Will someone help me with this, I PMed Perfect Hacker and he helped me but I am still a little unclear, but he isn't here and I am impatient.

My book asked to explain what uniform convergence meant in your own words. Would someone point out any mistakes in my comprehension if there is any.

Let

be convergent on the interval . Furthermore let [tex]

Now my understanding of uniform convergence (I really couldn't tell if this was wrong since TPH didn't adress it directly) is that not only does

as that but we have that

Next it asked to prove that

My first step was saying that not only is

But that

And also I noted that

Now we see that

Therefore

is convergent

Therefore

is uniformly convergent on by the Weirstrass M-test

This implies that

Does that look right?