Word of the Day - Paying tribute to my mathematical friends; (PS Who talks like this) Asymptotic, formally, given complex-valued functions f and g of a natural number variable n, one writes; f sim g quad ( ext{as } n oinfty) to express the fact, stated in terms of little-o notation, that f(n) = g(n) + o(g(n))quad( ext{as }n oinfty),, or equivalently f(n) = (1+o(1))g(n)quad( ext{as }n oinfty). Explicitly this means that for every positive constant ε there exists a constant N such that |f(n)-g(n)|leqvarepsilon|g(n)|qquad ext{for all }ngeq N~. Unless g(n) is infinity or zero (which would make the limit below undefined), this statement is also equivalent to lim_{n oinfty} frac{f(n)}{g(n)} = 1. This relation is an equivalence relation on the set of functions of n. The equivalence class of f informally consists of all functions g which are approximately equal to f in a relative sense, in the limit.
Posted on: Thu, 20 Jun 2013 18:51:45 +0000
Trending Topics
Recently Viewed Topics
© 2015