
Re: Can addition be defined in terms of multiplication?
Posted:
Aug 18, 2013 10:15 AM


On 08/17/2013 07:06 PM, grahamcooper7@gmail.com wrote: > 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
"Well, they?re ten digit numbers ... it?s a one time pad, but it has a pseudorandom, prime number expansion system ..."
>  > www.tinyurl.com/HowPrologWorks >
 The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's tortoises all the way down!"  Hawking, 1988, A Brief History of Time.

