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Almost All

Given a property $P$, if $P(x)\sim x$ as $x\to\infty$ (so the number of numbers less than $x$ not satisfying the property $P$ is $o(x)$), 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).

See also For All, Normal Order


Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, p. 8, 1979.

© 1996-9 Eric W. Weisstein