Uniform Continuity

This Demonstration illustrates a theorem of analysis: a function that is continuous on the closed interval is uniformly continuous on the interval.

A function is continuous if, for each point and each positive number , there is a positive number such that whenever , . A function is uniformly continuous if, for each positive number , there is a positive number such that for all , whenever, . In the first case depends on both and ; in the second, depends only on .