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Sufficiently Large


If P(n) is a sentential formula depending on a variable n ranging in a set of real numbers, the sentence

 P(n) for every sufficiently large n
(1)

means

  exists N such that P(n)  forall n>N.
(2)

An example is the proposition

 1/(n^2)<0.0001 for every sufficiently large n,
(3)

which is true, since the inequality is fulfilled for n>100.

The statement can also be rephrased as follows: the terms of the sequence {1/(n^2)}_(n=1)^infty become eventually smaller than 0.0001.

There are various mathematical jokes involving "sufficiently large." For example, "1=2 for sufficiently large values of 1" and "this feature will ship in version 1.0 for sufficiently large values of 1."


See also

Large Number

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Sufficiently Large." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SufficientlyLarge.html

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