03/21/2015, 12:35 AM

(03/20/2015, 10:41 PM)marraco Wrote: He will have a hard time, because he does not know what we call integer numbers. He only knows powers of n, so he will try to assign

a=1.a

a+a=n.a

a+a+a=n².a

a+a+a+a=n³.a

If n=2 then [only we know that] the correct addition would be

a=1.a

a+a=2.a

(a+a) + (a+a)=n².a

((a+a) + (a+a)) + ((a+a) + (a+a)) =n³.a

I terms of zeration, it should be

f=f+0

f°f=f+1

(f°f) ° (f°f)=f+2

((f°f) ° (f°f)) ° ((f°f) ° (f°f)) =f+3

(f+n)°(f+n)=f+(n+1)

and the natural choice for f, should be the neutral element of addition, so

0 = 0

0°0 = 1

(0°0) ° (0°0) = 1°1 = 2

((0°0) ° (0°0)) ° ((0°0) ° (0°0)) = 2°2 =3

(0+n)°(0+n) = n°n = (n+1)