Increment theorem

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In non-standard analysis, a field of mathematics, the increment theorem states the following: Suppose a function y = f(x) is differentiable at x and that Δx is infinitesimal. Then

for some infinitesimal ε, where

If then we may write

which implies that , or in other words that is infinitely close to , or is the standard part of .

See also[edit]