Quote by Flying_Goat
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.

Another approach is :
The description can also be interpreted as saying that one can find, for any ε>0, a value of δ>0 every point x in the interval:
(yδ,y+δ) on the xaxis
Is mapped into the interval (f(y)ε,f(y)+ε )
on the yaxis.
Try playing with relativelysimple functions like x
^{2}, and see what happens with
the expression f(x+δ)f(x), for different values of δ, and how you can choose δ to make the difference be within ε.