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In my study on the concept of limit, I've come across two different definitions:
Let's assume that $a \in \bar D$, i.e. $a$ belongs to the closure of the domain of function $f$. Then $\lim_{x\rightarrow a}f(x)=b$
$\forall_{\epsilon>0}\exists_{\delta>0}\forall_{x}\ \ x\in D
\land|x-a|<\delt...