i need to show the following function is not continuous anywhere else but 0.
if x is rational
if x is irrational
I have read the guide on epsilon delta proof and have managed to work out part of it, i have found that it is continuous at 0, and that is fine and completed.
I'm very stuck on the rest though. I tried to do this:
If a is a rational number there exists a set of numbers that converge to f(a).
If a is an irrational number, there exists a set of numbers that converge to f(a).
which are different, and therefore the function is not continuous when x is not 0.
Is this a valid proof?