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A **definition** is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories, intensional definitions (which try to give the essence of a term) and extensional definitions (which list every single object that a term describes). A term may have many different senses and multiple meanings, and thus require multiple definitions.

In mathematics, a definition is used to give a precise meaning to a new term, instead of describing a pre-existing term. Definitions and axioms are the basis on which all of mathematics is constructed.

An *Intensional definition*, also called a *connotative* definition, specifies the necessary and sufficient conditions for a thing being a member of a specific set. Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition.

An *extensional definition*, also called a *denotative* definition, of a concept or term specifies its *extension*. It is a list naming every object that is a member of a specific set.

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Definition

In calculus, the **(ε, δ)-definition of limit** ("epsilon-delta definition of limit") is a formalization of the notion of limit. It was first given by Bernard Bolzano in 1817. Augustin-Louis Cauchy never gave an () definition of limit in his Cours d'Analyse, but occasionally used arguments in proofs. The definitive modern statement was ultimately provided by Karl Weierstrass.

Isaac Newton was aware, in the context of the derivative concept, that the limit of the ratio of evanescent quantities was *not* itself a ratio, as when he wrote:

Occasionally Newton explained limits in terms similar to the epsilon-delta definition.Augustin-Louis Cauchy gave a definition of limit in terms of a more primitive notion he called a *variable quantity*. He never gave an epsilon-delta definition of limit (Grabiner 1981). Some of Cauchy's proofs contain indications of the epsilon-delta method. Whether or not his foundational approach can be considered a harbinger of Weierstrass's is a subject of scholarly dispute. Grabiner feels that it is, while Schubring (2005) disagrees. Nakane concludes that Cauchy and Weierstrass gave the same name to different notions of limit.

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/(ε,_δ)-definition_of_limit

* Definition* is the sixth album by the American crossover thrash band D.R.I., which was released in 1992.

**Bonus tracks**

LP - "Out of Mind"

Cassette - "Hide Your Eyes"

CD - "Dry Heaves"

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Definition_(album)

A **definition** is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories, intensional definitions (which try to give the essence of a term) and extensional definitions (which list every single object that a term describes). A term may have many different senses and multiple meanings, and thus require multiple definitions.

In mathematics, a definition is used to give a precise meaning to a new term, instead of describing a pre-existing term. Definitions and axioms are the basis on which all of mathematics is constructed.

An *Intensional definition*, also called a *connotative* definition, specifies the necessary and sufficient conditions for a thing being a member of a specific set. Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition.

An *extensional definition*, also called a *denotative* definition, of a concept or term specifies its *extension*. It is a list naming every object that is a member of a specific set.

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Definition

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