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I understand the axioms defined on the set of natural numbers that $m+0:=m$ and that $m+n’:=(m+n)’$. Where does the commutativity come into this?

Andrés E. Caicedo
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Partey5
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  • In particular, the problem I have is proving the base step where n=0. I do not know how to show that commutes. – Partey5 Nov 01 '19 at 11:39
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    Prove m+ 0= 0+ m as a separate induction. If m= 0, that is 0+ 0= 0+ 0 which is obviously true. Further, 0'= 0+1= 1 while 1+ 0= 1 from the definition of 0. Now suppose that for some m= k, k+ 0= 0+ k. Then k'+ 0= (k+1)+ 0= k+ (1+ 0)= k+ 1= k'= 0+ k'. – user247327 Nov 01 '19 at 11:51

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