If $a_{n} = \frac{-1}{2}, \frac{1}{3}, \frac{-1}{4}, \frac{1}{5} ...$ It is clear to me by intuition that the limit point is $0$. But according to Rudin, "A point $p$ is a limit point of the set $E$ if every neighborhood of $p$ contains a point $q \neq p$ such that $q \in E$.
I'm having trouble understanding why $\frac{-1}{2}$ is not a limit point by the definition given in Rudin. Could someone explain?