Finding a proper sequence The following function was given to me $$f(x)=\lfloor x\rfloor+\lfloor-x\rfloor$$ wherein $\lfloor x\rfloor$ is the floor function of $x$. I was asked to select a proper sequence for showing that this function has no limit at $\infty$. Honestly, my knowledge about analysis is weak. Thank you

Take $$f(n)=[n]+[-n]=n-n=0, \quad n\in\mathbb{N},$$ and then take $$f\left(\frac{2n+1}{2}\right)=n+(-n-1)=-1, \quad n\in\mathbb N$$

Then you have two different sequences with different limits when $\,n\to\infty\,$ and thus the limit at $\,\infty\,$ doesn't exist.