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Math Help - Limits and piece-wise defined function?

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    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?


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    Re: Limits and piece-wise defined function?

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    Re: Limits and piece-wise defined function?

    Quote Originally Posted by Fenixx09 View Post
    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?
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    If \alpha>0 then there is some t\in (-\alpha,\alpha) which is rational and there is an 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.
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    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.
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