Given a property 
,
if 
as 
(so, using asymptotic
notation, the number of numbers less than 
not satisfying the property 
is 
,
where 
is one of the so-called Landau
symbols), then 
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 All
See also
Almost Surely, Asymptotic Notation, For All, Landau Symbols, Normal OrderExplore with Wolfram|Alpha
References
Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, p. 50, 1999.Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, p. 8, 1979.Referenced on Wolfram|Alpha
Almost AllCite this as:
Weisstein, Eric W. "Almost All." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlmostAll.html