Let $$X$$ be a subset of $$\mathbb{R}$$, let $$f : X \to \mathbb{R}$$ be a function, let $$E$$ be a subset of $$X$$, let $$x_0$$ be an adherent point of $$E$$, let $$L$$ be a real, and let $$\varepsilon > 0$$ be a real. Then the following two statements are logically equivalent:
• $$f$$ converges to $$L$$ at $$x_0$$ in $$E$$.