I'm stuck on how to do this proof.

I thought I might start like this...Originally Posted byGaugan. Introduction To Analysis, 5th ed, p105

Choose . By definition of continuity, for each , there exists such that if and , then .

That way, if I can somehow show that , then I could just finish thusly:

Choose . Then for each and , if and , then .

But how do I show that ? Or, if that's impossible, then perhaps instead of setting , I could set it to , and then somehow show a relationship between and . But I wouldn't know how to do that, either.

Please advise.