Sufficiently large
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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
such that P is true for all 
.
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".
[edit] Other uses in mathematics
A Haken manifold is sometimes called sufficiently large.[citation needed]
