Hello

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).

So

If a is an irrational number, there exists a set of numbers

that converge to f(a).

So

which are different, and therefore the function is not continuous when x is not 0.

Is this a valid proof?

Many Thanks