>>12769092Eh, according to Wikipedia you have to assume a bunch of things by definition:
Firstly the peano axioms to define the natural numbers. In which case, the symbol "2" is defined as S(S(0)). These axioms also state that there does not exist an n, such that S(n) = 0. Though, I think you could alternatively just say that
0 =/= 1 .
Then you have to define multiplication. And again, by definition, 0*n = 0.
Therefore, 0*0 = 0
If 0*0 = 2, then 0 = 2
But then that means 0 = S(S(0)), which contradicts the assumption that 0 isn't the "successor" of anything.
Alternatively, if 0 = 2, then 0*(1/2) = 2*(1/2)
In which case, 0 = 1, which contradicts the alternative axiom I gave.
