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In set theory, when dealing with sets of infinite size, the term almost or nearly is used to refer to all but a negligible amount of elements in the set. The notion of "negligible" depends in the context, and may mean "of measure zero" (in a measure space), "countable" (when uncountably infinite sets are involved), or "finite" (when infinite sets are involved).
- The set is almost for any in , because only finitely many natural numbers are less than .
- The set of prime numbers is not almost , because there are infinitely many natural numbers that are not prime numbers.
- The set of transcendental numbers are almost , because the algebraic real numbers form a countable subset of the set of real numbers (which is uncountable).
- The Cantor set is uncountably infinite, but has Lebesgue measure zero. So almost all real numbers in (0, 1) are members of the complement of the Cantor set.
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- "The Definitive Glossary of Higher Mathematical Jargon — Almost". Math Vault. 2019-08-01. Retrieved 2019-11-16.
- "Almost All Real Numbers are Transcendental - ProofWiki". proofwiki.org. Retrieved 2019-11-16.
- "Theorem 36: the Cantor set is an uncountable set with zero measure". Theorem of the week. 2010-09-30. Retrieved 2019-11-16.