Re: Prove something about uniformly continuous

On 8 24 , 5 18 , "[Mr.] Lynn Kurtz" <ku...@xxxxxxxxxxxxxxx> wrote:
On Thu, 23 Aug 2007 13:02:49 -0700, Kenshin





<rurouni_sohj...@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- -

- -

I know the rough idea like that, but I can't have the concrete proof.


Sorry for my poor English and math skill ;(

.

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