# Math Help - Real Analysis Proof

1. ## Real Analysis Proof

Can someone check my work? I've attached it. Thanks!

2. It is wrong. Becauase $y\not = f(x)$, $y$ is some other point in the set. So $|x-y|<\delta$ are all points in the set so that this is true and not $|x-f(x)|<\delta$.

3. Originally Posted by ThePerfectHacker
It is wrong. Becauase $y\not = f(x)$, $y$ is some other point in the set. So $|x-y|<\delta$ are all points in the set so that this is true and not $|x-f(x)|<\delta$.
Ok, change all the f(x)'s to y's. Then, I think, it is correct.

4. TPH, how does it look now? Attached the new one.

5. Good proof.

In the second part where you show $(0,1]$ is not unfiormly continous, trying using the definition, i.e. show (without Cauchy sequences) that you can violate the definition of uniform continuity.