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Infinitely-large function

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A function of a variable whose absolute value becomes and remains larger than any given number as a result of variation of . More exactly, a function defined in a neighbourhood of a point is called an infinitely-large function as tends to if for any number it is possible to find a number such that for all satisfying the inequality holds. This fact may be written as follows:

The following are defined in a similar manner:

For example,

means that for any it is possible to find a such that the inequality is valid for all . The study of infinitely-large functions may be reduced to that of infinitely-small functions (cf. Infinitely-small function), since will be infinitely small.


Comments

See also Infinitesimal calculus.

How to Cite This Entry:
Infinitely-large function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Infinitely-large_function&oldid=33180
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article