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:
(y-δ,y+δ) on the x-axis
Is mapped into the interval (f(y)-ε,f(y)+ε )
on the y-axis.
Try playing with relatively-simple functions like x2
, 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.