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## Main Question or Discussion Point

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 [itex]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[/itex]

In words: A is a limit of f as x approaches a if and only if for every sequence [itex](x_n)[/itex] converging to

EDIT: tiny error correction

Limit of a function: Heine criterion:

Given [itex]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[/itex]

In words: A is a limit of f as x approaches a if and only if for every sequence [itex](x_n)[/itex] converging to

*a*such that [itex]x_n\neq a[/itex] their respective function f values converge to*A*.EDIT: tiny error correction

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