In the context of this answer to another question about representing I thought of the following possible description of the limit of a function:
$\lim_{x\to a}f(x)=y$ iff $(a,y)$ is an accumulation point of $f$ (interpreted as a set of pairs) and there's no $y′≠y$ so that $(a,y′)$ is also an accumulation point of $f$.
Now my question is: Is that claim correct?