Almost The Truth (Lawyers Cut)

In set theory, when dealing with set (mathematics), sets of infinite set, 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 $S = \$ is almost $\mathbb$ for any $k$ in $\mathbb$, because only finitely many natural numbers are less than ''$k$''.
*The set of prime numbers is not almost $\mathbb$, because there are infinitely many natural numbers that are not prime numbers.
*The set of transcendental numbers are almost $\mathbb$, because the algebraic number, algebraic real number, 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 (set theory), complement of the Cantor set.

See also

*Almost all
*Almost surely
*Approximation
*List of mathematical jargon

References

Mathematical terminology
Set theory

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