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?