# Identifying the name of a theorem

I can't find sufficient material for this theorem in my own languages so I have to resort to English, however, googling "Heine criterion" yields nothing significant so I think, once again I just can't get its English name right.

Limit of a function: Heine criterion:
Given $f\colon D\to\mathbb{R}, \lim\limits_{x\to a} f = A\Leftrightarrow \forall (x_n)\to a\colon x_n\neq a \Rightarrow f(x_n)\to A$
In words: A is a limit of f as x approaches a if and only if for every sequence $(x_n)$ converging to a such that $x_n\neq a$ their respective function f values converge to A.

EDIT: tiny error correction

Last edited: