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Prove the assumption of uniqueness is not necessary

  1. Sep 7, 2011 #1
    Is my proof correct?

    1. The problem statement, all variables and given/known data
    Show that, if there exists a number 0 for which x+0=x for all x∈R, and a number 0' for which x+0'=x for all x∈R, then 0=0'.

    3. The attempt at a solution
    Proof by contradiction:

    Assume, 0≠0'. Then,

    x+0=x and x+0'=x'

    Such that:

    x=x-0 and x=x'-0'

    Such that: x-0=x'-0'

    Which is a contradiction.
    Thus, 0=0'.
  2. jcsd
  3. Sep 7, 2011 #2
    I don't see the contradiction...
    And what is x'??
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