Given a property P, if P(x)~x as x->∞ (so, using asymptotic notation, the number of numbers less than x not satisfying the property P is o(x), where o(x) is one of the so-called Landau symbols), then P is said to hold true for almost all numbers. For example, almost all positive integers are composite numbers (which is not in conflict with the second of Euclid's theorems that there are an infinite number of primes).

almost surely | asymptotic notation | for all | Landau symbols | normal order