This Illustration shows that signum function can fulfil the ϵ{\displaystyle \epsilon }-δ{\displaystyle \delta }-criterion at the point x0=0{\displaystyle x_{0}=0} when ϵ{\displaystyle \epsilon } is big enough. Here ϵ=32{\displaystyle \epsilon ={\tfrac {3}{2}}} is choosen.
Own work
Stephan Kulla (User:Stephan Kulla)