Define this limit $\lim_{x\to a}f(x)=∞.$ If someone could give me a definition for that I would be eternally thankful. So far I have for any $N>0$, there exists a $\delta>0$ such that $0<x-a<\delta$, then $f(x)>N$. Is this right?

The definition is:

> For all $N>0$ there is a $\delta > 0$ such that if $0 < \lvert x - a \rvert < \delta$ then $f(x) > N$.

It looks like the limit you have written is the definition of the right-side limit. Note that $0 < \lvert x - a \rvert < \delta$ is equivalent to $-\delta < x-a < \delta$ and $x\
eq a$.