December 5th, 2017, 04:06 PM  #21  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,232 Thanks: 2411 Math Focus: Mainly analysis and algebra  Quote:
Taken together we then have $$(0) =( n) + n = 0$$ as I pointed out before. Also, if $(0)$ is the additive identity, we get $$0 = 0+0=\big((0)+0\big) + \big(0+(0)\big) = (0) + (0+0) + (0) = (0) + (0) = (0)$$  
December 5th, 2017, 04:11 PM  #22 
Senior Member Joined: May 2016 From: USA Posts: 922 Thanks: 368 
Without meaning to be obnoxious, is there not a theorem in group theory that proves an identity element to be unique? (Sorry: it has been literally decades since I worried about group theory, and I never studied the theory of rings or fields.) Whether your new mathematics is a group or not, what is the point of this particular new set of axioms? I GET that one view of mathematics is that it is simply a particularly difficult game, but I do not see why I should want to play this particular variant of the game. Perhaps computers may actually view  0 and + 0 as distinct floating point numbers, and the consequences of that distinction may be important. Without, however, any clue given as to why a different set of axioms may be worthwhile or even amusing to explore, I am a bit reluctant to drop down a rabbit hole for no particular reason. 
December 5th, 2017, 04:33 PM  #23  
Senior Member Joined: Aug 2012 Posts: 109 Thanks: 0  Quote:
Again please allow the following edits 0 =/= (0) 0 = 0 I apologize  
December 5th, 2017, 04:35 PM  #24  
Senior Member Joined: Aug 2012 Posts: 109 Thanks: 0  Quote:
(0) is constrained to being the divisor in division....always Last edited by Conway51; December 5th, 2017 at 04:51 PM.  
December 5th, 2017, 04:42 PM  #25  
Senior Member Joined: Aug 2012 Posts: 109 Thanks: 0  Quote:
Your equation is wrong. (0) + (0) =/= (0) as stated in the op (n) + (0) = n (n) + (0) = n therefore (n) + (n) = 0 therfore (0) + 0 = 0 (0) + (0) = 0 Last edited by Conway51; December 5th, 2017 at 04:49 PM.  
December 5th, 2017, 04:47 PM  #26  
Senior Member Joined: Aug 2012 Posts: 109 Thanks: 0  Quote:
I am not aware of any such theorems. I would be glad to. The last two sentences are the particular reason you may or may not want to drop down this rabbit hole  
December 5th, 2017, 05:08 PM  #27  
Senior Member Joined: May 2016 From: USA Posts: 922 Thanks: 368  Quote:
Quote:
The nexttolast sentence may be what you were referring to. If the imprecision of floating point numbers is the proposed motivation, my next question is why is this not satisfactorily covered in the theory of errors? In fact, when I studied numerical methods back in ancient times, the theory of errors was where the whole course started. The computer doesn't work quite right so you sort a set of numbers before adding them to reduce potential error, etc. It was a sort of revelation for me about nonPlatonic mathematics. The computer is not precise; the data are always somewhat dirty, so how do you cope? I built a rather successful business career on understanding, but avoiding naive credulity about, mathematical results.  
December 5th, 2017, 05:17 PM  #28  
Senior Member Joined: Aug 2012 Posts: 109 Thanks: 0  Quote:
"This is an exercise in theory and nothing more." However....it is my BELIEF that computers have trouble because division by zero is undefined... Find a way to define it....rewrite binary and computer "math" accordingly...and.....all the extra steps needed for computers to find a away around division by zero is no longer needed. Consider the last sentence.... Therefore...math...is relative. Last edited by Conway51; December 5th, 2017 at 05:29 PM.  
December 5th, 2017, 07:00 PM  #29 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,232 Thanks: 2411 Math Focus: Mainly analysis and algebra  
December 5th, 2017, 07:03 PM  #30 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,232 Thanks: 2411 Math Focus: Mainly analysis and algebra  I don't believe I said that it was. So it's not an additive identity element as you claimed. I'm rather afraid that all these rules turn out to be completely arbitrary and, as likely as not, contradictory. 

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