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Sufficiently large

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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:

\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.

See also

  • Mathematical jargon

References

MathWorld.

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