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Math Help - discrete math proof

  1. #1
    Member
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    Sep 2008
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    discrete math proof

    I need some urgent help on this question.

    It says we have to prove that


    floor of(5*x)- 5* (floor of x ) <4.1





    I have been struggling this problem from past goddamn 6 hours :| wth
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  2. #2
    MHF Contributor

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    You have \lfloor 5x\rfloor \leq 5x and \lfloor x\rfloor > x-1, hence \lfloor 5x\rfloor - 5\lfloor x\rfloor < 5x - 5(x-1)=5. Moreover, \lfloor 5x\rfloor - 5\lfloor x\rfloor is an integer, so that the previous inequality is equivalent to \lfloor 5x\rfloor - 5\lfloor x\rfloor\leq 4.
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