Set theory | Mathematical terminology
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). * 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. (Wikipedia).
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From playlist Stability and Testability
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From playlist Science Unplugged: Big Ideas