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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 on the context, and may mean "of measure zero" (in a measure space), "finite" (when infinite sets are involved), or "countable" (when uncountably infinite sets are involved).

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