ε-δ

The notation:

$\lim_{x\rightarrow c} f(x)=L$

... means:

$∀ε>0:∃δ(ε,x)>0:∀x:(0<|x-c|<δ\Rightarrow |f(x)-L|<ε)$

Continuity

$\lim_{x\rightarrow c} f(x)=f(c)$

If δ is only a function of ε, not of x.

Author: Danny (remove the ".nospam" to send)

Last modification on: Sat, 04 May 2024 .