A function defined on ℝ is continuous at x if given ε, there is a δ such that f(x)f(y)<ε whenever xy<δ. Does this imply that f(x+δ)f(x)=ε? The definition only deals with open intervals so i am not sure about this. If this is not true could someone please show me a counter example for it?
Any help would be appreciated. Thanks.
