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Math Help - Relation

  1. #1
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    Relation

    Define the relation R on the real numbers R by xRy if and only if [x] = [y] where [.] is the greatest integer function, that is, [t] is defined to be the greatest integer less than or equal to t.
    Prove that for every x E R there exists a y E Z such that x E y/R.

    I dont know where to start
    plz help thanks
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  2. #2
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    Quote Originally Posted by logglypop View Post
    Define the relation R on the real numbers R by xRy if and only if [x] = [y] where [.] is the greatest integer function, that is, [t] is defined to be the greatest integer less than or equal to t.
    Prove that for every x E R there exists a y E Z such that x E y/R.
    If \mathbb{Z} is the set of integers then x\mathcal{R}y if and only if \left( {\exists n \in \mathbb{Z}} \right)\left[ {\left\{ {x,y} \right\} \subset \left[n,n + 1\right)} \right]
    Last edited by Plato; April 1st 2010 at 02:21 PM.
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