# Almost

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In set theory, when dealing with sets of infinite size, the term **almost** or **nearly** is used to mean *all the elements except for finitely many*.

In other words, an infinite set *S* that is a subset of another infinite set *L*, is **almost** *L* if the subtracted set *L*\*S* is of finite size.

Examples:

- The set is almost
**N**for any*k*in**N**, because only finitely many natural numbers are less than*k*. - The set of prime numbers is not almost
**N**because there are infinitely many natural numbers that are not prime numbers.

This is conceptually similar to the *almost everywhere* concept of measure theory, but is not the same. For example, the Cantor set is uncountably infinite, but has Lebesgue measure zero. So a real number in (0, 1) is a member of the complement of the Cantor set *almost everywhere*, but it is not true that the complement of the Cantor set is *almost* the real numbers in (0, 1).