"Almost all" is sometimes used synonymously with "all but finitely many" (formally, a cofinite set) or "all but a countable set" (formally, a cocountable set); see almost. An example of this usage is the Frivolous Theorem of Arithmetic, which states that almost all natural numbers are very, very, very large.
When speaking about the reals, sometimes it means "all reals but a set of Lebesgue measure zero" (formally, almost everywhere). In this sense we can say "almost all reals are not a member of the Cantor set".
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 (not prime), however there are still an infinite number of primes.
Stand-Down of Los Alamos National Laboratory: Total Costs Uncertain; Almost All Mission-Critical Programs Were Affected but Have Recovered.
Jan 01, 2006; GAO-06-83 November 18, 2005 On July 16, 2004, the director of the Los Alamos National Laboratory (LANL) declared a suspension, or...