I was solving this problem:
For the following {$f_n$} sequence, determine the pointwise limit of {$f_n$} (if it exists) on the invterval, and indicate if {$f_n$} converges uniformly towards this function.$$f_n(x)=\sqrt[n]{x}, on [0,1]$$
I ended up with the pointwise limit being $\lim_{n\to\infty}x^{1/n}=1$ if $0<x\leq 1$ and $\lim_{n\to\infty}x^{1/n}=0$ if $x=0$. My problem is to determine if it does or doesn't converge uniformly, I saw a question about it on this website, but I didn't understand it. The answer was that it doesn't converge uniformly, can you explain me why? Thanks.
Hint:
$$|1 -f_n(2^{-n})| = \frac{1}{2} \not\to 0$$