In mathematics, the phrase sufficiently large is used in contexts such as:
f(x) is true for sufficiently large x
which is actually shorthand for:
there exists an such that f(x) 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 "π = 3, for sufficiently large values of 3".
Other uses in mathematics
A Haken manifold is sometimes called sufficiently large.
Often the audience is not quite aware just how large, 'sufficientlylarge' really is. It can be as large, or considerably larger than the number of fundamental particles (atoms, (baryons, leptons)) in the universe.
Sufficientlylarge can be really big in the way that space is not.
For those with sufficient experience it serves as a marker to ask the question "How large are we talking about?" For example, HeapSort is faster than BubbleSort for sufficientlylarge N - how large, when does the change-over occur?
In mathematics, the phrase sufficientlylarge is used in contexts such as:
The phrase "sufficientlylarge" should not be confused with the phrases "arbitrarily large" or "infinitely large".
"Sufficientlylarge" is sometimes the subject of mathematical humor; for example, as in the mathematician's joke "π = 3, for sufficientlylarge values of 3".
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