Thread: uniform continuity theorem

The uniform continuity theorem says if f: A->N is continuous and Kin A is compact, then f is uniformly continuous on K.

But if I take 1/n on [0,1] it is not uniformly continuous because as we approach 0 from the left the y values get further and further apart. Is tehre something I'm missing in this theorem?

Originally Posted by cp05

The uniform continuity theorem says if f: A->N is continuous and Kin A is compact, then f is uniformly continuous on K.

But if I take 1/n on [0,1] it is not uniformly continuous because as we approach 0 from the left the y values get further and further apart. Is tehre something I'm missing in this theorem?

This makes no sense whatsoever. What's your function? Are you saying that isn't Cauchy?

I meant f=1/x, f:[0,1] -> R

f is not defined at 0, therefore not continuous there. That theorem requires (although you didn't state it) that f is continuous in K.