# uniform continuity theorem

• May 20th 2010, 09:34 AM
cp05
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?
• May 20th 2010, 09:41 AM
Drexel28
Quote:

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 $\displaystyle f\left(\frac{1}{n}\right)$ isn't Cauchy?
• May 20th 2010, 10:03 AM
cp05
I meant f=1/x, f:[0,1] -> R
• May 20th 2010, 11:03 AM
Defunkt
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.