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", "finite", or "countable".
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.
- The Cantor set is uncountably infinite, but has Lebesgue measure zero. So almost all real numbers in are members of the complement of the Cantor set.