Illustration that the signum function is not continuous at the point x=0{\displaystyle x=0} with ϵ=12{\displaystyle \epsilon ={\tfrac {1}{2}}} and δ=12{\displaystyle \delta ={\tfrac {1}{2}}}. The point x=δ2{\displaystyle x={\tfrac {\delta }{2}}} is marked red.
Own work
Stephan Kulla (User:Stephan Kulla)