$\epsilon - \delta$ definition of a limit Where can I find a good explanation of the $\epsilon - \delta$ definition of a limit. I have tried looking at my textbook and it doesn't make much sense, and I have also looked on Google as well looking for a definition. Or maybe someone can explain it on here? I really want to understand the definition of it, but I cant seem to find an explanation that makes sense to me.

So the definition says: $$\lim_{x \to a}f(x) = L$$ means: for all $\epsilon >0$, there exists a $\delta >0$ such that $$0<|x - a| < \delta \Rightarrow |f(x) - L| < \epsilon $$

To understand this definition, you have to know about quantifiers: (for all, there exists). In other words, If for every $\epsilon$, you are able to find a suitable $\delta$, then this proves the limit of $f$ is $L$. When you see in a statement, the word (THERE EXISTS), That means you need to find, to construct and so proving its existence. In this case, you have to find a $\delta$.