Show that the multiplication in N is commutative Prove nxmmx

Show that the multiplication in N is commutative. Prove: nxm=mxn

let 1n=n1 , trivial

assume unductive hypothesis

n1 = (n-1) 1 + 1 = n-1 + 1 =n

nm = (n-1)m + m = m(n-1) + m

= (m-1) (n-1) + (n-1) + m

= (m-1) (n-1) + (m-1) + n

= (n-1) (m-1) +(m-1) + n

= (m-1) n + n

= mn

hence proved