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Other usesUnreferenced|date=December 2009In 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 .
In other words, an infinite set S that is a subset of another infinite set L , is almost L if the subtracted set L \ S is of finite size.
Examples:
The set is almost N for any k in N , because only finitely many natural number s are less than k .
The set of prime number s 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 uncountable set|uncountably infinite , but has Lebesgue measure zero. So a real number in (0, 1) is a member of the Complement (set theory)|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).
See also
Wiktionarypar|almost
Almost all
Almost surely
Category:Mathematical terminology Category:Set theory
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