determined by such an operation. " } {TEXT 39 3 "2. " } {TEXT -1 2 "a " } {HYPERLNK 45 "mapping" 5 "Definition/mapping" "" }{TEXT -1 12 ", such as a " } {HYPERLNK 45 "linear operator" 5 "Definition/linearoperator" "" }{TEXT -1 2 ". " } } } 4{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 8 "operate," } } {PARA 0 "> " 0 "" {TEXT 22 3 "vb." } {TEXT -1 10 " to be an " } {HYPERLNK 45 "operation" 5 "Definition/operation" "" }{TEXT -1 140 " upon, to take as an argument. For example, negation and complementation operate respectively upon disjunctions and set unions according to " } {HYPERLNK 45 "de Morgan's laws" 5 "Definition/deMorganslaws" "" }{TEXT -1 2 ". " } } } MathDictionary,OpenDisk+open disk definitionMathDictionary,OpenIntervalopen interval definitionMathDictionary,OpenMappingV3open mapping definition!MathDictionary,OpenMappingTheorem"open mapping theorem definitionMathDictionary,OpenSentenceopen sentence definitionMathDictionary,OpenSetTopen set definitionMathDictionary,OpenTheory open theory definitionMathDictionary,Open_Ball#open ball definitionMathDictionary,Open_Cover open cover definitionMathDictionary,Open_Covering open cover definitiondictionary,OpenSentenceopen sentence definitiondictionary,OpenSetTopen set definitiondictionary,OpenTheory open theory definitiondictionary,Open_Ball#open ball definitiondictionary,Open_Cover open cover definitiondictionary,Open_Covering open cover definitiondictionary,Open_Disk+open disk definitiondictionary,Open_Intervalopen interval definitiondictionary,Open_MappingV3open mapping definitiondictionary,Open_Mapping_Theorem"open mapping theorem definitiondictionary,Open_Sentenceopen sentence definitiondictionary,Open_SetTopen set definitiondictionary,Open_Theory open theory definitiondictionary,Open_ball#open ball definitiondictionary,Openintervalopen interval definitiondictionary,OpenmappingV3open mapping definitiondictionary,Openmappingtheorem"open mapping theorem definitiondictionary,Opensentenceopen sentence definitiondictionary,OpensetTopen set definitiondictionary,Opentheory open theory definitiondictionary,Operand$operand definitiondictionary,Operateoperate definitiondictionary,Operationjoperation definitiondictionary,OperatorCoperator definitionMathdictionary,OpenmappingV3open mapping definition!Mathdictionary,Openmappingtheorem"open mapping theorem definitionMathdictionary,Opensentenceopen sentence definitionMathdictionary,OpensetTopen set definitionMathdictionary,Opentheory open theory definitionMathdictionary,Operand$operand definitionMathdictionary,Operateoperate definitionMathdictionary,Operationjoperation definitionMathdictionary,OperatorCoperator definition}dictionary,Normalformcdictionary,Normaloperatordictionary,NormedVectorRingֆdictionary,Normedvectorring*dictionary,Nowhere_differentiable_functiondictionary,Np-Hard_Problem%dictionary,NpDecisionProblem<+dictionary,Nspacedictionary,Null_Hypothesis;dictionary,NullgraphPdictionary,Number_Fielddictionary,Numerablewdictionary,NumericalQuantifier$dictionary,Numerical_analysis݇dictionary,Numericalquadrature% Orthogonal_Complement,dictionary=$Orthogonal_Complement,mathdictionary=Orthogonal_Functions,Definition Orthogonal_Functions,Dictionary #Orthogonal_Functions,MathDictionary #Orthogonal_Functions,Mathdictionary Orthogonal_Functions,definition Orthogonal_Functions,dictionary #Orthogonal_Functions,mathdictionary Orthogonal_Group,DefinitionOrthogonal_Group,DictionaryOrthogonal_Group,MathDictionary~^dictionary,Indirect_proportion`dictionary,Initial_segmenta'dictionary,Integro-differentialequationlcdictionary,Intervalestimatee%dictionary,Jackson_Bernstein_Theorems!g$dictionary,KakutaniFixedPointTheoremh!dictionary,KolmogorovSmirnoffTestidictionary,LagrangesEquationsk*dictionary,LebesgueDecompositionOfAMeasuretm"dictionary,Lemniscate_Of_Bernoulliodictionary,LinearEquationCqdictionary,Lipschitz_conditionJpdictionary,Logistic_Spiralt>>Definition,resolventdefinition,resolventDefinition,Resolventdefinition,ResolventDictionary,resolventdictionary,resolventDictionary,Resolventdictionary,ResolventMathDictionary,resolventMathdictionary,resolventmathdictionary,resolventMathDictionary,ResolventMathdictionary,Resolventmathdictionary,Resolvent;.Mathdictionary,Nowhere_Differentiable_Function"Mathdictionary,Np-complete_problem"Mathdictionary,Np_Decision_ProblemMathdictionary,NspaceRMathdictionary,Null_Hypothesis=Mathdictionary,Null_setMathdictionary,NullspaceMathdictionary,Numerableއ"Mathdictionary,NumericalQuantifier'!Mathdictionary,Numerical_analysis Mathdictionary,Numericalidentity Mathdictionary,Oandonotation?!Mathdictionary,Objective_functionGMathdictionary,ObliqueAngle'OrdinaryDifferentialEquation,definitionݾ'OrdinaryDifferentialEquation,dictionaryݾ+OrdinaryDifferentialEquation,mathdictionaryݾOrdinaryPoint,Definition,OrdinaryPoint,Dictionary,OrdinaryPoint,MathDictionary,OrdinaryPoint,Mathdictionary,OrdinaryPoint,definition,OrdinaryPoint,dictionary,OrdinaryPoint,mathdictionary,!OrdinaryRepresentation,Definition!OrdinaryRepresentation,Dictionary%OrdinaryRepresentation,MathDictionary%OrdinaryRepresentation,Mathdictionary!OrdinaryRepresentation,definition!OrdinaryRepresentation,dictionary%OrdinaryRepresentation,mathdictionary)Ordinary_Differential_Equation,Definitionݾ)Ordinary_Differential_Equation,Dictionaryݾ-Ordinary_Differential_Equation,MathDictionaryݾ-Ordinary_Differential_Equation,Mathdictionaryݾ)Ordinary_Differential_Equation,definitionݾ!mathdictionary,Normed_vector_ring׆ mathdictionary,Nowhere_Dense_Set"mathdictionary,Np-Complete_Problem! mathdictionary,NpCompleteProblemmathdictionary,Np_hard_problemmathdictionary,NullHypothesisSmathdictionary,Null_measuremathdictionary,Nullsequencemathdictionary,Number_Linemathdictionary,Numeral9!mathdictionary,Numerical_Identity#mathdictionary,Numerical_quadrature"mathdictionary,NumericalquantifierSmathdictionary,Object_Language7Orientable,definition/Orientable,dictionary/Orientable,mathdictionary/Orientation,Definition:Orientation,Dictionary:Orientation,MathDictionary:Orientation,Mathdictionary:Orientation,definition:Orientation,dictionary:Orientation,mathdictionary:Origin,DefinitionOrigin,DictionaryOrigin,MathDictionaryOrigin,MathdictionaryOrigin,definitionOrigin,dictionary"Multiplicative_Identity,Dictionary~MuntzTheorem,dictionaryNano-,mathdictionary NaturalDeduction,dictionaryUNaturalbase,MathdictionaryNecker_cube,Mathdictionary#Negativesemidefinite,MathdictionaryF)Neumann-typeboundaryconditions,Dictionary"NewtonCotesFormulae,mathdictionaryCNewtonsIdentities,dictionaryNilpotentgroup,definition/Non-,DefinitionDNon-emptyword,dictionaryENon_Elementary,DictionaryЄNon_negative,DictionaryՅL O{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 17 "Penrose triangle," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 287 " a figure that appears to represent a three-dimensional triangular solid, but which is in fact impossible to construct. It is impossible to consistently shade the Penrose triangle, as in fact each vertex is a perspective drawing of a right angle. (Named after the British mathematician, " } {TEXT 22 13 "Roger Penrose" } {TEXT -1 51 ", and his geneticist father, who also designed the " } {HYPERLNK 45 "Penrose impossible staircase" 5 "Definition/Penroseimpossiblestaircase" "" }{TEXT -1 11 ") See also " } {HYPERLNK 45 "Necker cube" 5 "Definition/Neckercube" "" }{TEXT -1 2 ". " } } } Open_ball,definition#Open_ball,dictionary#Open_ball,mathdictionary#Open_cover,Definition Open_cover,Dictionary Open_cover,MathDictionary Open_cover,Mathdictionary Open_cover,definition Open_cover,dictionary Open_cover,mathdictionary Open_covering,Definition Open_covering,Dictionary Open_covering,MathDictionary Open_covering,Mathdictionary Open_covering,definition opencoveringDefinition,open_coveringdefinition,open_coveringDefinition,OpenCoveringdefinition,OpenCoveringDefinition,Open_Coveringdefinition,Open_CoveringDefinition,Opencoveringdefinition,OpencoveringDefinition,Open_coveringdefinition,Open_coveringDictionary,opencoveringdictionary,opencoveringDictionary,open_coveringdictionary,open_coveringDictionary,OpenCoveringdictionary,OpenCoveringDictionary,Open_Coveringdictionary,Open_CoveringDictionary,Opencoveringdictionary,OpencoveringDictionary,Open_coveringdictionary,Open_coveringMathDictionary,opencoveringMathdictionary,opencoveringmathdictionary,opencoveringMathDictionary,open_coveringMathdictionary,open_coveringmathdictionary,open_coveringMathDictionary,OpenCoveringMathdictionary,OpenCoveringmathdictionary,OpenCoveringMathDictionary,Open_CoveringMathdictionary,Open_Coveringmathdictionary,Open_CoveringMathDictionary,OpencoveringMathdictionary,Opencoveringmathdictionary,OpencoveringMathDictionary,Open_coveringMathdictionaˉry,Open_coveringmathdictionary,Open_coveringon,open_coveringDefinition,OpenCoveringdefinition,OpenCoveringDefinition,Open_Coveringdefinition,Open_CoveringDefinition,Opencoveringdefinition,OpencoveringDefinition,Open_coveringdefinition,Open_coveringDictionary,opencoveringdictionary,opencoveringDictionary,open_coveringdictionary,open_coveringDictionary,OpenCoveringdictionary,OpenCoveringDictionary,Open_Coveringdictionary,Open_CoveringDictionary,Opencoveringdictionary,OpencoveringDictionary,Open_coveringdictionary,Open_coveringMathDictionary,opencoveringMathdictionary,opencoveringmathdictionary,opencoveringMathDictionary,open_coveringMathdictionary,open_coveringmathdictionary,open_coveringMathDictionary,OpenCoveringMathdictionary,OpenCoveringmathdictionary,OpenCoveringMathDictionary,Open_CoveringMathdictionary,Open_Coveringmathdictionary,Open_CoveringMathDictionary,OpencoveringMathdictionary,Opencoveringmathdictionary,OpencoveringMathDictionary,Open_coveringMathdictionaˉ+{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 9 "triaxial," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 20 " having three axes. " } } } +{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 10 "open disk," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 4 " an " } {HYPERLNK 45 "open ball" 5 "Definition/openball" "" }{TEXT -1 20 ", especially in the " } {HYPERLNK 45 "Cartesian plane" 5 "Definition/Cartesianplane" "" }{TEXT -1 2 ", " } {TEXT 39 1 "R" } {TEXT -1 4 "^2. " } } } eDefinition,Z^+Definition,zdefinition,zDefinition,Zdefinition,ZDictionary,zdictionary,zDictionary,Zdictionary,ZMathDictionary,zMathdictionary,zmathdictionary,zMathDictionary,ZMathdictionary,Zmathdictionary,ZDefinition,z^definition,z^Definition,Z^definition,Z^Dictionary,z^dictionary,z^Dictionary,Z^dictionary,Z^MathDictionary,z^Mathdictionary,z^mathdictionary,z^MathDictionary,Z^Mathdictionary,Z^mathdictionary,Z^+9Definition,uniformconvexityuniform convexity definition+CDefinition,differentialstructuredifferential structure definition+-Definition,orderidealorder ideal definition+NDefinition,uniquefactorizationtheoremunique factorization theorem definition+$Definition,borrowborrow definition,9Definition,transferfunctiontransfer function definition#,4Definition,ClairautsformClairaut's form definitionJ,7Definition,additionformulaaddition formula definitionK,7Definition,myopicalgorithmmyopic algorithm definitionZ,$Definition,medianmedian definition`,(Definition,trilemmatrilemma 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definitionmathdictionary,Operateoperate definitionmathdictionary,Operationjoperation definitionmathdictionary,OperatorCoperator definitionMathDictionary,Opencovering open cover definitionMathDictionary,Opendisk+open disk definitionMathDictionary,Openintervalopen interval definitionMathDictionary,OpenmappingV3open mapping definition!MathDictionary,Openmappingtheorem"open mapping theorem definitionMathDictionary,Opensentenceopen sentence definitionMathDictionary,OpensetTopen set definitionMathDictionary,Opentheory open theory definitionMathDictionary,Operand$operand definitionDefinition,rateofchange rate of change definitionDefinition,rateofconvergence![rate of convergence definitionDefinition,ratioratio definitionDefinition,ratio_of_similitude!Vratio of similitude definitionDefinition,ratio_scale!ratio scale definitionDefinition,ratio_testWratio test definitionDefinition,ratio_theorem8 Xratio theorem definitionsection formula definitionDefinition,rational3.+rational number 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definitionsynthetic geometry definitionMathdictionary,pseudometric pseudo-metric definitionMathdictionary,pseudoprimeeypseudo-prime definitionMathdictionary,pseudorandom4pseudo-random definitionMathdictionary,pseudosphere:pseudo-sphere definitionMathdictionary,psi_function8؈digamma function definitionpsi function definitionMathdictionary,psifunction8؈digamma function definitionpsi function definitionMathdictionary,psubgrouplp-subgroup definitionMathdictionary,punctual$punctual definitionMathdictionary,Quotient_space6a^quotient space definitionfactor space definition Mathdictionary,Quotient_topologyquotient topology definitionMathdictionary,Quotientgroup6Kquotient group definition\factor group definitionMathdictionary,Quotientring4*factor ring definitionquotient ring definitionMathdictionary,Quotientrule-quotient rule definitionMathdictionary,Quotientspace6a^quotient space definitionfactor space definitionMathdictionary,Quotienttopologyquotient topology definitionPsifunction,definition؈Psifunction,dictionary؈Psifunction,mathdictionary؈Psubgroup,DefinitionlPsubgroup,DictionarylPsubgroup,MathDictionarylPsubgroup,MathdictionarylPsubgroup,definitionlPsubgroup,dictionarylPsubgroup,mathdictionarylPunctual,Definition$Punctual,Dictionary$Punctual,MathDictionary$Punctual,Mathdictionary$Punctual,definition$Punctual,dictionary$$MathDictionary,PropositionalFunction?propositional function definitionopen sentence definition%MathDictionary,Propositional_CalculusEGpropositional calculus definition~sentential calculus definition%MathDictionary,Propositional_Function?propositional function definitionopen sentence definition%MathDictionary,Propositional_calculusEGpropositional calculus definition~sentential calculus definition%MathDictionary,Propositional_function?propositional function definitionopen sentence definition$MathDictionary,PropositionalcalculusEGpropositional calculus definition~sentential calculus definitionProjectiveplane,dictionaryProjectiveplane,mathdictionary#Projectivetransformation,Definition#Projectivetransformation,Dictionary'Projectivetransformation,MathDictionary'Projectivetransformation,Mathdictionary#Projectivetransformation,definition#Projectivetransformation,dictionary'Projectivetransformation,mathdictionaryProjectivity,DefinitionProjectivity,DictionaryProjectivity,MathDictionaryorbitstabilizertheorem7Open_Sentence,DefinitionOpen_Sentence,DictionaryOpen_Sentence,MathDictionaryOpen_Sentence,MathdictionaryOpen_Sentence,definitionOpen_Sentence,dictionaryOpen_Sentence,mathdictionaryOpen_Set,DefinitionTOpen_Set,DictionaryTOpen_Set,MathDictionaryTOpen_Set,MathdictionaryTOpen_Set,definitionTOpen_Set,dictionaryTOpen_Set,mathdictionaryTOpen_Theory,Definition Open_Theory,Dictionary Open_Theory,MathDictionary Open_Theory,Mathdictionary Open_Theory,definition Open_Theory,dictionary Open_Theory,mathdictionary Open_ball,Definition#Open_ball,Dictionary#Open_ball,MathDictionary#Open_ball,Mathdictionary##Open_mapping_theorem,mathdictionaryOpen_sentence,DefinitionOpen_sentence,DictionaryOpen_sentence,MathDictionaryOpen_sentence,MathdictionaryOpen_sentence,definitionOpen_sentence,dictionaryOpen_sentence,mathdictionaryOpen_set,DefinitionTOpen_set,DictionaryTOpen_set,MathDictionaryTOpen_set,MathdictionaryTOpen_set,definitionTOpen_set,dictionaryTOpen_set,mathdictionaryTOpen_theory,Definition Open_theory,Dictionary Open_theory,MathDictionary Open_theory,Mathdictionary Open_theory,definition Open_theory,dictionary Open_theory,mathdictionary Openball,Definition#Openball,Dictionary#"Definition,operatedefinition,operateDefinition,Operatedefinition,OperateDictionary,operatedictionary,operateDictionary,Operatedictionary,OperateMathDictionary,operateMathdictionary,operatemathdictionary,operateMathDictionary,OperateMathdictionary,Operatemathdictionary,Operate {VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 12 "open theory," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 2 " (" } {TEXT 22 5 "Logic" } {TEXT -1 4 ") a " } {HYPERLNK 45 "theory" 5 "Definition/theory" "" }{TEXT -1 20 " that contains only " } {HYPERLNK 45 "open sentences" 5 "Definition/opensentence" "" }{TEXT -1 1 "." } } } Dictionary,PrisonersDilemma _prisoner's dilemma definitionDictionary,Prisoners_Dilemma _prisoner's dilemma definitionDictionary,Prisoners_dilemma _prisoner's dilemma definitionDictionary,Prisonersdilemma _prisoner's dilemma definitionDictionary,Probability*probability definition%Dictionary,ProbabilityDensityFunction*probability density function definition*Dictionary,ProbabilityDistributionFunction/probability distribution function definitionDictionary,ProbabilityFunctionQD)probability function definitionprobability distribution function definitionOperatorNorm,DefinitionTOperatorNorm,DictionaryTOperatorNorm,MathDictionaryTOperatorNorm,MathdictionaryTOperatorNorm,definitionTOperatorNorm,dictionaryTOperatorNorm,mathdictionaryTOperator_Norm,DefinitionTOperator_Norm,DictionaryTOperator_Norm,MathDictionaryTOperator_Norm,MathdictionaryTOperator_Norm,definitionTOperator_Norm,dictionaryTOperator_Norm,mathdictionaryTOperator_norm,DefinitionTT@{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 14 "operator norm," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 5 " the " } {HYPERLNK 45 "norm" 5 "Definition/norm" "" }{TEXT -1 42 " placed on the vector space of continuous " } {HYPERLNK 45 "linear operators" 5 "Definition/linearoperator" "" }{TEXT -1 60 ", B[X, Y], between two normed spaces X and Y by the formula " } } {PARA 0 "> " 0 "" {TEXT -1 14 "||T||=sup{||T(" } {TEXT 22 1 "x" } {TEXT -1 8 ")|| : ||" } {TEXT 22 1 "x" } {TEXT -1 10 "|| <= 1}. " } } {PARA 0 "> " 0 "" {TEXT -1 54 "With this norm B[X, Y] becomes a normed space that is " } {HYPERLNK 45 "complete" 5 "Definition/complete" "" }{TEXT -1 21 " precisely when Y is." } } } definition,optimal_control90control theory definitionFoptimal control definition#definition,optimalassignmentproblem(optimal assignment problem definitiondefinition,optimalcontrol90control theory definitionFoptimal control definitiondefinition,optimizationoptimization definitiondefinition,optimization_theory!ϻoptimization theory definitiondefinition,optimizationtheory!ϻoptimization theory definitiondefinition,optimizeRoptimize definitiondefinition,optimumoptimum definitiondefinition,paretoefficientpoint"rPareto optimal point definitiondefinition,paretooptimalpoint? " 0 "" {TEXT -1 24 "ordinary representation," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 3 " a " } {HYPERLNK 45 "representation" 5 "Definition/representation" "" }{TEXT -1 27 " over the complex numbers. " } } } Definition,Open_Disk+open disk definitionDefinition,Open_Intervalopen interval definitionDefinition,Open_MappingV3open mapping definitionDefinition,Open_Mapping_Theorem"open mapping theorem definitionDefinition,Open_Sentenceopen sentence definitionDefinition,Open_SetTopen set definitionDefinition,Open_Theory open theory definitionDefinition,Open_ball#open ball definitionDefinition,Open_cover open cover definitionon,Open_Covering open cover definitiondefinition,Opencovering open cover definitiondefinition,Opendisk+open disk definitiondefinition,Openintervalopen interval definitiondefinition,OpenmappingV3open mapping definitiondefinition,Openmappingtheorem"open mapping theorem definitiondefinition,Opensentenceopen sentence definitiondefinition,OpensetTopen set definitiondefinition,Opentheory open theory definitiondefinition,Operand$operand definitiondefinition,Operateoperate definitionOperator_norm,DictionaryTOperator_norm,MathDictionaryTOperator_norm,MathdictionaryTOperator_norm,definitionTOperator_norm,dictionaryTOperator_norm,mathdictionaryTOperatornorm,DefinitionTOperatornorm,DictionaryTOperatornorm,MathDictionaryTOperatornorm,MathdictionaryTOperatornorm,definitionTOperatornorm,dictionaryTOperatornorm,mathdictionaryTOphelmal,DefinitionOphelmal,DictionaryOpenSentence,mathdictionaryOpenSet,DefinitionTOpenSet,DictionaryTOpenSet,MathDictionaryTOpenSet,MathdictionaryTOpenSet,definitionTOpenSet,dictionaryTOpenSet,mathdictionaryTOpenTheory,Definition OpenTheory,Dictionary OpenTheory,MathDictionary OpenTheory,Mathdictionary OpenTheory,definition OpenTheory,dictionary OpenTheory,mathdictionary Open_Ball,Definition#Open_Ball,Dictionary#Open_Ball,MathDictionary#Open_Ball,Mathdictionary#Open_Ball,definition#Open_Ball,dictionary#theoryDefinition,opentheorydefinition,opentheoryDefinition,open_theorydefinition,open_theoryDefinition,OpenTheorydefinition,OpenTheoryDefinition,Open_Theorydefinition,Open_TheoryDefinition,Opentheorydefinition,OpentheoryDefinition,Open_theorydefinition,Open_theoryDictionary,opentheorydictionary,opentheoryDictionary,open_theorydictionary,open_theoryDictionary,OpenTheorydictionary,OpenTheoryDictionary,Open_Theorydictionary,Open_TheoryDictionary,Opentheorydictionary,OpentheoryDictionary,Open_theorydictionary,Open_theoryMathDictionary,opentheoryMathdictionary,opentheorymathdictionary,opentheoryMathDictionary,open_theoryMathdictionary,open_theorymathdictionary,open_theoryMathDictionary,OpenTheoryMathdictionary,OpenTheorymathdictionary,OpenTheoryMathDictionary,Open_TheoryMathdictionary,Open_Theorymathdictionary,Open_TheoryMathDictionary,OpentheoryMathdictionary,Opentheorymathdictionary,OpentheoryMathDictionary,Open_theoryMathdictionary,Open_theorymathdictionary,Open_Z$wx,TOf3j!7, s8 **3 j Gd hE Y  0 Ia d 1 r     5   9   ׂ8 lA E HO TZ 7` ( i Cl  [ ٪ H ־ e  K ܐ `B  84 J tnP z Q _T 9h q lt   |2  K   WK % ;  X "  e  g ݹ I J I! 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A real matrix is orthogonal if and only if its columns (rows) form an " } {HYPERLNK 45 "orthonormal" 5 "Definition/orthonormal" "" }{TEXT -1 173 " set using the Euclidean inner product. The complex matrix Matrix([,]) is orthogonal, but its columns (rows) do not form an orthonormal set. Compare " } {HYPERLNK 45 "unitary matrix" 5 "Definition/unitarymatrix" "" }{TEXT -1 2 ". " } } } mathdictionary,ordinalnumber)ordinal number definitionmathdictionary,ordinalscalelordinal scale definition-mathdictionary,ordinary_differential_equation,ݾordinary differential equation definitionmathdictionary,ordinary_point,ordinary point definition&mathdictionary,ordinary_representation%ordinary representation definition+mathdictionary,ordinarydifferentialequation,ݾordinary differential equation definitionmathdictionary,ordinarypoint,ordinary point definition MathDictionary,Nowhere_Dense_Set"MathDictionary,Np-Complete_Problem!MathDictionary,Np-decisionproblem&"MathDictionary,Np_Decision_ProblemMathDictionary,NspaceMathDictionary,Null_Measure{MathDictionary,Null_spaceMathDictionary,NullvectorMathDictionary,Number_lineMathDictionary,Numerical!MathDictionary,Numerical_Identity$MathDictionary,NumericaleccentricityMathDictionary,Oandonotation{ MathDictionary,Objectivefunction|Orthogonal_matrix,Definition,Orthogonal_matrix,Dictionary, Orthogonal_matrix,MathDictionary, Orthogonal_matrix,Mathdictionary,Orthogonal_matrix,definition,Orthogonal_matrix,dictionary, Orthogonal_matrix,mathdictionary, Orthogonal_projection,Definition Orthogonal_projection,Dictionary$Orthogonal_projection,MathDictionary$Orthogonal_projection,Mathdictionary Orthogonal_projection,definition Orthogonal_projection,dictionaryG ȉL O\ %#d iTe RDq Ȑt 0{w ,z K{ c| !  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" } } } Open_interval,mathdictionaryOpen_mapping,DefinitionV3Open_mapping,DictionaryV3Open_mapping,MathDictionaryV3Open_mapping,MathdictionaryV3Open_mapping,definitionV3Open_mapping,dictionaryV3Open_mapping,mathdictionaryV3Open_mapping_theorem,DefinitionOpen_mapping_theorem,Dictionary#Open_mapping_theorem,MathDictionary#Open_mapping_theorem,MathdictionaryOpen_mapping_theorem,definitionOpen_mapping_theorem,dictionaryopenmapping,DefinitionV3openmapping,DictionaryV3openmapping,MathDictionaryV3openmapping,MathdictionaryV3openmapping,definitionV3openmapping,dictionaryV3openmapping,mathdictionaryV3openmappingtheorem,Definitionopenmappingtheorem,Dictionary!openmappingtheorem,MathDictionary!openmappingtheorem,Mathdictionaryopenmappingtheorem,definitionopenmappingtheorem,dictionary!openmappingtheorem,mathdictionaryT{Definition,opensetdefinition,opensetDefinition,open_setdefinition,open_setDefinition,OpenSetdefinition,OpenSetDefinition,Open_Setdefinition,Open_SetDefinition,Opensetdefinition,OpensetDefinition,Open_setdefinition,Open_setDictionary,opensetdictionary,opensetDictionary,open_setdictionary,open_setDictionary,OpenSetdictionary,OpenSetDictionary,Open_Setdictionary,Open_SetDictionary,Opensetdictionary,OpensetDictionary,Open_setdictionary,Open_setMathDictionary,opensetMathdictionary,opensetmathdictionary,opensetMathDictionary,open_setMathdictionary,open_setmathdictionary,open_setMathDictionary,OpenSetMathdictionary,OpenSetmathdictionary,OpenSetMathDictionary,Open_SetMathdictionary,Open_Setmathdictionary,Open_SetMathDictionary,OpensetMathdictionary,Opensetmathdictionary,OpensetMathDictionary,Open_setMathdictionary,Open_setmathdictionary,Open_setȈogdoad,Definition2oh_notation,Mathdictionary omega,mathdictionary omegainconsistency,dictionaryone-one,mathdictionary(one-pointcompactification,Mathdictionaryone_many,definitionW%one_point_compactification,definition2onemany,MathDictionaryX'onepointcompactification,MathdictionaryVonetailed,definitiononlyif,Definitiononto,Mathdictionaryopacity,mathdictionaryopen_ball,Mathdictionaryopen_covering,definitionionary,Order_Preservingmathdictionary,Order_PreservingMathDictionary,OrderpreservingMathdictionary,Orderpreservingmathdictionary,OrderpreservingMathDictionary,Order_preservingMathdictionary,Order_preservingmathdictionary,Order_preservingdefinition,order-preservingDefinition,Order-Preservingdefinition,Order-PreservingDictionary,order-preservingdictionary,order-preservingDictionary,Order-Preservingdictionary,Order-PreservingMathDictionary,order-preservingMathdictionary,order-preservingmathdictionary,order-preservingMathDictionary,Order-PreservingMathdictionary,Order-Preservingmathdictionary,Order-PreservingeservingDictionary,Order_preservingdictionary,Order_preservingMathDictionary,orderpreservingMathdictionary,orderpreservingmathdictionary,orderpreservingMathDictionary,order_preservingMathdictionary,order_preservingmathdictionary,order_preservingMathDictionary,OrderPreservingMathdictionary,OrderPreservingmathdictionary,OrderPreservingMathDictionary,Order_PreservingMathdict^Definition,openmappingtheoremdefinition,openmappingtheoremDefinition,open_mapping_theoremdefinition,open_mapping_theoremDefinition,OpenMappingTheoremdefinition,OpenMappingTheoremDefinition,Open_Mapping_Theoremdefinition,Open_Mapping_TheoremDefinition,Openmappingtheoremdefinition,OpenmappingtheoremDefinition,Open_mapping_theoremdefinition,Open_mapping_theoremDictionary,openmappingtheoremdictionary,openmappingtheoremDictionary,open_mapping_theoremdictionary,open_mapping_theoremDictionary,OpenMappingTheoremdictionary,OpenMappingTheoremDictionary,Open_Mapping_Theoremdictionary,Open_Mapping_TheoremDictionary,Openmappingtheoremdictionary,OpenmappingtheoremDictionary,Open_mapping_theoremdictionary,Open_mapping_theoremMathDictionary,openmappingtheoremMathdictionary,openmappingtheoremmathdictionary,openmappingtheoremMathDictionary,open_mapping_theoremMathdictionary,open_mapping_theoremmathdictionary,open_mapping_theoremMathDictionary,OpenMappingTheoremMathdictionary,OpenMappingTheoremmathdictionary,OpenMappingTheoremMathDictionary,Open_Mapping_TheoremMathdictionary,Open_Mapping_Theoremmathdictionary,Open_Mapping_TheoremMathDictionary,OpenmappingtheoremMathdictionary,Openmappingtheoremmathdictionary,OpenmappingtheoremMathDictionary,Open_mapping_theoremMathdictionary,Open_mapping_theoremmathdictionary,Open_mapping_theoremn_mapping_theoremDictionary,openmappingtheoremdictionary,openmappingtheoremDictionary,open_mapping_theoremdictionary,open_mapping_theoremDictionary,OpenMappingTheoremdictionary,OpenMappingTheoremDictionary,Open_Mapping_Theoremdictionary,Open_Mapping_TheoremDictionary,Openmappingtheoremdictionary,OpenmappingtheoremDictionary,Open_mapping_theore