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Math Help - help with proof

  1. #1
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    help with proof

    it says: Suppose S is a subset of Z which is closed under subtraction, and k is an element of S. Prove that 0 is an element of S and then use that to prove that -k is an element of S.
    Any ideas on how to start?
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  2. #2
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    Quote Originally Posted by alyssams View Post
    it says: Suppose S is a subset of Z which is closed under subtraction, and k is an element of S. Prove that 0 is an element of S and then use that to prove that -k is an element of S.
    Any ideas on how to start?

    1) There exists some element k\in S\Longrightarrow k-k\in S

    2) So now \forall\,k\in S\,,\,\,0,\,k\in S\Longrightarrow 0-k\in S

    Tonio
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