From Wikipedia:
For functions on the real line, one way to define the limit of a function is in terms of the limit of sequences. In this setting: $ \lim_{x\to a}f(x)=L $ if and only if for all sequences $x_n$ converging to $a$ the sequence $f(x_n)$ converges to $L$.
I was considering the case when $\lim_{x\to a}f(x) \neq f(a)$ and $x_n=a$ for any $n \geq n_0$ and some $n_0 \in \mathbb{N}$. Isn't this case a counterexample to both "if" and "only if" parts? If yes, how shall the quote be modified?
Thanks and regards!