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 $ainmathbb\{R\}$ 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.

See also

• Mathematical jargon