In asymptotic analysis, one says that a property holds asymptotically almost surely (a.a.s.) if, over a sequence of sets, the probability converges to 1. For instance, a large number is asymptotically almost surely composite, by the prime number theorem; and in random graph theory, the statement "G(n,pn) is connected" (where G(n,p) denotes the graphs on n vertices with edge probability p) is true a.a.s when pn > for any ε > 0.
In number theory this is referred to as "almost all", as in "almost all numbers are composite". Similarly, in graph theory, this is sometimes referred to as "almost surely".
Read more about this topic: Impossible Event
Famous quotes containing the word surely:
““Why visit the playhouse to see the famous Parisian models, ... when one can see the French damsels, Norma and Diana? Their names have been known on both continents, because everything goes as it will, and those that cannot be satisfied with these must surely be of a queer nature.””
—For the City of New Orleans, U.S. public relief program (1935-1943)