Java Applet: Illustrating Uniform Continuity

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Context Context
  1. Click on Options for Control panel
  2. Select a given epsilon
  3. Guess a positive delta
  4. Hit Apply to use new delta
  5. Slide and zoom using buttons
  • [+] zoom in and center
  • [-] zoom out and center
  • [ slide to left
  • [<]> slide to right
If, for any given epsilon you can find a positive delta such that the red area touches the graph always inside the green area no matter which part of the graph you are focusing on then your function is uniformly continuous.

Your browser can not handle Java Applets ...
  1. Click on Options for Control panel
  2. Select a given epsilon
  3. Guess a positive delta
  4. Hit Apply to use new delta
  5. Slide and zoom using buttons
  • [+] zoom in and center
  • [-] zoom out and center
  • [ slide to left
  • [<]> slide to right
If, for any given epsilon you can find a positive delta such that the red area touches the graph always inside the green area no matter which part of the graph you are focusing on then your function is uniformly continuous.
The first function is uniformly continuous, the second function is continuous, but not uniformly continuous on the real line.

Compare with regular continuity.

Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007