The formal $$\varepsilon$$-$$\delta$$ definition of a finite limit at a point $$a\in \mathbb{R}$$ is:
$$\Big(\lim_{x\rightarrow a} f(x) = L \Big)\iff \Big(\forall \varepsilon >0\, \exists \delta > 0: \forall x\in D\quad 0<\vert x-a\vert <\delta \implies \vert f(x)-L\vert <\varepsilon \Big)$$