
Re: Can addition be defined in terms of multiplication?
Posted:
Aug 19, 2013 9:07 PM


On Sunday, August 18, 2013 3:40:08 PM UTC7, graham...@gmail.com wrote: > > 2 x [ n^ X ] [ n^ [ s Y ] ] [ n^ [ s Z ] ] : > > > > > > > > > > > > + [ n^ X ] [ n^ Y ] [ n^ Z ] > > > > > > TYPO: > > > > x [ n^ X ] [ n^ [ s Y ] ] [ n^ [ s Z ] ] : > > > > x [ n^ X ] [ n^ Y ] [ n^ Z ] > > > > > > > > > > this is: > > > > 2^x * 2^(y+1) = 2^(z+1) > > < > > 2^x * 2^y = 2^z > > > > > > > > which is just an adaption of Peano Addition / same algorithm. > > > > x + y+1 = z+1 > > < > > x + y = z >
This still uses SUCCESSOR
2^x * 2^(y+1) = 2^(z+1) < 2^x * 2^y = 2^z
The only way to avoid that (if you consider successor addition)
would be a different number structure.
1 = 2^0 = 1 2 = 2^1 = t(1) 4 = 2^2 = t(t(1)) 8 = 2^3 = t(t(t(1))) ...
might be able to handle composite + composite = composite
1 + 2 = X 2^1 * 2^2 = 2^X X = t(1) + t(t(1))
but I have other things to work on....
Herc  www.phpPROLOG.com

