Infinity

Given $g:A\to \mathbb{R}$ and a Limit Point $c$ of $A$, we say that $\underset{x\to c}{lim}g(x)=\mathrm{\infty }$ if, $\mathrm{\forall }M>0$ then $\mathrm{\exists }\delta >0$ such that when $0<|x-c|<\delta$ then $g(x)\ge M$.
We define $\underset{x\to c}{lim}g(x)=-\mathrm{\infty }$ in a similar way by considering only $M<0$ instead.