While I'm looking at this assertion:
Suppose $f(x)$ is uniformly continuous on $[0,\infty)$ and $\forall h>0$，$\displaystyle\lim_{n\to\infty} f(nh)$ exists, then $\displaystyle\lim_{x\to\infty} f(x)$ exists.
I wonder what happens if we just assume nothing or $f$ is only continuous. Is there a counterexample?
