- #1

saminny

- 9

- 0

This may sound lame but I am not able to get the definition of uniform continuous functions past my head.

by definition:

A function f with domain D is called uniformly continuous on the domain D if for any eta > 0 there exists a delta > 0 such that: if s, t D and | s - t | < delta then | f(s) - f(t) | < eta. Click here for a graphical explanation.

I can just choose "delta" that is a large number that will make any 2 points on the curve satisfy this condition. 1/x would be uniform continuous if I simply choose a large enough delta.

moreover, what is the utility and application of uniform continuous fynctions?

thanks,

Sam