Definition,initialcondition = Definition,initialize < Definition,initialline ; Definition,initialsegment : Definition,initialvalueproblem 9 Definition,injection 8 Definition,injective 7 Definition,inn Definition,innerJordanmeasure 6 Definition,inner_automorphism 5 Definition,inner_jordan_content 6 Definition,inner_jordan_measure 6 Definition,inner_measure 4 Definition,inner_product 3 Definition,inner_product_space 2 ( Mathdictionary,Inhomogeneous_Coordinates > ( Mathdictionary,Inhomogeneous_coordinates > ' Mathdictionary,Inhomogeneouscoordinates > Mathdictionary,Inith Mathdictionary,InitialCondition = Mathdictionary,InitialLine ; Mathdictionary,InitialSegment : Mathdictionary,Initial_Condition = Mathdictionary,Initial_Line ; Mathdictionary,Initial_Segment : Mathdictionary,Initial_condition = Mathdictionary,Initial_line ; ates > ( MathDictionary,Inhomogeneous_Coordinates > ( MathDictionary,Inhomogeneous_coordinates > ' MathDictionary,Inhomogeneouscoordinates > MathDictionary,Inith MathDictionary,InitialCondition = MathDictionary,InitialLine ; MathDictionary,InitialSegment : MathDictionary,Initial_Condition = MathDictionary,Initial_Line ; MathDictionary,Initial_Segment : MathDictionary,Initial_condition = MathDictionary,Initial_line ; ates > dictionary,InherentRound-Off @ dictionary,InherentRoundOff @ dictionary,Inherent_Round-Off @ dictionary,Inherent_Round_Off @ dictionary,Inherent_round-off @ dictionary,Inherent_round_off @ dictionary,Inherentround-off @ dictionary,Inherentroundoff @ dictionary,Inhomogeneous ? # dictionary,InhomogeneousCoordinates > $ dictionary,Inhomogeneous_Coordinates > $ dictionary,Inhomogeneous_coordinates > # dictionary,Inhomogeneouscoordinates > definition,InherentRound-Off @ definition,InherentRoundOff @ definition,Inherent_Round-Off @ definition,Inherent_Round_Off @ definition,Inherent_round-off @ definition,Inherent_round_off @ definition,Inherentround-off @ definition,Inherentroundoff @ definition,Inhomogeneous ? # definition,InhomogeneousCoordinates > $ definition,Inhomogeneous_Coordinates > $ definition,Inhomogeneous_coordinates > # definition,Inhomogeneouscoordinates > ! Information_Theory,Mathdictionary A Information_Theory,definition A Information_Theory,dictionary A ! Information_Theory,mathdictionary A Information_theory,Definition A Information_theory,Dictionary A ! Information_theory,MathDictionary A ! Information_theory,Mathdictionary A Information_theory,definition A Information_theory,dictionary A ! Information_theory,mathdictionary A Informationtheory,Definition A Informationtheory,Dictionary A Informationtheory,MathDictionary A Informationtheory,Mathdictionary A Informationtheory,definition A Informationtheory,dictionary A Informationtheory,mathdictionary A InherentRound-Off,Definition @ InherentRound-Off,Dictionary @ InherentRound-Off,MathDictionary @ InherentRound-Off,Mathdictionary @ ! information_theory,MathDictionary A ! information_theory,Mathdictionary A information_theory,definition A information_theory,dictionary A ! information_theory,mathdictionary A informationtheory,Definition A informationtheory,Dictionary A informationtheory,MathDictionary A informationtheory,Mathdictionary A informationtheory,definition A informationtheory,dictionary A informationtheory,mathdictionary A inherent_round-off,Definition @ inherent_round-off,Dictionary @ ! inherent_round-off,MathDictionary @ theory definition,Informationtheory Definition,Informationtheory definition,Information_Theory Definition,Information_Theory definition,InformationTheory Definition,InformationTheory definition,information_theory Definition,information_theory definition,informationtheory Definition,informationtheory tion_Theory mathdictionary,InformationTheory Mathdictionary,InformationTheory MathDictionary,InformationTheory mathdictionary,information_theory Mathdictionary,information_theory MathDictionary,information_theory mathdictionary,informationtheory Mathdictionary,informationtheory MathDictionary,informationtheory dictionary,Information_theory Dictionary,Information_theory dictionary,Informationtheory Dictionary,Informationtheory dictionary,Information_Theory Dictionary,Information_Theory dictionary,InformationTheory Dictionary,InformationTheory dictionary,information_theory Dictionary,information_theory dictionary,informationtheory Dictionary,informationtheory definition,Information_theory Definition,Information_` I
infinite series,
n. the sum of an infinite sequence of terms, usually indexed by, or expressed as a function on, the natural numbers, and often written in the form NiMtSSRzdW1HNiI2JCZJImFHRiU2I0kiaUdGJS9GKjsiIiFJKWluZmluaXR5RyUqcHJvdGVjdGVkRw==, or, more briefly, information theory. 2. also called uncertainty. formally, a real-valued function of events in a probability space that depends only on the probability of events, and is such that events of probability one have zero uncertainty, that uncertainty increases as probability drops, and that the uncertainty of the simultaneous occurrence of two independent events is the sum of their individual uncertainties. The only measurable functions meeting these requirements are of the form
I(E) = -c log(P(E))
for positive constants c. Thus for a measurable partition x of the space, one has the corresponding information function
I(x) = -c SE\316x log(P(E))) cE,
the expected value of which is the entropy of the partition. Usually, c is chosen to yield a logarithm to base two with information measured in bits.
esponding
inflection
or inflexion, n. a change of curvature at a point from positive to negative or vice versa. See point of inflection.
inflection_point,Dictionary ? inflection_point,MathDictionary ? inflection_point,Mathdictionary ? inflection_point,definition ? inflection_point,dictionary ? inflection_point,mathdictionary ? inflectionpoint,Definition ? inflectionpoint,Dictionary ? inflectionpoint,MathDictionary ? inflectionpoint,Mathdictionary ? inflectionpoint,definition ? inflectionpoint,dictionary ? inflectionpoint,mathdictionary ? inflexion,Definition C inflexion,Dictionary C inflexion,MathDictionary C inflexion,Mathdictionary C inflexion,definition C inflexion,dictionary C inflexion,mathdictionary C information,Definition B information,Dictionary B information,MathDictionary B information,Mathdictionary B information,definition B information,dictionary B information,mathdictionary B information_theory,Definition A information_theory,Dictionary A dictionary ? inflexion,Dictionary C InflectionPoint,dictionary ? InflectionPoint,mathdictionary ? Inflection_Point,Definition ? Inflection_Point,Dictionary ? Inflection_Point,MathDictionary ? Inflection_Point,Mathdictionary ? Inflection_Point,definition ? Inflection_Point,dictionary ? Inflection_Point,mathdictionary ? Inflection_point,Definition ? Inflection_point,Dictionary ? Inflection_point,MathDictionary ? Inflection_point,Mathdictionary ? BZ mathdictionary,Information Mathdictionary,Information MathDictionary,Information mathdictionary,information Mathdictionary,information MathDictionary,information dictionary,Information Dictionary,Information dictionary,information Dictionary,information definition,Information Definition,Information definition,information Definition,information ctionary,Inflection MathDictionary,Inflection mathdictionary,inflection Mathdictionary,inflection MathDictionary,inflection dictionary,Inflection Dictionary,Inflection dictionary,inflection Dictionary,inflection definition,Inflection Definition,Inflection definition,inflection Definition,inflection t the nodes, as in the figure below, to represent the structure of an expression, the infix representation is obtained by reading the nodes from left to right; more properly, one starts at the top and reads in order at each node its left branch, the node itself, and its right branch, enclosing the whole in brackets, and iterating where necessary. Compare Polish notation, reverse Polish notation.
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bold="true">2. a notation for binary relations in which the symbol for the relation is written between its arguments; thus x has R to y is written xRy. This is less common for most relations than prefix notation, but identity is always written infix as x = y. See also
infinity norm
The infinity-norm of a function NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USFGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GKC8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRigvJSdvcGFxdWVHRjgvJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRjgvJSljb21wb3NlZEdGOC8lKmNvbnZlcnRlZEdGOC8lK2ltc2VsZW` 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saWNHUSV0cnVlRigvJSp1bmRlcmxpbmVHRjgvJSpzdWJzY3JpcHRHRjgvJSxzdXBlcnNjcmlwdEdGOC8lK2ZvcmVncm91bmRHUShbMCwwLDBdRigvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYoLyUnb3BhcXVlR0Y4LyUrZXhlY3V0YWJsZUdGOC8lKXJlYWRvbmx5R0Y4LyUpY29tcG9zZWRHRjgvJSpjb252ZXJ0ZWRHRjgvJStpbXNlbGVjdGVkR0Y4LyUscGxhY2Vob2xkZXJHRjgvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRigvJSptYXRoY29sb3JHRkQvJS9tYXRoYmFja2dyb3VuZEdGRy8lK2ZvbnRmYW1pbHlHRjIvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YoLyUpbWF0aHNpemVHRjU3IzYjSSJ4R0Yo in NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USFGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GKC8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRigvJSdvcGFxdWVHRjgvJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRjgvJSljb21wb3NlZEdGOC8lKmNvbnZlcn` 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` kiYUdGKEkiYkdGKA==.
The infinity-norm of a vector y = 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` 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` bkZcb0Zcc0Zfc0YsLUZkbzYzUSJdRigvRmhvUShwb3N0Zml4RihGam9GXHBGXnBGYXBGZHBGZnBGaHBGW3FGXnFGYHFGYnFGZHFGZnFGaHFGanEtRi02OVEiVEYoRjBGM0Y2RjlGPEY+RkBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLyUxc3VwZXJzY3JpcHRzaGlmdEdGXnNGLDcjNiMpNyUmSSJ5R0YoNiMiIiJJJC4uLkdGKCZGZnU2I0kibkdGKEkiVEdGKA== is || y ||NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USFGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GKC8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRigvJSdvcGFxdWVHRjgvJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRjgvJSljb21wb3NlZEdGOC8lKmNvbnZlcnRlZEdGOC8lK2ltc2VsZWN0ZWRHRjgvJSxwbGFjZWhvbGRlckdGOC8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGKC8lKm1hdGhjb2xvckdGRC8lL21hdGhiYWNrZ3JvdW5kR0ZHLyUrZm9udGZhbWlseUdGMi8lLG1hdGh2YXJpYW50R1Ena` XRhbGljRigvJSltYXRoc2l6ZUdGNS1JJW1zdWJHRiU2JkYsLUYkNiMtRi02OVEpaW5maW5pdHlGKEYwRjNGNkY5RjxGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZpbkZcby8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYoLyUscGxhY2Vob2xkZXJHRjhGLDcjNiMmSSFHRig2I0kpaW5maW5pdHlHJSpwcm90ZWN0ZWRH = NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USFGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GKC8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRigvJSdvcGFxdWVHRjgvJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRjgvJSljb21wb3NlZEdGOC8lKmNvbnZlcnRlZEdGOC8lK2ltc2VsZWN0ZWRHRjgvJSxwbGFjZWhvbGRlckdGOC8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGKC8lKm1hdGhjb2xvckdGRC8lL21hdGhiYWNrZ3JvdW5kR0ZHLyUrZm9udGZhbWlseUdGMi8lLG1hdGh2YXJpYW50R1EnaXRhbGljRigvJSltYXRoc2l6ZUdGN` 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` 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. As a consequence, the infinity-norm of the NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiMtSSNtaUdGJTY5USJyRigvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJmZhbHNlRigvJSdpdGFsaWNHUSV0cnVlRigvJSp1bmRlcmxpbmVHRjgvJSpzdWJzY3JpcHRHRjgvJSxzdXBlcnNjcmlwdEdGOC8lK2ZvcmVncm91bmRHUShbMCwwLDBdRigvJS` tiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYoLyUnb3BhcXVlR0Y4LyUrZXhlY3V0YWJsZUdGOC8lKXJlYWRvbmx5R0Y4LyUpY29tcG9zZWRHRjgvJSpjb252ZXJ0ZWRHRjgvJStpbXNlbGVjdGVkR0Y4LyUscGxhY2Vob2xkZXJHRjgvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRigvJSptYXRoY29sb3JHRkQvJS9tYXRoYmFja2dyb3VuZEdGRy8lK2ZvbnRmYW1pbHlHRjIvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YoLyUpbWF0aHNpemVHRjU3IzYjSSJyR0Yo x 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` b3JHRkQvJS9tYXRoYmFja2dyb3VuZEdGRy8lK2ZvbnRmYW1pbHlHRjIvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YoLyUpbWF0aHNpemVHRjU3IzYjSSJjR0Yo matrix 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` 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inequality,
n. 1. the relationship between two numbers, quantities, etc., that holds when they are comparable but not equal, so that they are related by a
infinite hotel paradox,
n. another name for Hilbert's paradox.
- Mathematical Dictionary/I/information theory! Definition,informationtheory - Mathematical Dictionary/I/inherent round-off! Definition,inherentround-off ( Mathematical Dictionary/I/inhomogeneous Definition,inhomogeneous 4 Mathematical Dictionary/I/inhomogeneous coordinates( Definition,inhomogeneouscoordinates , Mathematical Dictionary/I/initial condition Definition,initialcondition ' Mathematical Dictionary/I/initial line Definition,initialline inition,information \256 \245). In general, this usage is to be understood in terms of the limits of sequences of values, and is defined formally in terms of epsilon-delta notation; for example, to say that the quotient of 1 by 0 is infinity is to be interpreted as asserting that 1/x increases without bound as x tends to zero, that is, that for any positive e, however small, there is an N such that 1/x > N for all | x | < e. 2. the supposed value of an undefined expression regarded as the limit of a sequence of analogous expressions, such as the point at infinity at which parallel lines are said finally to meet, or the sum of certain series that do not converge. These are put on a proper footing by the addition to the relevant theory of ideal elements or by compactification. 3. an imprecise term for an aleph, an infinite cardinal. See also ininame.
="false" linktarget="Dictionary:Definition/idealelement" style="Dictionary Hyperlink" encoding="ISO8859-1">ideal elements or by
infimum
or greatest lower bound (abbrev. inf or glb), n. the unique largest member of the set of lower bounds for some given set, equal to its minimum if the given set has a least me>a dictionary,inherent_round-off @ dictionary,inherent_round_off @ dictionary,inherentround-off @ dictionary,inherentroundoff @ dictionary,inhomogeneous ? $ dictionary,inhomogeneous_coordinates > # dictionary,inhomogeneouscoordinates > dictionary,inith dictionary,initial_condition = dictionary,initial_line ; dictionary,initial_segment : dictionary,initialcondition = dictionary,initialize < dictionary,initialline ; Y
inessential,
adj. (depending upon context) not central, not difficult, not important, or removable, etc.
mathdictionary,Infixnotation D mathdictionary,Inflection C mathdictionary,InflectionPoint ? mathdictionary,Inflection_Point ? mathdictionary,Inflection_point ? mathdictionary,Inflectionpoint ? mathdictionary,Inflexion C mathdictionary,Information B mathdictionary,InformationTheory A ! mathdictionary,Information_Theory A ! mathdictionary,Information_theory A mathdictionary,Informationtheory A mathdictionary,InherentRound-Off @ Mathdictionary,inductiveorder ` Mathdictionary,inductivestep _ Mathdictionary,inelastic ^ Mathdictionary,inequality ] Mathdictionary,inertia \ Mathdictionary,inertia_tensor Z * Mathdictionary,inertial_frame_of_reference [ ' Mathdictionary,inertialframeofreference [ Mathdictionary,inertiatensor Z Mathdictionary,inessential Y Mathdictionary,inf X Mathdictionary,infeasible W Mathdictionary,inference V % Mathdictionary,inferential_statistics U $ Mathdictionary,inferentialstatistics U Mathdictionary,inferior_limit T Mathdictionary,inferiorlimit T Mathdictionary,infimal S " Mathdictionary,infimal_convolution R inertia_tensor,Mathdictionary Z inertia_tensor,definition Z inertia_tensor,dictionary Z inertia_tensor,mathdictionary Z & inertial_frame_of_reference,Definition [ & inertial_frame_of_reference,Dictionary [ * inertial_frame_of_reference,MathDictionary [ * inertial_frame_of_reference,Mathdictionary [ & inertial_frame_of_reference,definition [ & inertial_frame_of_reference,dictionary [ * inertial_frame_of_reference,mathdictionary [ # inertialframeofreference,Definition [# inertialframeofreference,Dictionary [ dictionary,Infix_Notation D dictionary,Infix_notation D dictionary,Infixnotation D dictionary,Inflection C dictionary,InflectionPoint ? dictionary,Inflection_Point ? dictionary,Inflection_point ? dictionary,Inflectionpoint ? dictionary,Inflexion C dictionary,Information B dictionary,InformationTheory A dictionary,Information_Theory A dictionary,Information_theory A dictionary,Informationtheory A ion D Dictionary,inflexion C Dictionary,information B Dictionary,information_theory A Dictionary,informationtheory A Dictionary,inherent_round-off @ Dictionary,inherent_round_off @ Dictionary,inherentround-off @ Dictionary,inherentroundoff @ Dictionary,inhomogeneous ? $ Dictionary,inhomogeneous_coordinates > # Dictionary,inhomogeneouscoordinates > Dictionary,inith Dictionary,initial_condition = Dictionary,inflectionpoint ? Definition,Inflectionpoint ? Definition,Inflexion C Definition,Information B Definition,InformationTheory A Definition,Information_Theory A Definition,Information_theory A Definition,Informationtheory A Definition,InherentRound-Off @ Definition,InherentRoundOff @ Definition,Inherent_Round-Off @ Definition,Inherent_Round_Off @ Definition,Inherent_round-off @ Definition,Inherent_round_off @ Definition,Inherentround-off @ definition,Infix_Notation D definition,Infix_notation D definition,Infixnotation D definition,Inflection C definition,InflectionPoint ? definition,Inflection_Point ? definition,Inflection_point ? definition,Inflectionpoint ? definition,Inflexion C definition,Information B definition,InformationTheory A definition,Information_Theory A definition,Information_theory A definition,Informationtheory A ion D definition,inherent_round-off @ definition,inherent_round_off @ definition,inherentround-off @ definition,inherentroundoff @ definition,inhomogeneous ? $ definition,inhomogeneous_coordinates > # definition,inhomogeneouscoordinates > definition,inith definition,initial_condition = definition,initial_line ; definition,initial_segment : definition,initialcondition = definition,initialize < definition,initialline ; Infinity,definition F Infinity,dictionary F Infinity,mathdictionary F InfinityNorm,Definition E InfixNotation,Definition D InfixNotation,Dictionary D InfixNotation,MathDictionary D InfixNotation,Mathdictionary D InfixNotation,definition D InfixNotation,dictionary D InfixNotation,mathdictionary D Infix_Notation,Definition D Infix_Notation,Dictionary D Infix_Notation,MathDictionary D nary F Infinity,Mathdictionary F ! infinitesimal_calculus,definition G ! infinitesimal_calculus,dictionary G % infinitesimal_calculus,mathdictionary G infinitesimalcalculus,Definition G infinitesimalcalculus,Dictionary G $ infinitesimalcalculus,MathDictionary G $ infinitesimalcalculus,Mathdictionary G infinitesimalcalculus,definition G infinitesimalcalculus,dictionary G $ infinitesimalcalculus,mathdictionary G infinity,Definition F infinity,Dictionary F infinity,MathDictionary F infinity,Mathdictionary F infinity,definition F infinity,dictionary F infinity,mathdictionary F infinitynorm,Definition E infinitynorm,definition E infix_notation,Definition D infix_notation,Dictionary D infix_notation,MathDictionary D % Infinitesimal_calculus,Mathdictionary G ! Infinitesimal_calculus,definition G ! 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Definition,inscribe - ary Hyperlink" encoding="ISO8859-1">derivative was treated as a ratio of infinitesimals and an integral as a sum of products of infinitesimals. These had to be nonzero for the ratio to be well-defined and the products to be nonzero, but zero for the rate of change so derived to be instantaneous and the upper and lower sums to be equal. This paradoxical conception was later largely abandoned in favor of the epsilon-delta treatment of limits, but see hyper-real numbers. 2. in non-standard analysis, having zero standard part. See Archimedean property.
ding="ISO8859-1">epsilon-delta treatment of limits, but see
inertia tensor,
n. (Continuum mechanics) (for a set of axes) the tensor represented by the symmetric matrix the entries of whose
inelastic,
adj. (of a function) having elasticity less than unity. In economics, demand for a good is said to be inelastic if an increase in the price results in a decrease in revenue. Compare elastic.
Or
infinite,
n. 1. (of a number or quantity) not finite; having a size or absolute value that is greater than any natural number. See tend to infinity. 2. (of a set or sequence) having an unbounded number of terms; .a Definition,information% Mathematical Dictionary/I/information Definition,informationtheory, Mathematical Dictionary/I/information theory Definition,inherentround-off, Mathematical Dictionary/I/inherent round-off Definition,inhomogeneous' Mathematical Dictionary/I/inhomogeneous# Definition,inhomogeneouscoordinates3 Mathematical Dictionary/I/inhomogeneous coordinates Definition,initialcondition+ Mathematical Dictionary/I/initial condition l Dictionary/I/infix notation Definition,inflection$ Mathematical Dictionary/I/inflection ">Si ai. If the sequence of partial sums tends to a limit as the number of terms increases, the series is said to converge; for example, the series NiMvLUkkc3VtRzYiNiQqJiIiIkYpKSIiI0kibkdGJiEiIi9JImlHRiY7IiIhSSlpbmZpbml0eUclKnByb3RlY3RlZEcsKkYpRikqJkYpRilGK0YtRikqJkYpRikiIiVGLUYpKiZGKUYpIiIpRi1GKQ== +... converges to 2.
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Mathdictionary,Inflection_point ? % MathDictionary,Infinitesimal_Calculus G % MathDictionary,Infinitesimal_calculus G $ MathDictionary,Infinitesimalcalculus G MathDictionary,Infinity F MathDictionary,InfixNotation D MathDictionary,Infix_Notation D MathDictionary,Infix_notation D MathDictionary,Infixnotation D MathDictionary,Inflection C MathDictionary,InflectionPoint ? MathDictionary,Inflection_Point ? MathDictionary,Inflection_point ? Mathdictionary,inflectionpoint ? Mathdictionary,inflexion C Mathdictionary,information B ! Mathdictionary,information_theory A Mathdictionary,informationtheory A ! Mathdictionary,inherent_round-off @ ! Mathdictionary,inherent_round_off @ Mathdictionary,inherentround-off @ Mathdictionary,inherentroundoff @ Mathdictionary,inhomogeneous ? ( Mathdictionary,inhomogeneous_coordinates > ' Mathdictionary,inhomogeneouscoordinates > inflection_point ? 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infinite sequence,
n. a sequence the members of which are indexed by the natural numbers, N; the range of a function of N. Thus the sequence is equinumerous with, and ordered by, N # Definition,inhomogeneouscoordinates > Definition,inith Definition,initial_condition = Definition,initial_line ; Definition,initial_segment : Definition,information B mathdictionary,Infinite_series I mathdictionary,Infinitedescent N # mathdictionary,Infinitehotelparadox M 0 mathdictionary,Infiniteorder P mathdictionary,Infiniteproduct L mathdictionary,Infiniteregress K mathdictionary,Infinitesequence J mathdictionary,Infiniteseries I mathdictionary,Infinitesimal H $ mathdictionary,InfinitesimalCalculus G % mathdictionary,Infinitesimal_Calculus G % mathdictionary,Infinitesimal_calculus G $ mathdictionary,Infinitesimalcalculus G mathdictionary,Infinity F mathdictionary,InfixNotation D mathdictionary,Infix_Notation D mathdictionary,Infix_notation D Dictionary,Infix_Notation D Dictionary,Infix_notation D Dictionary,Infixnotation D Dictionary,Inflection C Dictionary,InflectionPoint ? Dictionary,Inflection_Point ? Dictionary,Inflection_point ? Dictionary,Inflectionpoint ? Dictionary,Inflexion C Dictionary,Information B Dictionary,InformationTheory A Dictionary,Information_Theory A Dictionary,Information_theory A Dictionary,Informationtheory A nary,InfixNotation D P mathdictionary,Infinite-Order Mathdictionary,Infinite-Order MathDictionary,Infinite-Order mathdictionary,infinite-order Mathdictionary,infinite-order MathDictionary,infinite-order dictionary,Infinite-Order Dictionary,Infinite-Order dictionary,infinite-order Dictionary,infinite-order definition,Infinite-Order Definition,Infinite-Order definition,infinite-order Definition,infinite-order mathdictionary,Infinite_order Mathdictionary,Infinite_order MathDictionary,Infinite_order mathdictionary,Infiniteorder Mathdictionary,Infiniteorder MathDictionary,Infiniteorder mathdictionary,Infinite_Order Mathdictionary,Infinite_Order MathDictionary,Infinite_Order mathdictionary,InfiniteOrder Mathdictionary,InfiniteOrder MathDictionary,InfiniteOrder mathdictionary,infinite_order Mathdictionary,infinite_order MathDictionary,infinite_order mathdictionary,infiniteorder Mathdictionary,infiniteorder MathDictionary,infiniteorder dictionary,Infinite_order Dictionary,Infinite_order dictionary,Infiniteorder Dictionary,Inf
infinite regress,
n. a putative explanation or construction in terms of something that itself requires a similar explanation or construction; such an explanation is therefore vacuous. However, it should not be confused with an infinite progression of elements, each of which is constructed from those already constructed. For example, Peano's axioms for arithmetic do not constitute a regress since each number is generated from the preceding, and the first is given by an axiom; thus anything can be shown to be a number by tracing back a finite number of steps to that axiom. However, it is not possible to dispense with that axiom, sa ince without it the process of establishing that anything is an integer would be regressive, and would never terminate. See also vicious circle.
"Text">n. a putative explanation or construction in terms of something that itself requires a similar explanation or construction; such an explanation is therefore vacuous. However, it should not be confused with an infinite progression of elements, each of which is constructed from those already constructed. For example, Peano's axioms for arithmetic do not constitute a regress since each number is generated from the preceding, and the first is given by an axiom; thus anything can be shown to be a number by tracing back a finite number of steps to that axiom. However, it is not possible to dispense with that axiom, sa Infinite_Series,mathdictionary I Infinite_descent,Definition N Infinite_descent,Dictionary N Infinite_descent,MathDictionary N Infinite_descent,Mathdictionary N Infinite_descent,definition N Infinite_descent,dictionary N Infinite_descent,mathdictionary N ! Infinite_hotel_paradox,Definition M 0 ! Infinite_hotel_paradox,Dictionary M 0 % Infinite_hotel_paradox,MathDictionary M 0 % Infinite_hotel_paradox,Mathdictionary M 0 ! Infinite_hotel_paradox,definition M 0 ! Infinite_hotel_paradox,dictionary M 0 % Infinite_hotel_paradox,mathdictionary M 0 Infinite_order,Definition P Infinite_order,Dictionary P Infinite_order,MathDictionary P Infinite_order,Mathdictionary P Infinite_order,definition P Infinite_order,dictionary P Infinite_order,mathdictionary P Infinite_product,Definition L Infinite_product,Dictionary L ! Definition,Infinitesimal_Calculus G ! Definition,Infinitesimal_calculus G Definition,Infinitesimalcalculus G Definition,Infinity F Definition,InfinityNorm E Definition,InfixNotation D Definition,Infix_Notation D Definition,Infix_notation D Definition,Infixnotation D Definition,Inflection C Definition,InflectionPoint ? Definition,Inflection_Point ? Definition,Inflection_point ? infinite_regress,definition K infinite_regress,dictionary K infinite_regress,mathdictionary K infinite_sequence,Definition J infinite_sequence,Dictionary J infinite_sequence,MathDictionary J infinite_sequence,Mathdictionary J infinite_sequence,definition J infinite_sequence,dictionary J infinite_sequence,mathdictionary J infinite_series,Definition I infinite_series,Dictionary I infinite_series,MathDictionary I infinite_series,Mathdictionary I inition,Infinite_Regress Definition,Infinite_Regress definition,InfiniteRegress Definition,InfiniteRegress definition,infinite_regress Definition,infinite_regress definition,infiniteregress Definition,infiniteregress inite_Regress Mathdictionary,Infinite_Regress MathDictionary,Infinite_Regress mathdictionary,InfiniteRegress Mathdictionary,InfiniteRegress MathDictionary,InfiniteRegress mathdictionary,infinite_regress Mathdictionary,infinite_regress MathDictionary,infinite_regress mathdictionary,infiniteregress Mathdictionary,infiniteregress MathDictionary,infiniteregress dictionary,Infinite_regress Dictionary,Infinite_regress dictionary,Infiniteregress Dictionary,Infiniteregress dictionary,Infinite_Regress Dictionary,Infinite_Regress dictionary,InfiniteRegress Dictionary,InfiniteRegress dictionary,infinite_regress Dictionary,infinite_regress dictionary,infiniteregress Dictionary,infiniteregress definition,Infinite_regress Definition,Infinite_regress definition,Infiniteregress Definition,Infiniteregress defa L
infinite product,
n. the product of an infinite sequence of
terms, usually indexed by, or expressed as a function on, the natural numbers, and often written in the form NiMtSShwcm9kdWN0RzYiNiQmSSJhR0YlNiNJImlHRiUvRio7IiIiSSlpbmZpbml0eUclKnByb3RlY3RlZEc=,
or, more briefly, \325i ai. An infinite product of nonzero complex numbers is said to converge if, as n tends to infinity, the partial product NiMtSShwcm9kdWN0RzYiNiQmSSJhR0YlNiNJImlHRiUvRio7IiIiSSJuR0Yl
converges to a nonzero limit, and diverges to zero if that limit exists but is zero. For example, <
a Equation style="2D Math" input-equation="product((1 + z^(2^(i))),i=0..infinity) = (1)/(1 - z);">NiMvLUkocHJvZHVjdEc2IjYkLCYiIiJGKSlJInpHRiYpIiIjSSJpR0YmRikvRi47IiIhSSlpbmZpbml0eUclKnByb3RlY3RlZEcqJkYpRiksJkYpRilGKyEiIkY2
for |z| < 1. If a sequence has a finite number of zero te rms, one determines its convergence by considering convergence of the nonzero tail; the value of the product will, however, be zero in both the convergent and divergent cases. These conventions allow one to convert products securely into series by taking logarithms. A series {ai} is absolutely convergent exactly if NiMyLUkocHJvZHVjdEc2IjYkLCYiIiJGKS1JJGFic0clKnByb3RlY3RlZEc2IyZJImFHRiY2I0kiaUdGJkYpL0YxOyIiIUkpaW5maW5pdHlHRixGNQ==.
See also Wallis's product for pi.
< 1. If a sequence has a finite number of zero te rms, one determines its convergence by considering convergence of the nonzero tail; the value of the product will, however, be zero in both the convergent and divergent cases. These conventions allow one to convert products securely into series by taking logarithms. A series {ai} is absolutely convergent exactly if NiMyLUkocHJvZHVjdEc2IjYkLCYiIiJGKS1JJGFic0clKnByb3RlY3RlZEc2IyZJImFHRiY2I0kiaUdGJkYpL0YxOyIiIUkpaW5maW5pdHlHRixGNQ==
inferior limit,
n. another name for limit inferior.
) Mathematical Dictionary/I/infinite-order Definition,infinite-order ( Mathematical Dictionary/I/infinitesimal Definition,infinitesimal 1 Mathematical Dictionary/I/infinitesimal calculus% Definition,infinitesimalcalculus # Mathematical Dictionary/I/infinity Definition,infinity ( Mathematical Dictionary/I/infinity norm Definition,infinitynorm ) Mathematical Dictionary/I/infix notation Definition,infixnotation % Mathematical Dictionary/I/inflection Definition,inflection & Mathematical Dictionary/I/information Definition,information RI mathdictionary,Infimal_convolution Mathdictionary,Infimal_convolution MathDictionary,Infimal_convolution mathdictionary,Infimalconvolution Mathdictionary,Infimalconvolution MathDictionary,Infimalconvolution mathdictionary,Infimal_Convolution Mathdictionary,Infimal_Convolution MathDictionary,Infimal_Convolution mathdictionary,InfimalConvolution Mathdictionary,InfimalConvolution MathDictionary,InfimalConvolution mathdictionary,infimal_convolution Mathdictionary,infimal_convolution MathDictionary,infimal_convolution mathdictionary,infimalconvolution Mathdictionary,infimalconvolution MathDictionary,infimalconvolution dictionary,Infimal_convolution Dictionary,Infimal_convolution dictionary,Infimalconvolution Dictionary,Infimalconvolution dictionary,Infimal_Convolution Dictionary,Infimal_Convolution dictionary,InfimalConvolution Dictionary,InfimalConvolution dictionary,infimal_convolution Dictionary,infimal_convolution dictionary,infimalconvolution Dictionary,infimalconvolution definition,Infimal_convGa Dictionary,Infinite_series I Dictionary,Infinitedescent N Dictionary,Infinitehotelparadox M 0 Dictionary,Infiniteorder P Dictionary,Infiniteproduct L Dictionary,Infiniteregress K Dictionary,Infinitesequence J Dictionary,Infiniteseries I Dictionary,Infinitesimal H Dictionary,InfinitesimalCalculus G ! Dictionary,Infinitesimal_Calculus G ! Dictionary,Infinitesimal_calculus G Dictionary,Infinitesimalcalculus G Dictionary,Infinity F Dictionary,InfixNotation D dictionary,infiniteseries I dictionary,infinitesimal H ! dictionary,infinitesimal_calculus G dictionary,infinitesimalcalculus G dictionary,infinity F dictionary,infix_notation D dictionary,infixnotation D dictionary,inflection C dictionary,inflection_point ? dictionary,inflectionpoint ? dictionary,inflexion C dictionary,information B dictionary,information_theory A dictionary,informationtheory A ! infinite_hotel_paradox,definition M 0 ! infinite_hotel_paradox,dictionary M 0 % infinite_hotel_paradox,mathdictionary M 0 infinite_order,Definition P infinite_order,Dictionary P infinite_order,MathDictionary P infinite_order,Mathdictionary P infinite_order,definition P infinite_order,dictionary P infinite_order,mathdictionary P infinite_product,Definition L infinite_product,Dictionary L infinite_product,MathDictionary L infinite_product,Mathdictionary L infinite_product,definition L infinite_product,dictionary L infinite_product,mathdictionary L infinite_regress,Definition K infinite_regress,Dictionary K infinite_regress,MathDictionary K infinite_regress,Mathdictionary K nfinitehotelparadox Dictionary,infinitehotelparadox definition,Infinite_hotel_paradox Definition,Infinite_hotel_paradox definition,Infinitehotelparadox Definition,Infinitehotelparadox definition,Infinite_Hotel_Paradox Definition,Infinite_Hotel_Paradox definition,InfiniteHotelParadox Definition,InfiniteHotelParadox definition,infinite_hotel_paradox Definition,infinite_hotel_paradox definition,infinitehotelparadox Definition,infinitehotelparadox radox mathdictionary,infinite_hotel_paradox Mathdictionary,infinite_hotel_paradox MathDictionary,infinite_hotel_paradox mathdictionary,infinitehotelparadox Mathdictionary,infinitehotelparadox MathDictionary,infinitehotelparadox dictionary,Infinite_hotel_paradox Dictionary,Infinite_hotel_paradox dictionary,Infinitehotelparadox Dictionary,Infinitehotelparadox dictionary,Infinite_Hotel_Paradox Dictionary,Infinite_Hotel_Paradox dictionary,InfiniteHotelParadox Dictionary,InfiniteHotelParadox dictionary,infinite_hotel_paradox Dictionary,infinite_hotel_paradox dictionary,i a N
infinite descent,
n. a method of proof by contradiction, introduced by Fermat and used in number theory, that may be used to prove that a result known to be false for some, normally small, positive integer p is false for all positive integers, or to prove that a result that is assumed to be true for all integers n \263 n0 > 0 and false for all n a < n0 is in fact false for all positive integers. In particular, if a result is assumed to be true for some positive integer m, and it can be shown that it would follow for m-k, and so by iteration m-2k, m-3k, and so forth, it then remains to show that for any m there exists a positive integer r of the form r = m-ik, for integral i, r = p or r < n0, contradicting the assumption.
>n a ! Definition,Inferential_statistics U Definition,Inferentialstatistics U Definition,InferiorLimit T Definition,Inferior_Limit T Definition,Inferior_limit T Definition,Inferiorlimit T Definition,Infimal S Definition,InfimalConvolution R Definition,Infimal_Convolution R Definition,Infimal_convolution R Definition,Infimalconvolution R Definition,Infimum Q Definition,Infinite O Definition,Infinite-Order P Definition,InfiniteDescent N mathdictionary,InfiniteSeries I mathdictionary,Infinite_Descent N % mathdictionary,Infinite_Hotel_Paradox M 0 mathdictionary,Infinite_Order P mathdictionary,Infinite_Product L mathdictionary,Infinite_Regress K mathdictionary,Infinite_Sequence J mathdictionary,Infinite_Series I mathdictionary,Infinite_descent N % mathdictionary,Infinite_hotel_paradox M 0 mathdictionary,Infinite_order P mathdictionary,Infinite_product L mathdictionary,Infinite_regress K mathdictionary,Infinite_sequence J # mathdictionary,infinitehotelparadox M 0 mathdictionary,infiniteorder P mathdictionary,infiniteproduct L mathdictionary,infiniteregress K mathdictionary,infinitesequence J mathdictionary,infiniteseries I mathdictionary,infinitesimal H % mathdictionary,infinitesimal_calculus G $ mathdictionary,infinitesimalcalculus G mathdictionary,infinity F mathdictionary,infix_notation D mathdictionary,infixnotation D mathdictionary,inflection C mathdictionary,inflection_point ? # MathDictionary,infinitehotelparadox M 0 MathDictionary,infiniteorder P MathDictionary,infiniteproduct L MathDictionary,infiniteregress K MathDictionary,infinitesequence J MathDictionary,infiniteseries I MathDictionary,infinitesimal H % MathDictionary,infinitesimal_calculus G $ MathDictionary,infinitesimalcalculus G MathDictionary,infinity F MathDictionary,infix_notation D MathDictionary,infixnotation D MathDictionary,inflection C MathDictionary,inflection_point ? Dictionary,infinitedescent N Dictionary,infinitehotelparadox M 0 Dictionary,infiniteorder P Dictionary,infiniteproduct L Dictionary,infiniteregress K Dictionary,infinitesequence J Dictionary,infiniteseries I Dictionary,infinitesimal H ! Dictionary,infinitesimal_calculus G Dictionary,infinitesimalcalculus G Dictionary,infinity F Dictionary,infix_notation D Dictionary,infixnotation D Dictionary,inflection C Dictionary,inflection_point ? Dictionary,inflectionpoint ? ! Definition,Infinite_hotel_paradox M 0 Definition,Infinite_order P Definition,Infinite_product L Definition,Infinite_regress K Definition,Infinite_sequence J Definition,Infinite_series I Definition,Infinitedescent N Definition,Infinitehotelparadox M 0 Definition,Infiniteorder P Definition,Infiniteproduct L Definition,Infiniteregress K Definition,Infinitesequence J Definition,Infiniteseries I Definition,Infinitesimal H Definition,InfinitesimalCalculus G Infinite_product,MathDictionary L Infinite_product,Mathdictionary L Infinite_product,definition L Infinite_product,dictionary L Infinite_product,mathdictionary L Infinite_regress,Definition K Infinite_regress,Dictionary K Infinite_regress,MathDictionary K Infinite_regress,Mathdictionary K Infinite_regress,definition K Infinite_regress,dictionary K Infinite_regress,mathdictionary K Infinite_sequence,Definition J Infiniteproduct,Mathdictionary L Infiniteproduct,definition L Infiniteproduct,dictionary L Infiniteproduct,mathdictionary L Infiniteregress,Definition K Infiniteregress,Dictionary K Infiniteregress,MathDictionary K Infiniteregress,Mathdictionary K Infiniteregress,definition K Infiniteregress,dictionary K Infiniteregress,mathdictionary K Infinitesequence,Definition J Infinitesequence,Dictionary J Infiniteproduct,MathDictionary L Infinite_Product,Dictionary L Infinite_Product,MathDictionary L Infinite_Product,Mathdictionary L Infinite_Product,definition L Infinite_Product,dictionary L Infinite_Product,mathdictionary L Infinite_Regress,Definition K Infinite_Regress,Dictionary K Infinite_Regress,MathDictionary K Infinite_Regress,Mathdictionary K Infinite_Regress,definition K Infinite_Regress,dictionary K Infinite_Regress,mathdictionary K InfiniteOrder,Definition P InfiniteOrder,Dictionary P InfiniteOrder,MathDictionary P InfiniteOrder,Mathdictionary P InfiniteOrder,definition P InfiniteOrder,dictionary P InfiniteOrder,mathdictionary P InfiniteProduct,Definition L InfiniteProduct,Dictionary L InfiniteProduct,MathDictionary L InfiniteProduct,Mathdictionary L InfiniteProduct,definition L InfiniteProduct,dictionary L InfiniteProduct,mathdictionary L InfiniteRegress,Definition K InfiniteRegress,Dictionary K InfiniteRegress,MathDictionary K InfiniteRegress,Mathdictionary K InfiniteRegress,definition K InfiniteRegress,dictionary K infiniteproduct,Dictionary L infiniteproduct,MathDictionary L infiniteproduct,Mathdictionary L infiniteproduct,definition L infiniteproduct,dictionary L infiniteproduct,mathdictionary L infiniteregress,Definition K infiniteregress,Dictionary K infiniteregress,MathDictionary K infiniteregress,Mathdictionary K infiniteregress,definition K infiniteregress,dictionary K infiniteregress,mathdictionary K teproduct,Definition L inition,Infinite_Descent Definition,Infinite_Descent definition,InfiniteDescent Definition,InfiniteDescent definition,infinite_descent Definition,infinite_descent definition,infinitedescent Definition,infinitedescent inite_Descent Mathdictionary,Infinite_Descent MathDictionary,Infinite_Descent mathdictionary,InfiniteDescent Mathdictionary,InfiniteDescent MathDictionary,InfiniteDescent mathdictionary,infinite_descent Mathdictionary,infinite_descent MathDictionary,infinite_descent mathdictionary,infinitedescent Mathdictionary,infinitedescent MathDictionary,infinitedescent dictionary,Infinite_descent Dictionary,Infinite_descent dictionary,Infinitedescent Dictionary,Infinitedescent dictionary,Infinite_Descent Dictionary,Infinite_Descent dictionary,InfiniteDescent Dictionary,InfiniteDescent dictionary,infinite_descent Dictionary,infinite_descent dictionary,infinitedescent Dictionary,infinitedescent definition,Infinite_descent Definition,Infinite_descent definition,Infinitedescent Definition,Infinitedescent def+a V
inference,
n. 1. any process or mode of reasoning from premises to a conclusion. In this sense one says `his inference was invalid', since the inference is an argument rather than a statement and so cannot be said to be true or false. 2. the conclusion inferred. In this sense one says `his inference was false', since the inference is a statement, not an argument, and so can be true or false but not valid or invalid. See also a, b] are an infinite set, even though it is not unbounded. 3. (of a set) able to be put into one-to-one correspondence with a proper subset of itself. See also Cantor's diagonal theorem. 4. (of a group) having infinite order. 5. (of an integral) having infinity as one or both limits of integration. See improper integral.
8859-1">Cantor's diagonal theorem. 4. (of a group) having infinite mathdictionary,Inference Mathdictionary,Inference MathDictionary,Inference mathdictionary,inference Mathdictionary,inference MathDictionary,inference dictionary,Inference Dictionary,Inference dictionary,inference Dictionary,inference definition,Inference Definition,Inference definition,inference Definition,inference WL mathdictionary,Infeasible Mathdictionary,Infeasible MathDictionary,Infeasible mathdictionary,infeasible Mathdictionary,infeasible MathDictionary,infeasible dictionary,Infeasible Dictionary,Infeasible dictionary,infeasible Dictionary,infeasible definition,Infeasible Definition,Infeasible definition,infeasible Definition,infeasible Inductivedefinition,Definition a Inductivedefinition,Dictionary a " Inductivedefinition,MathDictionary a " Inductivedefinition,Mathdictionary a Inductivedefinition,definition a Inductivedefinition,dictionary a " Inductivedefinition,mathdictionary a Inductiveorder,Definition ` Inductiveorder,Dictionary ` Inductiveorder,MathDictionary ` Inductiveorder,Mathdictionary ` Inductiveorder,definition ` Inductiveorder,dictionary ` Inductiveorder,mathdictionary ` Inductivestep,Definition _ Inductivestep,Dictionary _ Inductivestep,MathDictionary _ Inductivestep,Mathdictionary _ Inductivestep,definition _ Inductivestep,dictionary _ dictionary,InfiniteSequence J dictionary,InfiniteSeries I dictionary,Infinite_Descent N ! dictionary,Infinite_Hotel_Paradox M 0 dictionary,Infinite_Order P dictionary,Infinite_Product L dictionary,Infinite_Regress K dictionary,Infinite_Sequence J dictionary,Infinite_Series I dictionary,Infinite_descent N ! dictionary,Infinite_hotel_paradox M 0 dictionary,Infinite_order P dictionary,Infinite_product L definition,InfiniteSequence J definition,InfiniteSeries I definition,Infinite_Descent N ! definition,Infinite_Hotel_Paradox M 0 definition,Infinite_Order P definition,Infinite_Product L definition,Infinite_Regress K definition,Infinite_Sequence J definition,Infinite_Series I definition,Infinite_descent N ! definition,Infinite_hotel_paradox M 0 definition,Infinite_order P definition,Infinite_product L Definition,infinitesequence J Definition,infiniteseries I Definition,infinitesimal H ! Definition,infinitesimal_calculus G Definition,infinitesimalcalculus G Definition,infinity F Definition,infinitynorm E Definition,infix_notation D Definition,infixnotation D Definition,inflection C Definition,inflection_point ? Definition,inflectionpoint ? Definition,inflexion C Definition,information B InfiniteDescent,Dictionary N InfiniteDescent,MathDictionary N InfiniteDescent,Mathdictionary N InfiniteDescent,definition N InfiniteDescent,dictionary N InfiniteDescent,mathdictionary N InfiniteHotelParadox,Definition M 0 InfiniteHotelParadox,Dictionary M 0 # InfiniteHotelParadox,MathDictionary M 0 # InfiniteHotelParadox,Mathdictionary M 0 InfiniteHotelParadox,definition M 0 InfiniteHotelParadox,dictionary M 0 # InfiniteHotelParadox,mathdictionary M 0 initeorder dictionary,Infinite_Order Dictionary,Infinite_Order dictionary,InfiniteOrder Dictionary,InfiniteOrder dictionary,infinite_order Dictionary,infinite_order dictionary,infiniteorder Dictionary,infiniteorder definition,Infinite_order Definition,Infinite_order definition,Infiniteorder Definition,Infiniteorder definition,Infinite_Order Definition,Infinite_Order definition,InfiniteOrder Definition,InfiniteOrder definition,infinite_order Definition,infinite_order definition,infiniteorder Definition,infiniteorder dictionary,Infiniteorder MathDictionary,Infiniteorder mathdictionary,Infinite_Order Mathdictionary,Infinite_Order MathDictionary,Infinite_Order mathdictionary,InfiniteOrder Mathdictionary,InfiniteOrder MathDictionary,InfiniteOrder mathdictionary,infinite_order Mathdictionary,infinite_order MathDictionary,infinite_order mathdictionary,infiniteorder Mathdictionary,infiniteorder MathDictionary,infiniteorder dictionary,Infinite_order Dictionary,Infinite_order dictionary,Infiniteorder Dictionary,Inft of a set T may be defined as satisfying the two conditions, that t \243 t for all t in T, and that for all t > t there is a t' < t in T. For example, the geometric sequence 1/2, 1/4, 1/8,... has as a lower bound every real number less than or equal to zero; it has no least member, and so no minimum but its infimum is 0. Compare supremum.
fimum t of a set T may be defined as satisfying the two conditions, that t \243 t for all t in T, and that for all t > t there is a t' < t in T. For example, the geometric sequence 1/2, 1/4, 1/8,... has as a lower bound every real number less than or equal to zero; it has no least member, and so no minimum but its infimum is 0. Compare supremum.
infimal,
n. constituting or relating to an infimum.
R^
infimal convolution,
see convolution.
Dictionary,Inferentialstatistics U Dictionary,InferiorLimit T Dictionary,Inferior_Limit T Dictionary,Inferior_limit T Dictionary,Inferiorlimit T Dictionary,Infimal S Dictionary,InfimalConvolution R Dictionary,Infimal_Convolution R Dictionary,Infimal_convolution R Dictionary,Infimalconvolution R Dictionary,Infimum Q Dictionary,Infinite O Dictionary,Infinite-Order P Dictionary,InfiniteDescent N Dictionary,InfiniteHotelParadox M 0 Dictionary,InfiniteOrder P Dictionary,InfiniteProduct L Dictionary,InfiniteRegress K Dictionary,InfiniteSequence J Dictionary,InfiniteSeries I Dictionary,Infinite_Descent N ! Dictionary,Infinite_Hotel_Paradox M 0 Dictionary,Infinite_Order P Dictionary,Infinite_Product L Dictionary,Infinite_Regress K Dictionary,Infinite_Sequence J Dictionary,Infinite_Series I Dictionary,Infinite_descent N ! Dictionary,Infinite_hotel_paradox M 0 Dictionary,Infinite_order P Dictionary,Infinite_product L Dictionary,Infinite_regress K Dictionary,Infinite_sequence J Infinite,Definition O Infinite,Dictionary O Infinite,MathDictionary O Infinite,Mathdictionary O Infinite,definition O Infinite,dictionary O Infinite,mathdictionary O Infinite-Order,Definition P Infinite-Order,Dictionary P Infinite-Order,MathDictionary P Infinite-Order,Mathdictionary P Infinite-Order,definition P Infinite-Order,dictionary P Infinite-Order,mathdictionary P InfiniteDescent,Definition N Q " infimal_convolution,Mathdictionary R infimal_convolution,definition R infimal_convolution,dictionary R " infimal_convolution,mathdictionary R infimalconvolution,Definition R infimalconvolution,Dictionary R ! infimalconvolution,MathDictionary R ! infimalconvolution,Mathdictionary R infimalconvolution,definition R infimalconvolution,dictionary R ! infimalconvolution,mathdictionary R infimum,Definition Q infimum,Dictionary Q infimum,MathDictionary Q infimum,Mathdictionary Q infimum,definition Q infimum,dictionary Q infimum,mathdictionary Q infinite,Definition O " Infimal_convolution,Mathdictionary R Infimal_convolution,definition R Infimal_convolution,dictionary R " Infimal_convolution,mathdictionary R Infimalconvolution,Definition R Infimalconvolution,Dictionary R ! Infimalconvolution,MathDictionary R ! Infimalconvolution,Mathdictionary R Infimalconvolution,definition R Infimalconvolution,dictionary R ! Infimalconvolution,mathdictionary R Infimum,Definition Q Infimum,Dictionary Q Infimum,MathDictionary Q Infimum,Mathdictionary Q Infimum,definition Q Infimum,dictionary Q Infimum,mathdictionary Q olution Definition,Infimal_convolution definition,Infimalconvolution Definition,Infimalconvolution definition,Infimal_Convolution Definition,Infimal_Convolution definition,InfimalConvolution Definition,InfimalConvolution definition,infimal_convolution Definition,infimal_convolution definition,infimalconvolution Definition,infimalconvolution lConvolution Mathdictionary,InfimalConvolution MathDictionary,InfimalConvolution mathdictionary,infimal_convolution Mathdictionary,infimal_convolution MathDictionary,infimal_convolution mathdictionary,infimalconvolution Mathdictionary,infimalconvolution MathDictionary,infimalconvolution dictionary,Infimal_convolution Dictionary,Infimal_convolution dictionary,Infimalconvolution Dictionary,Infimalconvolution dictionary,Infimal_Convolution Dictionary,Infimal_Convolution dictionary,InfimalConvolution Dictionary,InfimalConvolution dictionary,infimal_convolution Dictionary,infimal_convolution dictionary,infimalconvolution Dictionary,infimalconvolution definition,Infimal_convGa Q" mathdictionary,Infimum Mathdictionary,Infimum MathDictionary,Infimum mathdictionary,infimum Mathdictionary,infimum MathDictionary,infimum dictionary,Infimum Dictionary,Infimum dictionary,infimum Dictionary,infimum definition,Infimum Definition,Infimum definition,infimum Definition,infimum volution Definition,infimalconvolution lConvolution Mathdictionary,InfimalConvolution MathDictionary,InfimalConvolution mathdictionary,infimal_convolution Mathdictionary,infimal_convolution MathDictionary,infimal_convolution mathdictionary,infimalconvolution Mathdictionary,infimalconvolution MathDictionary,infimalconvolution dictionary,Infimal_convolution Dictionary,Infimal_convolution dictionary,Infimalconvolution Dictionary,Infimalconvolution dictionary,Infimal_Convolution Dictionary,Infimal_Convolution dictionary,InfimalConvolution Dictionary,InfimalConvolution dictionary,infimal_convolution Dictionary,infimal_convolution dictionary,infimalconvolution Dictionary,infimalconvolution definition,Infimal_convGa 4 Definition,Definition 5 Definition,Definition 6 Definition,Definition 7 Definition,Definition 8 Definition,Definition 9 Definition,Definition : Definition,Definition ; Definition,Definition < Definition,Definition = Definition,Definition > Definition,Definition ? Definition,Definition @ Definition,Definition A Definition,Definition B Definition,Definition C Definition,Definition D Definition,Definition u mathdictionary,Index_set Mathdictionary,Index_set MathDictionary,Index_set mathdictionary,Indexset Mathdictionary,Indexset MathDictionary,Indexset mathdictionary,Index_Set Mathdictionary,Index_Set MathDictionary,Index_Set mathdictionary,IndexSet Mathdictionary,IndexSet MathDictionary,IndexSet mathdictionary,index_set Mathdictionary,index_set MathDictionary,index_set mathdictionary,indexset Mathdictionary,indexset MathDictionary,indexset dictionary,Index_set Dictionary,Index_set dictionary,Indexset Dictionary,Indexset dictionary,Index_Set Dictionary,Index_Set dictionary,IndexSet Dictionary,IndexSet dictionary,index_set Dictionary,index_set dictionary,indexset Dictionary,indexset definition,Index_set Definition,Index_set definition,Indexset Definition,Indexset definition,Index_Set Definition,Index_Set definition,IndexSet Definition,IndexSet definition,index_set Definition,index_set definition,indexset Definition,indexset InfimalConvolution,dictionary R ! InfimalConvolution,mathdictionary R Infimal_Convolution,Definition R Infimal_Convolution,Dictionary R " Infimal_Convolution,MathDictionary R " Infimal_Convolution,Mathdictionary R Infimal_Convolution,definition R Infimal_Convolution,dictionary R " Infimal_Convolution,mathdictionary R Infimal_convolution,Definition R Infimal_convolution,Dictionary R " Infimal_convolution,MathDictionary R [
inertial frame of reference,
n. (Mechanics) a frame of reference in which the rates of change of position of the origin and basis vectors are constant.
+ Mathematical Dictionary/I/infinite descent Definition,infinitedescent 1 Mathematical Dictionary/I/infinite hotel paradox$ Definition,infinitehotelparadox + Mathematical Dictionary/I/infinite product Definition,infiniteproduct + Mathematical Dictionary/I/infinite regress Definition,infiniteregress , Mathematical Dictionary/I/infinite sequence Definition,infinitesequence * Mathematical Dictionary/I/infinite series Definition,infiniteseries n,infinite MathDictionary,Inductive_Order ` MathDictionary,Inductive_Step _ # MathDictionary,Inductive_definition a MathDictionary,Inductive_order ` MathDictionary,Inductive_step _ " MathDictionary,Inductivedefinition a MathDictionary,Inductiveorder ` MathDictionary,Inductivestep _ MathDictionary,Inelastic ^ MathDictionary,Inequality ] MathDictionary,Inertia \ MathDictionary,InertiaTensor Z MathDictionary,Inertia_Tensor Z MathDictionary,Inertia_tensor Z ' MathDictionary,InertialFrameOfReference [ * MathDictionary,Inertial_Frame_Of_Reference [ * MathDictionary,Inertial_frame_of_reference [ ' MathDictionary,Inertialframeofreference [ MathDictionary,Inertiatensor Z MathDictionary,Inessential Y MathDictionary,Inf X " Mathdictionary,Infimal_Convolution R " Mathdictionary,Infimal_convolution R ! Mathdictionary,Infimalconvolution R Mathdictionary,Infimum Q Mathdictionary,Infinite O Mathdictionary,Infinite-Order P Mathdictionary,InfiniteDescent N # Mathdictionary,InfiniteHotelParadox M 0 Mathdictionary,InfiniteOrder P Mathdictionary,InfiniteProduct L Mathdictionary,InfiniteRegress K Mathdictionary,InfiniteSequence J Mathdictionary,InfiniteSeries I " MathDictionary,Infimal_Convolution R " MathDictionary,Infimal_convolution R ! MathDictionary,Infimalconvolution R MathDictionary,Infimum Q MathDictionary,Infinite O MathDictionary,Infinite-Order P MathDictionary,InfiniteDescent N # MathDictionary,InfiniteHotelParadox M 0 MathDictionary,InfiniteOrder P MathDictionary,InfiniteProduct L MathDictionary,InfiniteRegress K MathDictionary,InfiniteSequence J MathDictionary,InfiniteSeries I " mathdictionary,Infimal_Convolution R " mathdictionary,Infimal_convolution R ! mathdictionary,Infimalconvolution R mathdictionary,Infimum Q mathdictionary,Infinite O mathdictionary,Infinite-Order P mathdictionary,InfiniteDescent N # mathdictionary,InfiniteHotelParadox M 0 mathdictionary,InfiniteOrder P mathdictionary,InfiniteProduct L mathdictionary,InfiniteRegress K mathdictionary,InfiniteSequence J Definition,InfiniteHotelParadox M 0 Definition,InfiniteOrder P Definition,InfiniteProduct L Definition,InfiniteRegress K Definition,InfiniteSequence J Definition,InfiniteSeries I Definition,Infinite_Descent N ! Definition,Infinite_Hotel_Paradox M 0 Definition,Infinite_Order P Definition,Infinite_Product L Definition,Infinite_Regress K Definition,Infinite_Sequence J Definition,Infinite_Series I Definition,Infinite_descent N Inferiorlimit,Mathdictionary T Inferiorlimit,definition T Inferiorlimit,dictionary T Inferiorlimit,mathdictionary T Infimal,Definition S Infimal,Dictionary S Infimal,MathDictionary S Infimal,Mathdictionary S Infimal,definition S Infimal,dictionary S Infimal,mathdictionary S InfimalConvolution,Definition R InfimalConvolution,Dictionary R ! InfimalConvolution,MathDictionary R ! InfimalConvolution,Mathdictionary R InfimalConvolution,definition R inferior_limit,Mathdictionary T inferior_limit,definition T inferior_limit,dictionary T inferior_limit,mathdictionary T inferiorlimit,Definition T inferiorlimit,Dictionary T inferiorlimit,MathDictionary T inferiorlimit,Mathdictionary T inferiorlimit,definition T inferiorlimit,dictionary T inferiorlimit,mathdictionary T infimal,Definition S infimal,Dictionary S infimal,MathDictionary S infimal,Mathdictionary S infimal,definition S infimal,dictionary S infimal,mathdictionary S infimal_convolution,Definition R infimal_convolution,Dictionary R " infimal_convolution,MathDictionary R ja inequality,Dictionaryia inertia_tensor,MathDictionary` # inertialframeofreference,Dictionarya inessential,Definitionua infeasible,MathDictionaryfa % inferential_statistics,MathDictionary` inferior_limit,MathDictionaryTa " infimal_convolution,MathDictionaryEa infinite,Definition\ % infinite_hotel_paradox,Mathdictionary a infinite_regress,Mathdictionarya infinite_series,Mathdictionary ^ infiniteproduct,Definition*a infiniteregress,mathdictionarya infiniteseries,dictionary` % infinitesimal_calculus,Mathdictionary` infix_notation,MathDictionary` inflection_point,Definition` inflexion,Dictionary` ` ! inherent_round-off,MathDictionary^` inherentround-off,dictionary
` $ inhomogeneous_coordinates,Dictionaryl` inith,Definition3 initial_segment,Mathdictionary` initialize,Mathdictionarya` initialsegment,MathdictionaryO` injective,Mathdictionary\ inner_jordan_content,Dictionary` inner_product,Dictionary)] innerautomorphism,Definition_ ! innerjordancontent,mathdictionary` innerproduct,Mathdictionary_ on_point,Definition` inflexion,Dictionary` Y+ ! Inferential_Statistics,dictionary| $ Inferentialstatistics,MathDictionary` Inferior_Limit,MathDictionary}` Inferiorlimit,MathDictionarySa InfimalConvolution,definitionKa " Infimal_convolution,MathDictionaryFa Infimum,mathdictionaryDa InfiniteDescent,Definition;a # InfiniteHotelParadox,mathdictionary)a InfiniteRegress,dictionarya InfiniteSeries,definition^ Infinite_Product,Definition(a Infinite_Regress,mathdictionarya Infinite_Series,dictionarya &a Infinite_sequence,Definitiona Infinite_series,mathdictionary Infiniteproduct,MathDictionary'a Infinitesequence,Dictionarya Infinitesimal,Definition` InfinitesimalCalculus,dictionaryo` % Infinitesimal_calculus,MathDictionary` Infinity,Mathdictionary` Infix_Notation,MathDictionary` Infixnotation,MathDictionary] InflectionPoint,definition` Inflection_point,Mathdictionary_ Information,Mathdictionary` rya Infinite_Series,dictionarya S" mathdictionary,Infimal Mathdictionary,Infimal MathDictionary,Infimal mathdictionary,infimal Mathdictionary,infimal MathDictionary,infimal dictionary,Infimal Dictionary,Infimal dictionary,infimal Dictionary,infimal definition,Infimal Definition,Infimal definition,infimal Definition,infimal t Mathdictionary,InferiorLimit MathDictionary,InferiorLimit mathdictionary,inferior_limit Mathdictionary,inferior_limit MathDictionary,inferior_limit mathdictionary,inferiorlimit Mathdictionary,inferiorlimit MathDictionary,inferiorlimit dictionary,Inferior_limit Dictionary,Inferior_limit dictionary,Inferiorlimit Dictionary,Inferiorlimit dictionary,Inferior_Limit Dictionary,Inferior_Limit dictionary,InferiorLimit Dictionary,InferiorLimit dictionary,inferior_limit Dictionary,inferior_limit dictionary,inferiorlimit Dictionary,inferiorlimit definition,Inferior_limit Definition,Inferior_limit definition,Inferiorlimit Definition,Inferiorlimit definition,Inferior_Limit Definition,Inferior_Limit definition,Inferior` U mathdictionary,Inferential_statistics Mathdictionary,Inferential_statistics MathDictionary,Inferential_statistics mathdictionary,Inferentialstatistics Mathdictionary,Inferentialstatistics MathDictionary,Inferentialstatistics mathdictionary,Inferential_Statistics Mathdictionary,Inferential_Statistics MathDictionary,Inferential_Statistics mathdictionary,InferentialStatistics Mathdictionary,InferentialStatistics MathDictionary,InferentialStatistics mathdictionary,inferential_statistics Mathdictionary,inferential_statistics MathDictionary,inferential_statistics mathdictionary,inferentialstatistics Mathdictionary,inferentialstatistics MathDictionary,inferentialstatistics dictionary,Inferential_statistics Dictionary,Inferential_statistics dictionary,Inferentialstatistics Dictionary,Inferentialstatistics dictionary,Inferential_Statistics Dictionary,Inferential_Statistics dictionary,InferentialStatistics Dictionary,InferentialStatistics dictionary,inferential_statistics Dictionary,inferential_statistics[a dictionary,inferentialstatistics Dictionary,inferentialstatistics definition,Inferential_statistics Definition,Inferential_statistics definition,Inferentialstatistics Definition,Inferentialstatistics definition,Inferential_Statistics Definition,Inferential_Statistics definition,InferentialStatistics Definition,InferentialStatistics definition,inferential_statistics Definition,inferential_statistics definition,inferentialstatistics Definition,inferentialstatistics onary,inferential_statistics Mathdictionary,inferential_statistics MathDictionary,inferential_statistics mathdictionary,inferentialstatistics Mathdictionary,inferentialstatistics MathDictionary,inferentialstatistics dictionary,Inferential_statistics Dictionary,Inferential_statistics dictionary,Inferentialstatistics Dictionary,Inferentialstatistics dictionary,Inferential_Statistics Dictionary,Inferential_Statistics dictionary,InferentialStatistics Dictionary,InferentialStatistics dictionary,inferential_statistics Dictionary,inferential_statistics[a e
induced measure,
n. the measure induced by the outer measure, m*, on the m*-measurable sets.
Definition,infiniteseries I Definition,infinitesimal H Definition,infinitesimalcalculus G Definition,infinity F Definition,infinitynorm E Definition,infixnotation D Definition,inflection C Definition,information B Definition,informationtheory A Definition,inherentround-off @ Definition,inhomogeneous ? # Definition,inhomogeneouscoordinates > Definition,initialcondition = Definition,initialize < Definition,infinite-order( Mathematical Dictionary/I/infinite-order Definition,infinitedescent* Mathematical Dictionary/I/infinite descent Definition,infinitehotelparadox0 Mathematical Dictionary/I/infinite hotel paradox Definition,infiniteproduct* Mathematical Dictionary/I/infinite product Definition,infiniteregress* Mathematical Dictionary/I/infinite regress Definition,infinitesequence+ Mathematical Dictionary/I/infinite sequence thematical Dictionary/I/infimum Definition,infinite" Mathematical Dictionary/I/infinite encoding="ISO8859-1">induction, deduction.
ormal" style="Heading 1">inference,
n. 1. any process or mode of reasoning from premises to a conclusion. In this sense one says `his inference was invalid', since the inference is an argument rather than a statement and so cannot be said to be true or false. 2. the conclusion inferred. In this sense one says `his inference was false', since the inference is a statement, not an argument, and so can be true or false but not valid or invalid. See also % Definition,inhomogeneouscoordinates ? Definition,inhomogeneous @ Definition,inherentround-off A Definition,informationtheory B Definition,information C Definition,inflection D Definition,infixnotation E Definition,infinitynorm F Definition,infinity G" Definition,infinitesimalcalculus H Definition,infinitesimal ˞L mathdictionary,Hypothesis Mathdictionary,Hypothesis MathDictionary,Hypothesis mathdictionary,hypothesis Mathdictionary,hypothesis MathDictionary,hypothesis dictionary,Hypothesis Dictionary,Hypothesis dictionary,hypothesis Dictionary,hypothesis definition,Hypothesis Definition,Hypothesis definition,hypothesis Definition,hypothesis ̞L mathdictionary,Hypotenuse Mathdictionary,Hypotenuse MathDictionary,Hypotenuse mathdictionary,hypotenuse Mathdictionary,hypotenuse MathDictionary,hypotenuse dictionary,Hypotenuse Dictionary,Hypotenuse dictionary,hypotenuse Dictionary,hypotenuse definition,Hypotenuse Definition,Hypotenuse definition,hypotenuse Definition,hypotenuse W
infeasible,
adj. 1. (of a constrained optimization problem) possessing inconsistent constraints; having an empty feasible set. 2. (of a point) not lying in a prescribed feasible set.
bold="true">1. (of a constrained optimization problem) possessing inconsistent constraints; having an empty
inductive,
adj. of, relating to, or using induction. For example, inductive proof or inductive argument is argument by induction.
ctionary:Definition/principaldiagonal" style="Dictionary Hyperlink" encoding="ISO8859-1">principal diagonal are the moments of inertia of the rigid body, and whose other elements are the negative of the products of inertia for the respective coordinate planes.
trix the entries of whose
inertia,
n. (of a Hermitian matrix) the ordered triple of which the entries are the number of positive, negative, and zero characteristic roots of the matrix. Compare signature.
or="6" minor="0"/>
inertia,
n. (of a Hermitian matrix) the ordered triple of which the entries are the number of positive, negative, and zero characteristic roots of the matrix. Compare
induced topology
or relative topology, n. the topology defined on a subset of the underlying set of a given topological space by taking its open sets to be intersections of the open sets of the given topology with the subset. For example, the open sets of the induced topology on a line in the Euclidean plane are the segments of the line in the interior of the open disks.
Definition,inference# Mathematical Dictionary/I/inference Definition,inferentialstatistics0 Mathematical Dictionary/I/inferential statistics Definition,inferiorlimit( Mathematical Dictionary/I/inferior limit Definition,infimal! Mathematical Dictionary/I/infimal Definition,infimalconvolution- Mathematical Dictionary/I/infimal convolution Definition,infimum! Mathematical Dictionary/I/infimum Definition,infinite" Mathematical Dictionary/I/infinite Definition,infeasible$ Mathematical Dictionary/I/infeasible se" linktarget="Dictionary:Definition/strict" style="Dictionary Hyperlink" encoding="ISO8859-1">strict ordering. 2. a statement that such a relation holds; the negation of an equality or equation, written a \271 b. 3. any of the specific relationships:
a < b (a is less than b),
a \243 b (a is less than or equal to b),
a > b (a is greater than b), or
a \263 b (a is greater than or equal to b).
See also Student[Precalculus][LinearInequalitiesTutor].
< b (a is less than b),
a" inhomogeneou coordinat homogeneou ? inhomogeneou adj @ inher round off error A informat theor B informat C inflect inflex D infix notat tree diagram amp E infinit norm funct vector F infinit G infinitesimal calculu H infinitesimal adj I infinit seri more brief converg J infinit sequenc K infinit regres LK infinit product more brief converg nonzero limit diverg zero also walli pi s mathdictionary,Indicial_equation Mathdictionary,Indicial_equation MathDictionary,Indicial_equation mathdictionary,Indicialequation Mathdictionary,Indicialequation MathDictionary,Indicialequation mathdictionary,Indicial_Equation Mathdictionary,Indicial_Equation MathDictionary,Indicial_Equation mathdictionary,IndicialEquation Mathdictionary,IndicialEquation MathDictionary,IndicialEquation mathdictionary,indicial_equation Mathdictionary,indicial_equation MathDictionary,indicial_equation mathdictionary,indicialequation Mathdictionary,indicialequation MathDictionary,indicialequation dictionary,Indicial_equation Dictionary,Indicial_equation dictionary,Indicialequation Dictionary,Indicialequation dictionary,Indicial_Equation Dictionary,Indicial_Equation dictionary,IndicialEquation Dictionary,IndicialEquation dictionary,indicial_equation Dictionary,indicial_equation dictionary,indicialequation Dictionary,indicialequation definition,Indicial_equation Definition,Indicial_equation definition,Indicialequati1b K
inclusion,
n. the relation between two sets that is obtained when all the members of the one are members of the other. It is usually written S \314 T for strict inclusion, that is, if there exists an element a of T that is not a member of S, and S \315 T if the inclusion is weak, that is, if the two sets may also be identical; however, some authors use S \314 T for weak inclusion, and
indiscrete topology,
n. the topology on a given space whose only open sets are the whole space and the empty set.
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inductive definition,
n. another name for recursive definition.
improperfraction,Definition improperfraction,Dictionary improperfraction,MathDictionary improperfraction,Mathdictionary improperfraction,definition improperfraction,dictionary improperfraction,mathdictionary improperintegral,Definition improperintegral,Dictionary improperintegral,MathDictionary improperintegral,Mathdictionary improperintegral,definition improperintegral,dictionary improperintegral,mathdictionary improperpoint,Definition improperpoint,Dictionary improperpoint,MathDictionary improperpoint,Mathdictionary improperpoint,definition improperpoint,dictionary lI mathdictionary,Indirect_proportion Mathdictionary,Indirect_proportion MathDictionary,Indirect_proportion mathdictionary,Indirectproportion Mathdictionary,Indirectproportion MathDictionary,Indirectproportion mathdictionary,Indirect_Proportion Mathdictionary,Indirect_Proportion MathDictionary,Indirect_Proportion mathdictionary,IndirectProportion Mathdictionary,IndirectProportion MathDictionary,IndirectProportion mathdictionary,indirect_proportion Mathdictionary,indirect_proportion MathDictionary,indirect_proportion mathdictionary,indirectproportion Mathdictionary,indirectproportion MathDictionary,indirectproportion dictionary,Indirect_proportion Dictionary,Indirect_proportion dictionary,Indirectproportion Dictionary,Indirectproportion dictionary,Indirect_Proportion Dictionary,Indirect_Proportion dictionary,IndirectProportion Dictionary,IndirectProportion dictionary,indirect_proportion Dictionary,indirect_proportion dictionary,indirectproportion Dictionary,indirectproportion definition,Indirect_proa nition definition,Inductive_definition Definition,Inductive_definition definition,Inductivedefinition Definition,Inductivedefinition definition,Inductive_Definition Definition,Inductive_Definition definition,InductiveDefinition Definition,InductiveDefinition definition,inductive_definition Definition,inductive_definition definition,inductivedefinition Definition,inductivedefinition ctiveDefinition MathDictionary,InductiveDefinition mathdictionary,inductive_definition Mathdictionary,inductive_definition MathDictionary,inductive_definition mathdictionary,inductivedefinition Mathdictionary,inductivedefinition MathDictionary,inductivedefinition dictionary,Inductive_definition Dictionary,Inductive_definition dictionary,Inductivedefinition Dictionary,Inductivedefinition dictionary,Inductive_Definition Dictionary,Inductive_Definition dictionary,InductiveDefinition Dictionary,InductiveDefinition dictionary,inductive_definition Dictionary,inductive_definition dictionary,inductivedefinition Dictionary,inductivedefia i
indiscernible,
adj. qualitatively identical. See identity.
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(ii) the recursion clause: if P(n) for an integer n, then P(n + 1).
For any finite m, P(m) now follows by a finite number of steps of modus ponens; the universal generalization is a consequence of Peano's axioms. For example, one may prove by induction that Sn, the sum of the first n natural numbers is equal to 1/2 n(n + 1) by first observing that the base clause is obviously true for n = 1.
The recursion clause requires us to show that if the hypothesis is true of n it is true of n + 1:
Sn+1 = 1 + 2 +...+ n + (n + 1) = Sn + (n + 1),
which ex hypothesi is 1/2 n(n + 1) + (n + 1); extracting the common factor yields NiMvKiYsJkkibkc2IiIiIkYoRihGKCwmKiZGJkYoIiIjISIiRihGKEYoRigqKEYlRigsJkYmRihGK0YoRihGK0Ys as required, so that the result is established for all n. b. also called complete, general, or second-kind induction. inductive argument in which the inductive step is from all integers less than n to all integers less than n + 1; that is, the recursion clause
concerns proper subsets, rather than members, of the set in question. Compare transfinite induction. 2. the application of recursive rules. See recursion. 3. (Logic) a process of reasoning in which a general conclusion is
drawn from a set of particular premises, often drawn from experience or from experimental evidence. The conclusion goes beyond the information contained in the premises and does not follow necessarily from them. Thus an inductive argument may be highly probable, yet lead from true premises to a false conclusion; for example, large numbers of sightings at widely varying times and places provide very strong grounds for the falsehood that all swans are a white. Compare deduction. See also Goodman's paradox, Hempel's paradox.
oes beyond the information contained in the premises and does not follow necessarily from them. Thus an inductive argument may be highly probable, yet lead from true premises to a false conclusion; for example, large numbers of sightings at widely varying times and places provide very strong grounds for the falsehood that all swans are a k
indirect variation,
n. another term for inverse proportion.
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indifference,
n. 1a. the fact that some given ordering is indifferent between the members of some set. b. the relation that holds between such elements with respect to such an ordering. 2#b Induction,definition c Induction,dictionary c Induction,mathdictionary c Inductive,Definition b Inductive,Dictionary b Inductive,MathDictionary b Inductive,Mathdictionary b Inductive,definition b Inductive,dictionary b Inductive,mathdictionary b InductiveDefinition,Definition a InductiveDefinition,Dictionary a " InductiveDefinition,MathDictionary a " InductiveDefinition,Mathdictionary a Induction,Mathdictionary c induction,definition c induction,dictionary c induction,mathdictionary c inductive,Definition b inductive,Dictionary b inductive,MathDictionary b inductive,Mathdictionary b inductive,definition b inductive,dictionary b inductive,mathdictionary b inductive_definition,Definition a inductive_definition,Dictionary a # inductive_definition,MathDictionary a # inductive_definition,Mathdictionary a Mathdictionary c indirectvariation,definition ٝ k indirectvariation,dictionary ٝ k indirectvariation,mathdictionary ٝ k ) indiscernibility_of_identicals,Definition j ) indiscernibility_of_identicals,Dictionary j - 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independent variable,
n. 1. a variable in a mathematical equation or statement, whose value determines that of the dependent variable: in y = f(x
indivisible,
adj. (usually of integers or polynomials) 1. not able to be exactly divided, prime. 2. not exactly divisible by a given number or quantity, relatively prime. For example, 8 is indivisible ba y 3.
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indivisible,
adj. (usually of integers or polynomials) 1. not able to be exactly divided, prime. 2. not exactly divisible by a given number or quantity, relatively prime. For example, 8 is indivisible ba dictionary,Induced_measure e dictionary,Induced_topology d dictionary,Inducedmeasure e dictionary,Inducedtopology d dictionary,Induction c dictionary,Inductive b dictionary,InductiveDefinition a dictionary,InductiveOrder ` dictionary,InductiveStep _ dictionary,Inductive_Definition a dictionary,Inductive_Order ` dictionary,Inductive_Step _ dictionary,Inductive_definition a tionary,Induced_Topology d dictionary,Indirect_Proof m dictionary,Indirect_Proportion l dictionary,Indirect_Variation ٝ k dictionary,Indirect_proof m dictionary,Indirect_proportion l dictionary,Indirect_variation ٝ k dictionary,Indirectproof m dictionary,Indirectproportion l dictionary,Indirectvariation ٝ k ' dictionary,IndiscernibilityOfIdenticals j ) dictionary,Indiscernibility_Of_Identicals j ) dictionary,Indiscernibility_of_identicals j ' dictionary,Indiscernibilityofidenticals j dictionary,Indiscernible i dictionary,IndiscreteTopology h dictionary,Indiscrete_Topology h dictionary,Indiscrete_topology h dictionary,Indiscretetopology h dictionary,Individual g dictionary,Indivisible f dictionary,InducedMeasure e dictionary,InducedTopology d dictionary,Induced_Measure e dictionary,Induced_Topology d g1
individual,
n. (Logic) 1. a unique object as opposed to a property or class. See also particular. 2. any element in the domain of a given theory.
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indifference sets,
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adj. (Numerical analysis) 1. (of a problem) having a large condition number. 2. (of a computation) numerically unstable. While it is possible to have an ill-conditioned group_ring,definition > group_ring,dictionary > group_ring,mathdictionary > grouphomorphism,Definition < grouphomorphism,Dictionary < grouphomorphism,MathDictionary < grouphomorphism,Mathdictionary < grouphomorphism,definition < grouphomorphism,dictionary < grouphomorphism,mathdictionary < groupoid,Definition ; groupoid,Dictionary ; groupoid,MathDictionary ; groupoid,Mathdictionary ; groupoid,definition ; groupoid,dictionary ; groupoid,mathdictionary ; grouprepresentation,Definition : grouprepresentation,Dictionary : Indefinite,Mathdictionary ~ Indefinite,definition ~ Indefinite,dictionary ~ Indefinite,mathdictionary ~ IndefiniteIntegral,Definition } IndefiniteIntegral,Dictionary } ! IndefiniteIntegral,MathDictionary } ! IndefiniteIntegral,Mathdictionary } IndefiniteIntegral,definition } IndefiniteIntegral,dictionary } ! IndefiniteIntegral,mathdictionary } Indefinite_Integral,Definition } Indefinite_Integral,Dictionary } thDictionary ~ - Indiscernibility_Of_Identicals,Mathdictionary j ) Indiscernibility_Of_Identicals,definition j ) Indiscernibility_Of_Identicals,dictionary j - Indiscernibility_Of_Identicals,mathdictionary j ) Indiscernibility_of_identicals,Definition j ) Indiscernibility_of_identicals,Dictionary j - Indiscernibility_of_identicals,MathDictionary j - Indiscernibility_of_identicals,Mathdictionary j ) Indiscernibility_of_identicals,definition j ) Indiscernibility_of_identicals,dictionary j - Indiscernibility_of_identicals,mathdictionary j ' Indiscernibilityofidenticals,Definition j ' Indiscernibilityofidenticals,Dictionary j + Indiscernibilityofidenticals,MathDictionary j + Indiscernibilityofidenticals,Mathdictionary j ' Indiscernibilityofidenticals,definition j ' Indiscernibilityofidenticals,dictionary j + Indiscernibilityofidenticals,mathdictionary j ' indiscernibilityofidenticals,definition j ' indiscernibilityofidenticals,dictionary j + indiscernibilityofidenticals,mathdictionary j indiscernible,Definition i indiscernible,Dictionary i indiscernible,MathDictionary i indiscernible,Mathdictionary i indiscernible,definition i indiscernible,dictionary i indiscernible,mathdictionary i indiscrete_topology,Definition h indiscrete_topology,Dictionary h " indiscrete_topology,MathDictionary h icals Dictionary,Indiscernibility_Of_Identicals dictionary,IndiscernibilityOfIdenticals Dictionary,IndiscernibilityOfIdenticals dictionary,indiscernibility_of_identicals Dictionary,indiscernibility_of_identicals dictionary,indiscernibilityofidenticals Dictionary,indiscernibilityofidenticals definition,Indiscernibility_of_identicals Definition,Indiscernibility_of_identicals definition,Indiscernibilityofidenticals Definition,Indiscernibilityofidenticals definition,Indiscernibility_Of_Identicals Definition,Indiscernibility_Of_Identicals definition,IndiscernibilityOfIdenticals Definition,IndiscernibilityOfIdenticals definition,indiscernibility_of_identicals Definition,indiscernibility_of_identicals definition,indiscernibilityofidenticals Definition,indiscernibilityofidenticals ionary,indiscernibilityofidenticals dictionary,Indiscernibility_of_identicals Dictionary,Indiscernibility_of_identicals dictionary,Indiscernibilityofidenticals Dictionary,Indiscernibilityofidenticals dictionary,Indiscernibility_Of_Identa iv mathdictionary,Indiscernible Mathdictionary,Indiscernible MathDictionary,Indiscernible mathdictionary,indiscernible Mathdictionary,indiscernible MathDictionary,indiscernible dictionary,Indiscernible Dictionary,Indiscernible dictionary,indiscernible Dictionary,indiscernible definition,Indiscernible Definition,Indiscernible definition,indiscernible Definition,indiscernible ndiscernibilityofidenticals Definition,Indiscernibilityofidenticals definition,Indiscernibility_Of_Identicals Definition,Indiscernibility_Of_Identicals definition,IndiscernibilityOfIdenticals Definition,IndiscernibilityOfIdenticals definition,indiscernibility_of_identicals Definition,indiscernibility_of_identicals definition,indiscernibilityofidenticals Definition,indiscernibilityofidenticals ionary,indiscernibilityofidenticals dictionary,Indiscernibility_of_identicals Dictionary,Indiscernibility_of_identicals dictionary,Indiscernibilityofidenticals Dictionary,Indiscernibilityofidenticals dictionary,Indiscernibility_Of_Identa Definition,inducedmeasure) Mathematical Dictionary/I/induced measure Definition,inducedtopology* Mathematical Dictionary/I/induced topology Definition,induction# Mathematical Dictionary/I/induction Definition,inductive# Mathematical Dictionary/I/inductive Definition,inductivedefinition. Mathematical Dictionary/I/inductive definition Definition,inductiveorder) Mathematical Dictionary/I/inductive order Definition,inductivestep( Mathematical Dictionary/I/inductive step Definition,inelastic# Mathematical Dictionary/I/inelastic k mathdictionary,Indirect_variation Mathdictionary,Indirect_variation MathDictionary,Indirect_variation mathdictionary,Indirectvariation Mathdictionary,Indirectvariation MathDictionary,Indirectvariation mathdictionary,Indirect_Variation Mathdictionary,Indirect_Variation MathDictionary,Indirect_Variation mathdictionary,IndirectVariation Mathdictionary,IndirectVariation MathDictionary,IndirectVariation mathdictionary,indirect_variation Mathdictionary,indirect_variation MathDictionary,indirect_variation mathdictionary,indirectvariation Mathdictionary,indirectvariation MathDictionary,indirectvariation dictionary,Indirect_variation Dictionary,Indirect_variation dictionary,Indirectvariation Dictionary,Indirectvariation dictionary,Indirect_Variation Dictionary,Indirect_Variation dictionary,IndirectVariation Dictionary,IndirectVariation dictionary,indirect_variation Dictionary,indirect_variation dictionary,indirectvariation Dictionary,indirectvariation definition,Indirect_variation Definition,Indirect_vara iation definition,Indirectvariation Definition,Indirectvariation definition,Indirect_Variation Definition,Indirect_Variation definition,IndirectVariation Definition,IndirectVariation definition,indirect_variation Definition,indirect_variation definition,indirectvariation Definition,indirectvariation t_Variation mathdictionary,IndirectVariation Mathdictionary,IndirectVariation MathDictionary,IndirectVariation mathdictionary,indirect_variation Mathdictionary,indirect_variation MathDictionary,indirect_variation mathdictionary,indirectvariation Mathdictionary,indirectvariation MathDictionary,indirectvariation dictionary,Indirect_variation Dictionary,Indirect_variation dictionary,Indirectvariation Dictionary,Indirectvariation dictionary,Indirect_Variation Dictionary,Indirect_Variation dictionary,IndirectVariation Dictionary,IndirectVariation dictionary,indirect_variation Dictionary,indirect_variation dictionary,indirectvariation Dictionary,indirectvariation definition,Indirect_variation Definition,Indirect_vara l
indirect proportion,
n. another term for inverse proportion.
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indirect proof,
n. a common mathematical term for reductio ad absurdum, proof of a conclusion by showing its negation to be self-contradictory or to contradict known axioms. Compare direct proof.
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indifferent,
adj. 1a. (of an ordering) giving no precedence to any element of a given set in the sense that it orders each of these elements above the other or others; that is, the ordering holds between any pair of members of this set, but is symmetric upon it. For example, in the set of combinations of k elements chosen from n, cardinality is an indifferent ordea ring, since all elements have cardinality k. b. (of elements of an ordering) mutually preferred one to the other. This is not to be confused with being incomparable, when neither can be said to be preferred to the other; the set of such elements is an indifference set. 2. (Statistics) not showing or having preferences, not rendering any of the possible outcomes more probable than the others. See also unbiased.
ements of an ordering) mutually preferred one to the other. This is not to be confused with being incomparable, when neither can be said to be preferred to the other; the set of such elements is an indifference set. 2. (Statistics) not showing or having preferences, not rendering any of the possible outcomes more probable than the others. See also
indefinite integral,
n. any function whose derivative is a given function; it is usually written as a function of the given function as NiMtSSRpbnRHNiI2JC1JImZHRiU2I0kieEdGJUYq,
where f(x) is the given function. For example, x
indefinite,
adj. (of a quadratic form or matrix) neither positive (semi-) definite nor
index set,
n. a set whose elements are used to index those of some other set, such as L in \310l\316LAweak ordering is indifferent. These are all singletons exactly when the order is antisymmetric.
bold="false" executable="false" family="Times New Roman" italic="false" linktarget="Dictionary:Definition/equivalenceclass" style="Dictionary Hyperlink" encoding="ISO8859-1">equivalence classes of points that are pairwise preferred to one another under a given ordering; that is, the sets of points between which the
indifference curve,
n. a set of points for which a given utility function maintains constant value, and which are therefore indifferent to one another with respect to that function. For example, an isotherm, which passes through all points on a mapb where the temperature is equal, is an indifference curve for any utility function that depends solely upon temperature; a contour map likewise shows a set of indifference curves with respect to height. Similarly, one speaks of indifference surfaces in more than two dimensions. The term is due to Edgeworth; see Edgeworth box.
yle="Dictionary Hyperlink" encoding="ISO8859-1">utility function maintains constant value, and which are therefore indifferent to one another with respect to that function. For example, an isotherm, which passes through all points on a mapb mathdictionary,Inclusive Mathdictionary,Inclusive MathDictionary,Inclusive mathdictionary,inclusive Mathdictionary,inclusive MathDictionary,inclusive dictionary,Inclusive Dictionary,Inclusive dictionary,inclusive Dictionary,inclusive definition,Inclusive Definition,Inclusive definition,inclusive Definition,inclusive mathdictionary,Inclusive_disjunction Mathdictionary,Inclusive_disjunction MathDictionary,Inclusive_disjunction mathdictionary,Inclusivedisjunction Mathdictionary,Inclusivedisjunction MathDictionary,Inclusivedisjunction mathdictionary,Inclusive_Disjunction Mathdictionary,Inclusive_Disjunction MathDictionary,Inclusive_Disjunction mathdictionary,InclusiveDisjunction Mathdictionary,InclusiveDisjunction MathDictionary,InclusiveDisjunction mathdictionary,inclusive_disjunction Mathdictionary,inclusive_disjunction MathDictionary,inclusive_disjunction mathdictionary,inclusivedisjunction Mathdictionary,inclusivedisjunction MathDictionary,inclusivedisjunction dictionary,Inclusive_disjunction Di!c mathdictionary,indifferencecurve q mathdictionary,indifferencesets p " mathdictionary,indifferencesurface o mathdictionary,indifferent n mathdictionary,indirect_proof m " mathdictionary,indirect_proportion l ! mathdictionary,indirect_variation ٝ k mathdictionary,indirectproof m ! mathdictionary,indirectproportion l mathdictionary,indirectvariation ٝ k - mathdictionary,indiscernibility_of_identicals j indifference_sets p # mathdictionary,indifference_surface o MathDictionary,hyperbolicspiral ٞ ' MathDictionary,hyperboloid_of_one_sheet ؞ ( MathDictionary,hyperboloid_of_two_sheets מ $ MathDictionary,hyperboloidofonesheet ؞ % MathDictionary,hyperboloidoftwosheets מ # MathDictionary,hypercomplex_numbers ֞ " MathDictionary,hypercomplexnumbers ֞ MathDictionary,hypercube ՞ MathDictionary,hyperelastic Ԟ q 3 MathDictionary,hypergeometric_differential_equation Ӟ oa mathdictionary,infimalpa mathdictionary,infinitedescent"a mathdictionary,inflection_pointR` mathdictionary,initiallineu` ! mathdictionary,innerjordanmeasure*` mathdictionary,inside_ mathdictionary,integerlattice_ mathdictionary,integral_partQ_ ! mathdictionary,integralpolynomialG] , mathdictionary,integro-differential_equation^ mathdictionary,interior_angles^ & mathdictionary,internal_direct_product,^ mathdictionary,indiscernibility_of_identicalsa dictionary,IndifferenceSurface o dictionary,Indifference_Curve q dictionary,Indifference_Sets p dictionary,Indifference_Surface o dictionary,Indifference_curve q dictionary,Indifference_sets p dictionary,Indifference_surface o dictionary,Indifferencecurve q dictionary,Indifferencesets p dictionary,Indifferencesurface o dictionary,Indifferent n dictionary,IndirectProof m dictionary,IndirectProportion l dictionary,IndirectVariation ٝ k definition,IndifferenceSurface o definition,Indifference_Curve q definition,Indifference_Sets p definition,Indifference_Surface o definition,Indifference_curve q definition,Indifference_sets p definition,Indifference_surface o definition,Indifferencecurve q definition,Indifferencesets p definition,Indifferencesurface o definition,Indifferent n definition,IndirectProof m definition,IndirectProportion l definition,IndirectVariation ٝ k IndifferenceSurface,Dictionary o " IndifferenceSurface,MathDictionary o " IndifferenceSurface,Mathdictionary o IndifferenceSurface,definition o IndifferenceSurface,dictionary o " IndifferenceSurface,mathdictionary o Indifference_Curve,Definition q Indifference_Curve,Dictionary q ! Indifference_Curve,MathDictionary q ! Indifference_Curve,Mathdictionary q Indifference_Curve,definition q Indifference_Curve,dictionary q ! Indifference_Curve,mathdictionary q Indifference_Sets,Definition p Indifference_Sets,Dictionary p _curve definition,Indifferencecurve Definition,Indifferencecurve definition,Indifference_Curve Definition,Indifference_Curve definition,IndifferenceCurve Definition,IndifferenceCurve definition,indifference_curve Definition,indifference_curve definition,indifferencecurve Definition,indifferencecurve rence_Curve mathdictionary,IndifferenceCurve Mathdictionary,IndifferenceCurve MathDictionary,IndifferenceCurve mathdictionary,indifference_curve Mathdictionary,indifference_curve MathDictionary,indifference_curve mathdictionary,indifferencecurve Mathdictionary,indifferencecurve MathDictionary,indifferencecurve dictionary,Indifference_curve Dictionary,Indifference_curve dictionary,Indifferencecurve Dictionary,Indifferencecurve dictionary,Indifference_Curve Dictionary,Indifference_Curve dictionary,IndifferenceCurve Dictionary,IndifferenceCurve dictionary,indifference_curve Dictionary,indifference_curve dictionary,indifferencecurve Dictionary,indifferencecurve definition,Indifference_curve Definition,Indifference b
incomplete,
adj. 1. (Logic) (of a formal theory) not so constructed that the addition to the axioms of a proposition that is not a theorem renders the whole theory inconsistent; thus the theory does not coc Definition,inducedmeasure e Definition,inducedtopology d Definition,induction c Definition,inductive b Definition,inductivedefinition a Definition,inductiveorder ` Definition,inductivestep _ Definition,inelastic ^ Definition,inequality ] Definition,inertia \ # Definition,inertialframeofreference [ Definition,inertiatensor Z Definition,inessential Y Definition,inf X g Definition,indivisible f Definition,indirectproportion- Mathematical Dictionary/I/indirect proportion Definition,indirectvariation, Mathematical Dictionary/I/indirect variation' Definition,indiscernibilityofidenticals8 Mathematical Dictionary/I/indiscernibility of identicals Definition,indiscernible' Mathematical Dictionary/I/indiscernible Definition,indiscretetopology- Mathematical Dictionary/I/indiscrete topology Definition,individual$ Mathematical Dictionary/I/individual Definition,indivisible% Mathematical Dictionary/I/indivisible . principle of indifference. the principle that in the absence of any reason to the contrary, each possible outcome of an experiment is to be treated as equiprobable. See mathematical probability.
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indicial equation,
n. the equation that determines the index that is to be used in Frobenius method for solving second-order regular differential equations.
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indifference_curve,MathDictionary q ! indifference_curve,Mathdictionary q indifference_curve,definition q indifference_curve,dictionary q ! indifference_curve,mathdictionary q indifference_sets,Definition p r mathdictionary,Incomplete_elliptic_integral Mathdictionary,Incomplete_elliptic_integral MathDictionary,Incomplete_elliptic_integral mathdictionary,Incompleteellipticintegral Mathdictionary,Incompleteellipticintegral MathDictionary,Incompleteellipticintegral mathdictionary,Incomplete_Elliptic_Integral Mathdictionary,Incomplete_Elliptic_Integral MathDictionary,Incomplete_Elliptic_Integral mathdictionary,IncompleteEllipticIntegral Mathdictionary,IncompleteEllipticIntegral MathDictionary,IncompleteEllipticIntegral mathdictionary,incomplete_elliptic_integral Mathdictionary,incomplete_elliptic_integral MathDictionary,incomplete_elliptic_integral mathdictionary,incompleteellipticintegral Mathdictionary,incompleteellipticintegral MathDictionary,incompleteellipticintegral dictionary,Incomplete_elliptic_integral Dictionary,Incomplete_elliptic_integral dictionary,Incompleteellipticintegral Dictionary,Incompleteellipticintegral dictionary,Incomplete_Elliptic_Integral Dictionary,Incomplete_Elliptic_Integral c on Definition,Indicialequation definition,Indicial_Equation Definition,Indicial_Equation definition,IndicialEquation Definition,IndicialEquation definition,indicial_equation Definition,indicial_equation definition,indicialequation Definition,indicialequation al_Equation MathDictionary,Indicial_Equation mathdictionary,IndicialEquation Mathdictionary,IndicialEquation MathDictionary,IndicialEquation mathdictionary,indicial_equation Mathdictionary,indicial_equation MathDictionary,indicial_equation mathdictionary,indicialequation Mathdictionary,indicialequation MathDictionary,indicialequation dictionary,Indicial_equation Dictionary,Indicial_equation dictionary,Indicialequation Dictionary,Indicialequation dictionary,Indicial_Equation Dictionary,Indicial_Equation dictionary,IndicialEquation Dictionary,IndicialEquation dictionary,indicial_equation Dictionary,indicial_equation dictionary,indicialequation Dictionary,indicialequation definition,Indicial_equation Definition,Indicial_equation definition,Indicialequati1b rh mathdictionary,Indifference Mathdictionary,Indifference MathDictionary,Indifference mathdictionary,indifference Mathdictionary,indifference MathDictionary,indifference dictionary,Indifference Dictionary,Indifference dictionary,indifference Dictionary,indifference definition,Indifference Definition,Indifference definition,indifference Definition,indifference ctionary,IndicialEquation mathdictionary,indicial_equation Mathdictionary,indicial_equation MathDictionary,indicial_equation mathdictionary,indicialequation Mathdictionary,indicialequation MathDictionary,indicialequation dictionary,Indicial_equation Dictionary,Indicial_equation dictionary,Indicialequation Dictionary,Indicialequation dictionary,Indicial_Equation Dictionary,Indicial_Equation dictionary,IndicialEquation Dictionary,IndicialEquation dictionary,indicial_equation Dictionary,indicial_equation dictionary,indicialequation Dictionary,indicialequation definition,Indicial_equation Definition,Indicial_equation definition,Indicialequati1b family="Times New Roman" italic="false" linktarget="Dictionary:Definition/supportfunction" style="Dictionary Hyperlink" encoding="ISO8859-1">support function.
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indicator function,
n. the extended real-valued function that takes value zero on a given set and +\245 off the set. It is denoted ic or d c, and is convex precisely if the set C is. Compare characteristic function. See also b |_K
independent,
adj. 1. (of a system of linear equations or a set of vectors), see linearly independent. 2. (Statistics) a. (of two or more random variables) distributed so that the value of one variable will have no effect on that taken by the others. Thus the probability of each random variable taking each of some sequence of specifib , Mathematical Dictionary/I/indifference sets Definition,indifferencesets / Mathematical Dictionary/I/indifference surface# Definition,indifferencesurface & Mathematical Dictionary/I/indifferent Definition,indifferent ) Mathematical Dictionary/I/indirect proof Definition,indirectproof . Mathematical Dictionary/I/indirect proportion" Definition,indirectproportion - Mathematical Dictionary/I/indirect variation! Definition,indirectvariation ionary/I/indifference curve! Definition,indifferencecurve 59-1">l, the union of all the sets Al, one for each l in L.
Heading 1">index set,
n. a set whose elements are used to index those of some other set, such as L in \310l\316LA
index of determination
The index of determination
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where NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USFGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GKC8lK2JhY2tncm91bmRHUS5bMjU1ab 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dyIiIkkkLi4uR0YoSSJtR0Yo, are the data points, 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, is a measure of the goodness of fit of the least-squares model 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 JGYXM=, A = 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 3VGW3RGZXBGZ3BGanBGXXFGX3FGYXFGY3FGZXFGZ3FGaXEtRiQ2JS1GY282M1EiKEYoRmZvRmlvRltwRl1wRmBwRmNwRmVwRmdwRmpwRl1xRl9xRmFxRmNxRmVxRmdxRmlxLUYkNiVGLC1GXnI2Ji1GLTY5USJ4RihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG8tRiQ2Iy1GLTY5USJpRihGMEYzRjZGOUY8Rj5GQEZCRkVGSEZKRkxGTkZQRlJGVEZWRllGZW5GZ25GaW5GXG9GaHJGW3NGLC1GY282M1EiKUYoRmBzRmlvRltwRl1wRmBwRmNwRmVwRmdwRmpwRl1xRl9xRmFxRmNxRmVxRmdxRmlxRixGLEZdc0YsRiw3IzYjLzwjJkkiYUdGKDYjSSNpakdGKDwjLSZJJHBoaUdGKDYjSSJqR0YoNiMmSSJ4R0YoNiNJImlHRig=, u = NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USFGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GKC8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRigvJSdvcGFxdWVHRjqb 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, NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USFGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GKC8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRigvJSdvcGsb 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 BGXXNGY3BGZXBGZ3BGanBGXXFGX3FGYXFGY3FGZXFGZ3FGaXFGYHJGLEYsNyM2Iy9JIk1HRigqJilJIkFHRihJIlRHRigiIiJGZXNGZ3M=, b = 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 kBGQkZFRkhGSkZMRk5GUEZSRlRGVkZZRmVuRmduRmluRlxvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGKEYsNyM2IylJIkFHRihJIlRHRig= y, and u satisfies Mu = b. If the number of data points exceeds the number of parameters by at least three, and R is close to 1, then NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USFGKC8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYoLyUlc2l6ZUdRIzEyRigvJSVib2xkR1EmZmFsc2VGKC8lJ2l0YWxpY0dRJXRydWVGKC8lKnVuZGVybGluZUdGOC8lKnN1YnNjcmlwdEdGOC8lLHN1cGVyc2NyaXB0R0Y4LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GKC8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRigvJSdvcGFxdWVHRjgvJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRjgvJSljb21wb3NlZEdGOC8lKmNvbnZlcnRlZEdGOC8lK2ltc2VsZWN0ZWRHRjgvJSxwbGFjZWhvbGRlckdGOC8lMGZvbnRfc3R5bGVfbmFtvb 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 fits the dwb ata well.
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 fits the dwb x
index laws,
n. the rules that govern the manipulation of powers of elements in a semigroup. The laws are NiMvKiYpSSJ4RzYiSSJtR0YnIiIiKUYmSSb wa
index number,
n. (Statistics) a measure of the change, relative to some specific base period, in some variable, such as the price, volume, or value of a commodity, the gross national product, or the general level of prices. The value of the variable in the base period is conventionally given the index number 100, and the index number of any other period is in proportion with it; thus an index number of 250 indicatezb s that the value of the variable is two and a half times that of the base period.
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index number,
n. (Statistics) a measure of the change, relative to some specific base period, in some variable, such as the price, volume, or value of a commodity, the gross national product, or the general level of prices. The value of the variable in the base period is conventionally given the index number 100, and the index number of any other period is in proportion with it; thus an index number of 250 indicatezb index,definition y O index,dictionary y O index,mathdictionary y O index_laws,Definition x index_laws,Dictionary x index_laws,MathDictionary x index_laws,Mathdictionary x index_laws,definition x index_laws,dictionary x index_laws,mathdictionary x index_number,Definition w index_number,Dictionary w index_number,MathDictionary w index_number,Mathdictionary w index_number,definition w index_number,dictionary w index_number,mathdictionary w index_set,Definition u index_set,Dictionary u index_set,MathDictionary u Index_Set,Dictionary u Index_Set,MathDictionary u Index_Set,Mathdictionary u Index_Set,definition u Index_Set,dictionary u Index_Set,mathdictionary u Index_laws,Definition x Index_laws,Dictionary x Index_laws,MathDictionary x Index_laws,Mathdictionary x Index_laws,definition x Index_laws,dictionary x Index_laws,mathdictionary x Index_number,Definition w Index_number,Dictionary w Index_number,MathDictionary w Index_number,Mathdictionary w Index_number,definition w Index_number,dictionary w Index_number,mathdictionary w Index_set,Definition u Index_set,Dictionary u Index_set,MathDictionary u Index_set,Mathdictionary u Index_set,definition u Index_set,dictionary u indexofdetermination,Definition v indexofdetermination,definition v indexset,Definition u indexset,Dictionary u indexset,MathDictionary u indexset,Mathdictionary u indexset,definition u indexset,dictionary u indexset,mathdictionary u indicator_function,Definition t indicator_function,Dictionary t ! indicator_function,MathDictionary t ! indicator_function,Mathdictionary t indicator_function,definition t dictionary w er definition,indexnumber Definition,indexnumber ary,Index_number MathDictionary,Index_number mathdictionary,Indexnumber Mathdictionary,Indexnumber MathDictionary,Indexnumber mathdictionary,Index_Number Mathdictionary,Index_Number MathDictionary,Index_Number mathdictionary,IndexNumber Mathdictionary,IndexNumber MathDictionary,IndexNumber mathdictionary,index_number Mathdictionary,index_number MathDictionary,index_number mathdictionary,indexnumber Mathdictionary,indexnumber MathDictionary,indexnumber dictionary,Index_number Dictionary,Index_number dictionary,Indexnumber Dictionary,Indexnumber dictionary,Index_Number Dictionary,Index_Number dictionary,IndexNumber Dictionary,IndexNumber dictionary,index_number Dictionary,index_number dictionary,indexnumber Dictionary,indexnumber definition,Index_number Definition,Index_number definition,Indexnumber Definition,Indexnumber definition,Index_Number Definition,Index_Number definition,IndexNumber Definition,IndexNumber definition,index_number Definition,index_numb~b v@ definition,indexofdetermination Definition,IndexOfDetermination ry,Index_number mathdictionary,Indexnumber Mathdictionary,Indexnumber MathDictionary,Indexnumber mathdictionary,Index_Number Mathdictionary,Index_Number MathDictionary,Index_Number mathdictionary,IndexNumber Mathdictionary,IndexNumber MathDictionary,IndexNumber mathdictionary,index_number Mathdictionary,index_number MathDictionary,index_number mathdictionary,indexnumber Mathdictionary,indexnumber MathDictionary,indexnumber dictionary,Index_number Dictionary,Index_number dictionary,Indexnumber Dictionary,Indexnumber dictionary,Index_Number Dictionary,Index_Number dictionary,IndexNumber Dictionary,IndexNumber dictionary,index_number Dictionary,index_number dictionary,indexnumber Dictionary,indexnumber definition,Index_number Definition,Index_number definition,Indexnumber Definition,Indexnumber definition,Index_Number Definition,Index_Number definition,IndexNumber Definition,IndexNumber definition,index_number Definition,index_numb~b JuR0YnRikpRiYsJkYoRilGK0Yp NiMvKSlJInhHNiJJIm1HRidJIm5HRicpRiYqJkYoIiIiRilGLA==.
In a group these can be extended by NiMvKUkieEc2IiwkSSJtR0YmISIiKSlGJUYoLCQiIiJGKQ== NiMvKiRJInhHNiIiIiFJImVHRiY=
where e is the identity element of t he group. See also exponent.
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In a group these can be extended by NiMvKUkieEc2IiwkSSJtR0YmISIiKSlGJUYoLCQiIiJGKQ== NiMvKiRJInhHNiIiIiFJImVHRiY=
where e is the identity element of t he group. See also n` ?^ @v_ AX` B` CK D` Definition,incident Definition,incidencematrix Definition,incidence Definition,incenter ! Definition,inaccessiblecardinal Definition,in-degree Definition,imputation Definition,impulse Definition,improperpoint Definition,improperintegral Definition,improperfraction $ Definition,impredicativedefinition Definition,impossibleset ! Definition,impossibilitytheorem Definition,importation mathdictionary,Indicatorfunction t mathdictionary,IndicialEquation s mathdictionary,Indicial_Equation s mathdictionary,Indicial_equation s mathdictionary,Indicialequation s mathdictionary,Indifference r mathdictionary,IndifferenceCurve q mathdictionary,IndifferenceSets p " mathdictionary,IndifferenceSurface o ! mathdictionary,Indifference_Curve q mathdictionary,Indifference_Sets p # mathdictionary,Indifference_Surface o n t Mathdictionary,Index_Number w Mathdictionary,Index_Set u Mathdictionary,Index_laws x Mathdictionary,Index_number w Mathdictionary,Index_set u Mathdictionary,Indexlaws x Mathdictionary,Indexnumber w Mathdictionary,Indexset u Mathdictionary,IndicatorFunction t ! Mathdictionary,Indicator_Function t ! Mathdictionary,Indicator_function t Mathdictionary,Indicatorfunction t Mathdictionary,IndicialEquation s nary,Index_Laws x MathDictionary,Index_Number w MathDictionary,Index_Set u MathDictionary,Index_laws x MathDictionary,Index_number w MathDictionary,Index_set u MathDictionary,Indexlaws x MathDictionary,Indexnumber w MathDictionary,Indexset u MathDictionary,IndicatorFunction t ! MathDictionary,Indicator_Function t ! MathDictionary,Indicator_function t MathDictionary,Indicatorfunction t MathDictionary,IndicialEquation s nary,Index_Laws x Definition,IndicialEquation s Definition,Indicial_Equation s Definition,Indicial_equation s Definition,Indicialequation s Definition,Indifference r Definition,IndifferenceCurve q Definition,IndifferenceSets p Definition,IndifferenceSurface o Definition,Indifference_Curve q Definition,Indifference_Sets p Definition,Indifference_Surface o Definition,Indifference_curve q Definition,Indifference_sets p on t