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Topic: Can addition be defined in terms of multiplication?
Replies: 58   Last Post: Aug 23, 2013 3:56 PM

 Messages: [ Previous | Next ]
 David C. Ullrich Posts: 3,555 Registered: 12/13/04
Re: Can addition be defined in terms of multiplication?
Posted: Aug 16, 2013 11:49 AM

On Fri, 16 Aug 2013 02:05:09 -0700, William Elliot <marsh@panix.com>
wrote:

>On Fri, 16 Aug 2013, 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?

>
>x + y = log(e^x * e^y)

If you don't know what "in the language of arithmetic" means
it would be a good idea to refrain from answering questions
about the language of arithmetic, lest you look silly.

>> 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.
>>

Date Subject Author
8/16/13 Peter Percival
8/16/13 William Elliot
8/16/13 Peter Percival
8/16/13 David C. Ullrich
8/16/13 namducnguyen
8/17/13 Peter Percival
8/17/13 namducnguyen
8/17/13 fom
8/23/13 tommy1729_
8/16/13 Peter Percival
8/16/13 Robin Chapman
8/16/13 Helmut Richter
8/16/13 Rotwang
8/16/13 Virgil
8/22/13 Rock Brentwood
8/16/13 Shmuel (Seymour J.) Metz
8/17/13 Helmut Richter
8/16/13 Jim Burns
8/16/13 fom
8/17/13 Robin Chapman
8/17/13 fom
8/17/13 Peter Percival
8/17/13 fom
8/17/13 Peter Percival
8/17/13 Peter Percival
8/18/13 William Elliot
8/18/13 Peter Percival
8/18/13 William Elliot
8/18/13 Peter Percival
8/18/13 Graham Cooper
8/18/13 David C. Ullrich
8/18/13 David C. Ullrich
8/17/13 Graham Cooper
8/18/13 David Bernier
8/18/13 Ben Bacarisse
8/18/13 Peter Percival
8/18/13 Jim Burns
8/18/13 fom
8/18/13 Ben Bacarisse
8/18/13 Graham Cooper
8/18/13 Graham Cooper
8/18/13 Graham Cooper
8/18/13 Graham Cooper
8/19/13 Graham Cooper
8/19/13 Alan Smaill
8/19/13 fom
8/19/13 Alan Smaill
8/20/13 Alan Smaill
8/20/13 Peter Percival
8/20/13 Graham Cooper
8/20/13 Graham Cooper
8/22/13 David Libert
8/22/13 Peter Percival
8/20/13 fom