Generalizations and Related Usages
The generalization to functions taking values in any normed vector space is straightforward (replacing absolute values by norms), where f and g need not take their values in the same space. A generalization to functions g taking values in any topological group is also possible. The "limiting process" x→xo can also be generalized by introducing an arbitrary filter base, i.e. to directed nets f and g. The o notation can be used to define derivatives and differentiability in quite general spaces, and also (asymptotical) equivalence of functions,
which is an equivalence relation and a more restrictive notion than the relationship "f is Θ(g)" from above. (It reduces to if f and g are positive real valued functions.) For example, 2x is Θ(x), but 2x − x is not o(x).
Read more about this topic: Big O Notation
Famous quotes containing the word related:
“Generally there is no consistent evidence of significant differences in school achievement between children of working and nonworking mothers, but differences that do appear are often related to maternal satisfaction with her chosen role, and the quality of substitute care.”
—Ruth E. Zambrana, U.S. researcher, M. Hurst, and R.L. Hite. “The Working Mother in Contemporary Perspectives: A Review of Literature,” Pediatrics (December 1979)