
Re: Can addition be defined in terms of multiplication?
Posted:
Aug 17, 2013 7:06 PM


On Friday, August 16, 2013 1:54:40 AM UTC7, Peter Percival wrote: > Can addition be defined in terms of multiplication? I.e., is there a > > formula in the language of arithmetic > > > > x + y = z <> ... > > > > such that in '...' any of the symbols of arithmetic except + may occur? > > Or, alternatively, is there a formula in the language of arithmetic > > > > x + y = ... > > > > with the same requirement? > > > > The symbols of arithmetic (for the purpose of this question) are either > > > > individual variables, (classical) logical constants including =, > > S, +, *, and punctuation marks; > > > > or the above with < as an additional binary predicate symbol. > > > >  > > Sorrow in all lands, and grievous omens. > > Great anger in the dragon of the hills, > > And silent now the earth's green oracles > > That will not speak again of innocence. > > David Sutton  Geomancies
Let's cheat a little and use a multiplication table...
Let's call this ummm... 'M'
M 
1 X 1 = 1 1 X 2 = 2 1 X 3 = 3 ..
2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 ..
M states which rules are to be used.
Can..
(x+1) X y = (z+y) <> x X y = z
(x+2) X y = (z+2Xy) <> x X y = z
...
cover all the bases?
Herc  www.tinyurl.com/HowPrologWorks

