Sufficiently large

Sufficiently large

In mathematics, the phrase sufficiently large is used in contexts such as::P is true for sufficiently large xwhich is actually shorthand for::there exists an ainmathbb{R} such that P is true for all xge a.This does not necessarily mean that any particular value for a is known, but only that such an a exists. The phrase "sufficiently large" should not be confused with the phrases "arbitrarily large" or "infinitely large".

"Sufficiently large" is sometimes the subject of mathematical humor; for example, as in the mathematician's joke "1+1 = 3, for sufficiently large values of 1".

Other uses in mathematics

A Haken manifold is sometimes called sufficiently large.

ee also

*Mathematical jargon


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