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Sufficiently large

 
Wikipedia: Sufficiently large

In mathematics, the phrase sufficiently large is used in contexts such as:

P is true for sufficiently large x

which is actually shorthand for:

there exists an a\in\mathbb{R} such that P is true for all x\ge 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.[citation needed]

See also


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