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Math Help - help understanding an equivalence relation

  1. #1
    Junior Member scottie.mcdonald's Avatar
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    Williamstown, Ontario, Canada
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    help understanding an equivalence relation

    I'm having trouble understanding what the professor ment when he wrote/explained this:

    A= integers, xRy iff 4|(x-y)

    [0]={yE integers: yR0}
    ={yE integers: 4|0}
    ={multiples of 4+1}

    note: -that yE integers means y is an element of integers
    -iff means if and only if
    -| means divides
    -yR0 means y is in relation to 0 (or so i read it)

    -why are we saying that yE integers instead of saying that x,yE integers? are we trying to show reflexivity in this case?

    -why does 4|0? if we were to use the equivalence relation [1] or [2], would it then be 4|[1] or 4|[2]?

    any brief explanation would be great =)
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  2. #2
    Junior Member scottie.mcdonald's Avatar
    Joined
    Jan 2009
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    Williamstown, Ontario, Canada
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    i've discovered the answer, but not enough to answer my new posted thread.

    sorry for the inconvenience
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