Re: Prove something about uniformly continuous

On Thu, 23 Aug 2007 13:02:49 -0700, Kenshin
<rurouni_sohjiro@xxxxxxxxxxx> wrote:

A is nonempty subset of R(eal number)
A : bounded

f : uniformly continuous

f : A -> R

f(A) is bounded?


I wanna prove this by using the definition of uniformly conti
positively...

I've already know the proof making the compact set(the set of limit
points of A).


Is that last sentence a sentence?

Hint: Let eps = 1, find delta. Pick a point p in A. How far away from
f(p) can f get in a 2 delta size interval from p? How many such
intervals to cover A? So...

--Lynn
.