Definition
We say that is the limit of a function (), at if the following holds:
For every there exists such that, if then .
(Then we write )
Observe that this uses the absolute value of complex numbers.
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We say that L∈C is the limit of a function (f:D→C), f at z0∈C if the following holds:
For every ε>0 there exists δ>0 such that, if ∣z−z0∣<δ then ∣f(z)−L∣<ε.
(Then we write L=limz→z0f(z))
Observe that this uses the absolute value of complex numbers.