1. ## Uniform Convergence

Am I right in saying that if I have $f_n=\frac{x^n}{x^n+1}$ and

$f(x) = \left\{\begin{array}{c l} 0 & x \in [0,1)\\ 0.5 & x =1 \\ 1 & x\in(1,\infty)\end{array}\right.$

definied on $(0,\infty)$ is not uniform convergent to f(x) (the problem being near the 1)?

Thanks for any help

2. ## Re: Uniform Convergence

According to the uniform limit theorem, the uniform limit of a sequence of continuous functions is continuous, so you are right.

3. ## Re: Uniform Convergence

Cool thanks (I have proved it from the definition, which is a lot longer, feel a bit foolish now for asking!) it is pointwise convergent to f(x) though right?

4. ## Re: Uniform Convergence

Yes.

Hint: To avoid <br/> in LaTeX formulas, remove all line breaks between $$and$$ (not LaTeX line breaks \\; just put the whole formula on one editor line).

5. ## Re: Uniform Convergence

Thanks very much for all the help (sorry about the poor LaTex and thanks for editing it)

6. ## Re: Uniform Convergence

Ha, it was Plato who edited it!