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

f(x) is true for sufficiently large x

which is actually shorthand for:

there exists an such that f(x) is true for all .

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 "π = 3, for sufficiently large values of 3".

Other uses in mathematics

A Haken manifold is sometimes called sufficiently large.