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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 $ainmathbb\{R\}$ such that $P$ is true for all $xge\; a$.
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".

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Other uses in mathematics

See also

Other uses in mathematics

A Haken manifold is sometimes called 'sufficiently large'.

See also

★ Mathematical jargon