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Math Help - Group Proof

  1. #1
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    Group Proof

    Let G be a set together with a binary operation. Suppose that this operation is associative, there exist an element e in G such that ae = a for each a in G, for each a in G, there is an element b in G such that ab = e.

    Prove G is a group.

    My Proof so far:

    Now, I understand that I need to show ea = a and ba = e.

    Is it proper for me to assume be = b? Or rather, would this help?
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Let G be a set together with a binary operation. Suppose that this operation is associative, there exist an element e in G such that ae = a for each a in G, for each a in G, there is an element b in G such that ab = e.
    Maybe you are missing that b is unique?
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  3. #3
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    I reread the problem and it doesn't say that b is unique. But I understand what you are saying, there can only exist one inverse of an element in a group.
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