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Homework Help: Equivalence relations 2

  1. Nov 3, 2009 #1
    This is a question from A consise introduction to pure mathematics (Martin Liebeck)

    Hi guys, just stuck on one problem was wondering if someone could lend me hand.

    Let ~ be an equivalence relation on all intergers with the property that for all "m" is an element of the set of intergers , we have,

    m ~ m +5
    and also m ~ m+8

    Prove that m~ n for all m, n is an element of intergers.

    This is on page 161 of Martin Liebeck's book, number 7.

    Im really stuck!
  2. jcsd
  3. Nov 3, 2009 #2


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    didn't i see this posted a few days ago?

    anyways, noinking the solution form those posts, use repeated applications of the equivalence relation to show for any n:
    n ~ n+1,

    then you're pretty much done, maybe with induction implicit, but it should be reasonably easy to see that any n is equivalent to any m, witr repeated application of the above
    Last edited: Nov 3, 2009
  4. Nov 3, 2009 #3


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    Hint: can you show m~m+15 and m~m+16? Then you are almost there.
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