I just want to make sure i'm doing these correctly.

I need to find when .Prove that is continuous at 0.

Let (since i'm interested in continuity at the origin).

Therefore I need to find when .

Let .

for .

(since ) for \ .

Therefore pick such that .

That's the preliminary work done, so here's the proof.

Let and define When :

for

for \

My one issue is that the method i've used is extremely similar to a method someone showed me how to use for another question. I also haven't used the properties of rational and irrational numbers as I would have liked.

Is this right?