Unredeemed
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Can you prove that 1+1=2 or is it an axiom?
Can you prove that 1+1=2 or is it an axiom?
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Unknot
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Well, use peano axioms. Look it up yourself!
Unredeemed
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Unknot said:Well, use peano axioms. Look it up yourself!
Could you say that:
x+1=S(x)
and, therefore
1+1=S(1)
S(1)=2
Would that work as a proof?
Unknot
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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.
Unredeemed
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Okay, thanks :)
Science Advisor
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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.