Show that if $a, b \in \mathbb{R}$ and $a \neq b$, the intersection of the $\epsilon$ neighborhoods of a and b is $\emptyset$

I know the $\epsilon$-neighbordhood for a $\in \mathbb{R}$ is defined as the set $V_\epsilon(a)$ of $x \in \mathbb{R}$ such that |x-a| < $\epsilon$. To prove that the intersection of two neighborhoods for two different elements is the empty set I think I need to show that there are no elements that exist in both neighborhoods. But I don't know how to do that.