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Math Help - Question about two functions..

  1. #1
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    Question about two functions..

    Is the following statement true?

    If two functions, f and g (both R -> R) have the same one-sided limit (left-sided limit, for isntance) in every real point, then f=g. In other words,



    Is it true? If it is.. is there a proof? If it isn't could you give me a counter-example? ..

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  2. #2
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    Re: Question about two functions..

    Quote Originally Posted by oneminiketchup View Post
    Is the following statement true?
    If two functions, f and g (both R -> R) have the same one-sided limit (left-sided limit, for isntance) in every real point, then f=g. In other words, Is it true? If it is.. is there a proof? If it isn't could you give me a counter-example? ..

    Consider f(x) = \left\lceil x \right\rceil  - 1\;\& \;g(x) = \left\lfloor x \right\rfloor
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    Re: Question about two functions..

    Well then for.. x0=1 for instance.. left-sided limit for f is 0-1=-1 and for g it's 0 ..
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    Re: Question about two functions..

    Quote Originally Posted by oneminiketchup View Post
    Well then for.. x0=1 for instance.. left-sided limit for f is 0-1=-1 and for g it's 0 ..
    No that is not correct: {\lim _{x \to {1^ - }}}\left\lceil x \right\rceil  - 1 = 0
    Last edited by Plato; March 11th 2013 at 04:11 AM.
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