Limit of real-valued function on $\mathbb{R}$

Asked Oct 25 '19 at 01:07

Active Oct 25 '19 at 01:07

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I have to give an answer to an assignment question and I don't know where to start. I would prefer the direction of how to solve it instead of an explicit answer since I have no work done on it yet.

Let $f$ be a continuous real-valued function on $\mathbb{R}$ with the property that for each real number $x$, $\lim_{n\rightarrow \infty} f(nx)=0$. Show that $\lim_{x\rightarrow \infty} f(x) = 0$.

Thank you!

asked Oct 25 '19 at 01:07

FatFeynman

Do you know the Baire Category Theorem? – Axion004 Oct 25 '19 at 01:16
you may make use of the following question and its answers https://math.stackexchange.com/q/3407107 – Mirko Oct 25 '19 at 03:04
This question was already asked and anwered here: enter link description here – Samdney Oct 25 '19 at 09:31

Limit of real-valued function on $\mathbb{R}$

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