Suppose x is real and epsilon > 0. Prove that $\displaystyle (x-\epsilon, \ x+\epsilon)$ is a neighborhood of each of its numbers; in other words, if $\displaystyle y\in (x-\epsilon, \ x+\epsilon)$, then there is a delta > 0 such that $\displaystyle (y-\delta, \ y+\delta)\in (x-\epsilon, \ x+\epsilon)$.

So since $\displaystyle y\in (x-\epsilon, \ x+\epsilon)$, then $\displaystyle x-\epsilon < y< \ x+\epsilon\Rightarrow |y-x|<\epsilon$

I am not sure what to do after that.