It relies on the following equivalent definition of differentiability at a point: A function g is differentiable at a if there exists a real number g ′( a ) and a function ε ( h ) that tends to zero as h tends to zero, and furthermore

The definition of a halting probability relies on the existence of prefix-free universal computable functions.

The Prime Minister has further elaborated, stating that the motion's definition of Québécois relies on personal decisions to self-identify as Québécois, and therefore is a personal choice.

However, an XHTML document is an XML document, which, while not having an explicit " document character " layer of abstraction, nevertheless relies upon a similar definition of permissible characters that cover most, but not all, of the Unicode / UCS character definitions.

The ampere is defined using Ampère's force law ; the definition relies in part on the mass of the international prototype kilogram, a metal cylinder housed in France.

Such elements include the essential idea of narrative structure, with identifiable beginnings, middles and endings, or exposition-development-climax-resolution-denouement, normally constructed into coherent plot lines ; a strong focus on temporality, which includes retention of the past, attention to present action, and protention / future anticipation ; a substantial focus on characters and characterization which is " arguably the most important single component of the novel "; a given heterogloss of different voices dialogically at play – " the sound of the human voice, or many voices, speaking in a variety of accents, rhythms and registers "; possesses a narrator or narrator-like voice, which by definition " addresses " and " interacts with " reading audiences ( see Reader Response theory ); communicates with a Wayne Booth-esque rhetorical thrust, a dialectic process of interpretation, which is at times beneath the surface, conditioning a plotted narrative, and other at other times much more visible, " arguing " for and against various positions ; relies substantially on now-standard aesthetic figuration, particularly including the use of metaphor, metonymy, synecdoche and irony ( see Hayden White, Metahistory for expansion of this idea ); is often enmeshed in intertextuality, with copious connections, references, allusions, similarities, parallels, etc.

This definition relies on the notion of the cartesian product.

Such elements include the essential idea of narrative structure, with identifiable beginnings, middles and ends, or exposition-development-climax-denouement, with important inciting incidents, normally constructed into coherent plot lines ; a strong focus on temporality that includes retention of the past, attention to present action and protention / future anticipation ; a substantial focus on characters and characterization which is " arguably the most important single component of the novel " ( David Lodge The Art of Fiction 67 ); a given hetergloss of different voices dialogically at play, " the sound of the human voice, or many voices, speaking in a variety of accents, rhythms and registers " ( Lodge The Art of Fiction 97 ; see also the theory of Mikhail Bakhtin for expansion of this idea ); possesses a narrator or narrator-like voice, which by definition " addresses " and " interacts with " reading audiences ( see Reader Response theory ); communicates with a Wayne Booth-esque rhetorical thrust, a dialectic process of interpretation, which is at times beneath the surface, conditioning a plotted narrative, and other at other times much more visible, " arguing " for and against various positions ; relies substantially on now-standard aesthetic figuration, particularly including the use of metaphor, metonymy, synecdoche and irony ( see Hayden White, Metahistory for expansion of this idea ); is often enmeshed in intertextuality, with copious connections, references, allusions, similarities, parallels, etc.

But the definition of homotopic relies on a notion of continuity, and hence a topology.

The definition of surface integral relies on splitting the surface into small surface elements.

Since the actual structure of objects is immaterial in category theory, the definition of subobject relies on a morphism which describes how one object sits inside another, rather than relying on the use of elements.

Another criticism is that it can be demonstrated that the only properties shared by all qualia are that they are not precisely describable, and thus are of indeterminate meaning within any philosophy which relies upon precise definition.

The definition of surface integral relies on splitting the surface Σ into small surface elements.

This definition of lens power relies upon an arbitrary decision to split the angular magnification of the instrument into separate factors for the eyepiece and the objective.

Since the definition of r < sub > SOI </ sub > relies on the presence of the Sun and a planet, the term is only applicable in a three body or greater system.

Hegel points out that the understanding and consequently writing of history always relies on a framework, be it religious, secular, ' postmodern ' - that word is the very definition of ambiguity.

Du Pont analysis relies upon the accounting identity, that is, a statement ( formula ) that is by definition true.

While in Quirin there was public law passed with the title " declaration of war " and three Articles ( 15, 81 and 82 ) of the Articles of War, President Bush's claim relies on a congressional Joint Resolution used as a formal declaration of war ( which has no precise legal definition in the US ) under the War Powers Resolution, and two provisions of the Uniform Code of Military Justice, the successor to the Articles of War.

This is evidenced by the fact that the introduction to the Topics contains and relies upon his definition of reasoning (, syllogismós ): a verbal expression (, lógos ) in which, certain things having been laid down, other things necessarily follow from these .. Dialectical reasoning is thereafter divided by Aristotle into inductive and deductive parts.

Educational Technology relies on a broad definition of the word " technology.

Augustan prose is somewhat ill-defined, as the definition of " Augustan " relies primarily upon changes in taste in poetry.

Its definition relies on the notion of a measured foliation invented by William Thurston, who also coined the term " pseudo-Anosov diffeomorphism " when he proved his classification of diffeomorphisms of a surface.

First, we can encourage responsibility by establishing as conditions for assistance on a substantial and sustained scale the definition of objectives and the assessment of costs.

Used in several sets of high reps once or twice each week it will not be long before your entire upper leg takes on a razor-sharp definition in which the muscles look like wire cables writhing and twisting under the skin!!

If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

It might be contended, of course, that Eichmann in stubbornly denying anti-Semitic feelings was lying or insisting on a private definition of anti-Semitism.

One definition of paternalism is `` The principle or practice, on the part of a government, of managing the affairs of a country in the manner of a father dealing with his children ''.

The appellate court will typically be deferential to the lower court's findings of fact ( such as whether a defendant committed a particular act ), unless clearly erroneous, and so will focus on the court's application of the law to those facts ( such as whether the act found by the court to have occurred fits a legal definition at issue ).

The new definition is expected to be formally proposed at the 25th General Conference on Weights and Measures ( CGPM ) in 2014.

Its domain is the powerset of A ( with the empty set removed ), and so makes sense for any set A, whereas with the definition used elsewhere in this article, the domain of a choice function on a collection of sets is that collection, and so only makes sense for sets of sets.

The exact definition of an automorphism depends on the type of " mathematical object " in question and what, precisely, constitutes an " isomorphism " of that object.

( The definition of a homomorphism depends on the type of algebraic structure ; see, for example: group homomorphism, ring homomorphism, and linear operator ).

* The Logicians or the School of Names, which focused on definition and logic.

This definition was adopted by the United Nations Sub-Commission on the Promotion and Protection of Human Rights in The Despouy Report on Human Rights and Extreme Poverty.

In this definition, it is implicitly assumed that storing a value into a variable U has no effect on the state of a distinct variable V. To make this assumption explicit, one could add the constraint that

In fact anode polarity depends on the device type, and sometimes even in which mode it operates, as per the above electric current direction-based universal definition.

Also running on a JOHANNIAC, the Logic Theory Machine constructed proofs from a small set of propositional axioms and three deduction rules: modus ponens, ( propositional ) variable substitution, and the replacement of formulas by their definition.

Celsius was the first to perform and publish careful experiments aiming at the definition of an international temperature scale on scientific grounds.

Heschel then goes on to explore the problems of doubts and faith ; what Judaism means by teaching that God is one ; the essence of humanity and the problem of human needs ; the definition of religion in general and of Judaism in particular ; and human yearning for spirituality.

This definition was proposed by Justus von Liebig circa 1838, based on his extensive works on the chemical composition of organic acids.

Meteorologists ( and most of the temperate countries in the southern hemisphere ) use a definition based on months, with autumn being September, October and November in the northern hemisphere, According to United States tradition, autumn runs from the day after Labor Day ( i. e. the Tuesday following the first Monday of September ) through Thanksgiving ( i. e. the fourth Thursday in November ), after which the holiday season that demarcates the unofficial beginning of winter begins.

Based on this definition, the drain efficiency cannot exceed 25 % for a class A amplifier that is supplied drain bias current through resistors ( because RF signal has its zero level at about 50 % of the input DC ).

The definition of ballroom dance also depends on the era: balls have featured popular dances of the day such as the Minuet, Quadrille, Polonaise, Polka, Mazurka, and others, which are now considered to be historical dances.

He goes on to define error as self-contradiction of definition (" an absurdity, or senselesse Speech ") or conclusions that do not follow the definitions on which they are supposed to be based.