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In mathematics, especially in set theory, when dealing with sets of infinite size, the term almost or nearly is used to mean all the elements except for finitely many. ## See also

In other words, an infinite set S that is a subset of another infinite set L, is almost L if the subtracted set LS is of finite size.

Examples:

- The set $S\; =\; \{\; n\; in\; mathbf\{N\}\; |\; n\; ge\; k\; \}$ is almost N for any k in N, because only finitely many natural numbers are less than k.
- The set of prime numbers is not almost N because there are infinitely many natural numbers that are not prime numbers.

This is conceptually similar to the almost everywhere concept of measure theory, but is not the same. For example, the Cantor set is uncountably infinite, but has Lebesgue measure zero. So a real number in (0, 1) is a member of the complement of the Cantor set almost everywhere, but it is not true that the complement of the Cantor set is almost the real numbers in (0, 1).

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Last updated on Tuesday September 30, 2008 at 18:35:47 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Tuesday September 30, 2008 at 18:35:47 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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