a) Show that $N$ = {1,2,...} is closed in $\mathbb R$
b) Show that $Z$ $\times$ $Z$, where $Z$ = {0, $\pm$1, $\pm$2,...} is closed in $\mathbb R^2$
I am not sure how to prove this homework question, should I start with claiming that $N$ is closed if $R$ \ $N$ is open. Could you help me to prove these two?