Sufficiently large

From Wikipedia, the free encyclopedia

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 $a\in\mathbb{R}$ such that

f (x)

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