> > ｼｮｰｷ(´ー｀)
> Proof that 1 + 1 = 2
> Date: 06/10/99 at 00:03:59
> From: mike 
> Subject: Need the math proof for 1 + 1 = 2
> My wife the math teacher wants the mathematical proof for
>   1 + 1 = 2
> I have spent quite a bit of time looking for it on the Web - help!
> 
> --------------------------------------------------------------------------------
> 
> Date: 06/10/99 at 10:15:58
> From: Doctor Rob
> Subject: Re: Need the math proof for 1 + 1 = 2
> The proof starts from the Peano Postulates, which define the natural 
> numbers N. N is the smallest set satisfying these postulates:
>   P1.  1 is in N.
>   P2.  If x is in N, then its "successor" x' is in N.
>   P3.  There is no x such that x' = 1.
>   P4.  If x isn't 1, then there is a y in N such that y' = x.
>   P5.  If S is a subset of N, 1 is in S, and the implication
>        (x in S => x' in S) holds, then S = N.
> Then you have to define addition recursively:
>   Def: Let a and b be in N. If b = 1, then define a + b = a'
>        (using P1 and P2). If b isn't 1, then let c' = b, with c in N
>        (using P4), and define a + b = (a + c)'.
> Then you have to define 2:
>   Def:  2 = 1'
> 2 is in N by P1, P2, and the definition of 2.
> Theorem:  1 + 1 = 2
> Proof: Use the first part of the definition of + with a = b = 1.
>        Then 1 + 1 = 1' = 2  Q.E.D.
> Note: There is an alternate formulation of the Peano Postulates which 
> replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the 
> definition of addition to this:
>   Def: Let a and b be in N. If b = 0, then define a + b = a.
>        If b isn't 0, then let c' = b, with c in N, and define
>        a + b = (a + c)'.
> You also have to define 1 = 0', and 2 = 1'. Then the proof of the 
> Theorem above is a little different:
> Proof: Use the second part of the definition of + first:
>        1 + 1 = (1 + 0)'
>        Now use the first part of the definition of + on the sum in
>        parentheses:  1 + 1 = (1)' = 1' = 2  Q.E.D.
> - Doctor Rob, The Math Forum
>   http://mathforum.org/dr.math/   
> (^Д^)

日本語じゃないのでわかりません(´ー｀)

参考：2002/05/13(月)18時26分10秒