自然數公設
# Peano Axiom #
The Natural Number satisfies the following properties:
1. For a set N, there exist n & n+ (after n) , n n+ (n+)+
2. The element "e" must be in N
3. There doesn't exist any one E s.t. E+ = e
4. For each element in N, a+ = b+ => a=b
5. Let S be a subset of N, "e" belongs to N; n is in N => n+ is in N
then S = N.
i.e. S is the so called "Natural Number set".
Also, e:=1 e+:= 2 (e+)+:=3 ......and so on
Define the additive operator <+> to be a function:
1. <+>(n,e) = n+ i.e. n <+> e = n+
2. <+>(n,m+) = (<+>(n,m))+ i.e. n <+> m+ = (n<+>m)+
<+>:= +
Existence: e, e+ ,(e+)+, ..... are in N
Uniqueness: For each n in N,
<+>(n,e) = n+
<+>(n,e+) = (<+>(n,e)) = (n+)+
<+>(n,(e+)+) = (<+>(n,(e+))+ = ( (<+>(n,e))+)+ = ((n+)+)+
...........
so <+>(e,e) = e+ ,say "1+1=2"


Sealed (Aug 19)
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1樓搶頭香
回訪 :D
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2樓頸推
我都忘了我有去你那邊留言了
!!!!!!
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