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Math Help - Identity Element

  1. #1
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    Identity Element

    I would appreciate any help given on this problem in abstract algebra. I spent an hour trying to figure it out but with no luck

    Let * be a binary operation on the nonempty set A. Prove that if A contains an identity element with respect to *, the identity element is unique. Prove using direct proof.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by TitaniumX View Post
    I would appreciate any help given on this problem in abstract algebra. I spent an hour trying to figure it out but with no luck
    please don't put your question in quote tags.

    i've never seen a direct proof for this.

    let a and b be the identity elements. since a is the identity, a*b = b. but since b is the identity, a*b = a. thus, we have a = b.
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