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Math Help - discontinuous and continuous

  1. #1
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    discontinuous and continuous

    Give an example of a function f: \mathbb R \rightarrow \mathbb R which is discontinuous at all points of \mathbb Z and continuous at all points of \mathbb R\\\setminus \mathbb Z. Then prove the example has these properties.

    Can anyone please help me with this question? Thanks a lot.
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  2. #2
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    What ideas have you had so far?
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  3. #3
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    Quote Originally Posted by tsang View Post
    Give an example of a function f: \mathbb R \rightarrow \mathbb R which is discontinuous at all points of \mathbb Z and continuous at all points of \mathbb R\\\setminus \mathbb Z. Then prove the example has these properties.
    HINT: Think stair step.
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    Quote Originally Posted by Plato View Post
    HINT: Think stair step.
    Hi,thank you.But I still don't really understand what I can do.
    Can I just say something like f(x)=1 for all \mathbb R\\\setminus \mathbb Z, and f(x)=0 for all  \mathbb Z
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  5. #5
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    Quote Originally Posted by tsang View Post
    Hi,thank you.But I still don't really understand what I can do.
    f(x) = \left\lfloor x \right\rfloor was my suggestion.

    But yes, f(x)=1 for all \mathbb R\\\setminus \mathbb Z, and f(x)=0 for all  \mathbb Z will work.
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