
Glossary: Prime Pages: Top 5000: 
Suppose f(x) and g(x) are real valued
functions defined for all x > x_{0}
(where x_{0} is a fixed positive real).
We write
f(x) = o(g(x))if the limit as x approaches infinity of f(x)/g(x) is zero (that is, if eventually f(x)/g(x) becomes less than any given positive number). Examples: 10000x = o(x^{2}), log(x) = o(x), and x^{n} = o(e^{x}). Notice that f(x) = o(g(x)) implies, and is stronger than, f(x) = O(g(x)). We often use the littleoh notation this way: f(x) = g(x) + o(h(x)).This intuitively means that the error in using g(x) to approximate f(x) is negligible in comparison to h(x). The littleoh notation was first used by E. Landau in 1909.
See Also: BigOh, SameOrderofMagnitude, AsymptoticallyEqual
Chris K. Caldwell © 19992018 (all rights reserved)
