Almost

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 $$ S = \{ n \in \mathbb{N}\,|\, n \ge k \} $$ is almost $$\mathbb{N}$$ for any $$k$$ in $$\mathbb{N}$$, because only finitely many natural numbers are less than $$k$$.
 * The set of prime numbers is not almost $$\mathbb{N}$$, because there are infinitely many natural numbers that are not prime numbers.
 * The set of transcendental numbers are almost $$\mathbb{R}$$, 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,&thinsp;1) are members of the complement of the Cantor set.