
Re: Can addition be defined in terms of multiplication?
Posted:
Aug 17, 2013 10:56 AM


On 17/08/2013 1:06 AM, Peter Percival wrote: > Nam Nguyen wrote: >> On 16/08/2013 9:49 AM, dullrich@sprynet.com wrote: >>> On Fri, 16 Aug 2013 02:05:09 0700, William Elliot <marsh@panix.com> >>> wrote: > >>>> 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. >> >> _That_ actually isn't silly. The language of arithmetic is either >> L1(0,S,+,*,<) or L2(0,S,+,*), so "in the language of arithmetic" >> technically just means "in L1" or "in L2". > > So given the language of arithmetic is what you say, it isn't silly to > use log and exp?
No. Take the "language of arithmetic" to be L1 (for example): you can formalize a real number system for log and exp.
My point is it's silly to claim L1 to be the "language of arithmetic" while it could also be the "the language of complete order field", or many ... many other alternatives.
That's just shows how we've _unjustifiably biased_ our logical reasoning, in favor of the concept of the natural numbers.
> Note that my post spelled out your L1 and L2.
(I only glanced through the conversation between Dave and William).
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI

