If $\{h_{k}\}_{k=1}^{\infty}$ is a sequence of real-valued continuous functions on the real line, and $0
Thanks for help in advance!
Ok, what I have tried: I'm trying to use induction on $x_{k}$: Fix any $x\in\mathbb{R}, $we have
for $x_{1}$: $h_{k}(x+x_{1})\to 0$
for $x_{2}$: $h_{k}(x+x_{2})\to 0$
for $x_{3}$: $h_{k}(x+x_{3})\to 0$
.
.
.
for $x_{m}$: $h_{k}(x+x_{m})\to 0$
so, its true for all $m$, hence for $k$. Not sure!
Edit: I had a typo, sorry. My previous question was about $h_{k}(x_{k})\to 0$, but the correct question is about $h_{k}(x+x_{k})\to 0$