# Almost all

In mathematics, the phrase**almost all**has three specialised uses:

- "Almost all" is sometimes used synonymous with "all but finitely many"; see almost.
- In number theory, if
*P*(*n*) is a property of positive integers, and if*p*(*N*) denotes the number of positive integers*n*less than*N*for which*P*(*n*) holds, and if*p*(*N*)/*N*tends to 1 as*N*tends to ∞ (see limit), then we say that "*P*(*n*) holds for almost all positive integers*n*". For example, the prime number theorem states that the number of prime numbers less than or equal to*N*is asymptotically equal to*N*/ln*N*. Therefore the proportion of prime integers is roughly 1/ln*N*, which tends to 0. Thus, almost all positive integers are composite. - Occasionally, "almost all" is used in the sense of "almost everywhere" in measure theory.

## See also