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Thread: One to one functions

  1. #1
    Junior Member
    Sep 2008

    Smile One to one functions

    I have two sets A,B where B is not the empty set. b is an element of B and a is an element of A.

    The function defined by j(a)=(a,b) where (a,b) is an element of AxB.

    Show j: A---> AxB for all b in B is one to one.

    So I want to show that if j(a1)=j(a2) that implies that a1=a2. I just don't know how to go about proving this. I tried to just assume that j(a1)=j(a2) but I don't think I can just assume that.

    Thanks so much for any help!!
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  2. #2
    Sep 2008
    well go ahead and assume that for a1 and a2 in A j(a1) = j(a2).

    By the definition of your function
    j(a1) = (a1, b1) for some a1 in A and b1 in B and
    j(a2) = (a2, b2) for some a2 in A and b2 in B.

    Since j(a1) = j(a2) this implies that (a1, b1) = (a2, b2). But this is only true if a1 = a2 and b1 = b2.
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