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.