```Date: Aug 18, 2013 10:15 AM
Author: David Bernier
Subject: Re: Can addition be defined in terms of multiplication?

On 08/17/2013 07:06 PM, grahamcooper7@gmail.com wrote:> On Friday, August 16, 2013 1:54:40 AM UTC-7, 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/How-Prolog-Works>-- 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.
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