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A thesaurus (pl.: thesauri or thesauruses), sometimes called a synonym dictionary or dictionary of synonyms, is a reference work which arranges words by their meanings (or in simpler terms, a book where one can find different words with similar meanings to other words), [1] [2] sometimes as a hierarchy of broader and narrower terms, sometimes simply as lists of synonyms and antonyms.
This can also apply to limits: see Vanish at infinity. weak, weaker The converse of strong. well-defined Accurately and precisely described or specified. For example, sometimes a definition relies on a choice of some object; the result of the definition must then be independent of this choice.
A thesaurus or synonym dictionary lists similar or related words; these are often, but not always, synonyms. [15] The word poecilonym is a rare synonym of the word synonym. It is not entered in most major dictionaries and is a curiosity or piece of trivia for being an autological word because of its meta quality as a synonym of synonym.
WordNet is a lexical database of semantic relations between words that links words into semantic relations including synonyms, hyponyms, and meronyms. The synonyms are grouped into synsets with short definitions and usage examples. It can thus be seen as a combination and extension of a dictionary and thesaurus.
In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.
Limit of a function (ε,_δ)-definition of limit, formal definition of the mathematical notion of limit; Limit of a sequence; One-sided limit, either of the two limits of a function as a specified point is approached from below or from above; Limit inferior and limit superior; Limit of a net; Limit point, in topological spaces; Limit (category ...
In these limits, the infinitesimal change is often denoted or .If () is differentiable at , (+) = ′ ().This is the definition of the derivative.All differentiation rules can also be reframed as rules involving limits.
The definition of limit given here does not depend on how (or whether) f is defined at p. Bartle [9] refers to this as a deleted limit, because it excludes the value of f at p. The corresponding non-deleted limit does depend on the value of f at p, if p is in the domain of f. Let : be a real-valued function.