# Thread: Limits and piece-wise defined function?

1. ## Limits and piece-wise defined function?

My TA (teacher's assistant) told me that these kind of problems (with rational/irrational) are always undefined. He's not around right now, so could anyone explain why this is the case?

3. ## Re: Limits and piece-wise defined function?

Originally Posted by Fenixx09
My TA (teacher's assistant) told me that these kind of problems (with rational/irrational) are always undefined. He's not around right now, so could anyone explain why this is the case?
If $\displaystyle \alpha>0$ then there is some $\displaystyle t\in (-\alpha,\alpha)$ which is rational and there is an $\displaystyle s\in (-\alpha,\alpha)$ which is irrational. That is, in any open interval there is a rational and an irrational number. So there are two places 16 units apart. Continuous functions must have values 'close together' at points of continuity.

4. ## Re: Limits and piece-wise defined function?

Thanks, you guys, you helped me a little bit.. I still don't get all of it, so for now I'll just take his word for it.