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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).^{[1]}

For example:

- 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 number (the latter of which is uncountable).**^{[2]} - The Cantor set is uncountably infinite, but has Lebesgue measure zero.
^{[3]}So almost all real numbers in (0, 1) are member of the complement of the Cantor set.

Look up in Wiktionary, the free dictionary.almost |

**^**"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.

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