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Can you prove that 1+1=2 or is it an axiom?

  1. Feb 22, 2009 #1
    Can you prove that 1+1=2 or is it an axiom?
     
  2. jcsd
  3. Feb 22, 2009 #2
    Re: 1+1=2

    Well, use peano axioms. Look it up yourself! :smile:
     
  4. Feb 22, 2009 #3

    Hurkyl

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    Re: 1+1=2

    Most commonly, that (or something very similar) is taken as the definition of the symbol '2'.
     
  5. Feb 22, 2009 #4
    Re: 1+1=2

    Could you say that:

    x+1=S(x)

    and, therefore
    1+1=S(1)
    S(1)=2

    Would that work as a proof?
     
  6. Feb 22, 2009 #5
    Re: 1+1=2

    I wouldn't call that a proof, unless you were proving it a la Russell/Whitehead.

    As Hurkyl said, it probably is a definition more than anything else. 2 is the number next to 1.
     
  7. Feb 22, 2009 #6
    Re: 1+1=2

    Okay, thanks :)
     
  8. Feb 22, 2009 #7

    CRGreathouse

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    Re: 1+1=2

    I consider S(S(0)) to be the definition of "2". As such, "1 + 1 = 2" unpacks as "S(0) + S(0) = S(S(0))". From the definition of addition, S(0) + S(0) is S(S(0) + 0). Also from the definition of addition, S(0) + 0 is S(0). Thus S(0) + S(0) = S(S(0)) and so 1 + 1 = 2.
     
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