Which of the following functions f are continuous at the point a=3 and a=2.5:
f(x)=x if x is an integer.
f(x)=0 if x is not an integer.
I know the function is not continuous at a=3 and is continuous at a=2.5 but how do i prove this using Cauchy definition (epsilon-delta) of continuous functions.
Thank you.
The usual definition of continuity is; f is continuous at a point x if . If you want to use your definition, think about what happens if . You don't need to worry about large distances away from a (if you prove it for small h, then if 0<h<"a number bigger than 1", then you pick h<1).