Sufficiently large

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

A sufficiently large manifold is a manifold containing a properly embedded 2-sided incompressible surface.

References

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

Sufficiently large

Other uses in mathematics

See also

References