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.