Sufficiently large

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

P is true for sufficiently large x

which is actually shorthand for:

\exists~ a\in\mathbb{R} such that P is true \forall~ 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".

Other uses in mathematics[edit]

See also[edit]


Weisstein, Eric W., "Sufficiently Large", MathWorld.