December 24th, 2016, 11:44 PM  #21 
Member Joined: Jan 2014 Posts: 86 Thanks: 4  This is semantics, and not helpful to the discussion. De facto it is a real number and has properties that complex numbers don't have and vice versa. I answered your question. How about you comment on that i = 1/1/1/1/... ?

December 24th, 2016, 11:50 PM  #22 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,398 Thanks: 2105 Math Focus: Mainly analysis and algebra 
You should read and understand the second half of JeffM1's post #8: "I strongly suspect that the highly confusing use of the − symbol in mathematics has led you astray".

December 25th, 2016, 12:36 AM  #23 
Member Joined: Jan 2014 Posts: 86 Thanks: 4 
Not at all, for a positive real n, n is negative. For an imaginary number like i it doesn't mean that i is positive (i.e. greater than zero) and i is negative, they are just conventions and we decide to run with i by default, all it means is that i + ( i) = 0. But, here's the catch, we can't substitute i for i willynilly, we have to be consistent. We either use i in all of mathematics (in place for (1)^(1/2) ) or use i in all of mathematics. For simplicity we chose the former. So far so good, but nobody yet has debunked my strongest reasoning thus far that taking the common wisdom "i is neither positive nor negative" actually results in "i is both positive and negative". I rewrite it again: "i is neither positive nor negative" becomes "i is not positive and not negative" becomes "i is not (not negative) and not (not positive)" becomes "i is (not not) negative and (not not) positive" becomes "i is negative and positive" Of course I'm not suggesting writing it as +/i as that means either +i or i. We apparently need a new notation to denote "both positive and negative". Impossible you say? i is an impossible number to start with. Oh well. 
December 26th, 2016, 06:46 PM  #24  
Senior Member Joined: Feb 2016 From: Australia Posts: 782 Thanks: 287 Math Focus: Yet to find out.  Quote:
Quote:
 
December 26th, 2016, 07:26 PM  #25  
Senior Member Joined: May 2016 From: USA Posts: 480 Thanks: 204  Quote:
The socalled logic is that because an elephant is not a bird and not a fish, it must be both a bird and a fish. Anyone who finds that compelling will not be dissuaded by pointing out that "not positive" does not mean "negative" even within the real numbers Last edited by JeffM1; December 26th, 2016 at 07:31 PM.  
December 26th, 2016, 08:16 PM  #26  
Senior Member Joined: Feb 2016 From: Australia Posts: 782 Thanks: 287 Math Focus: Yet to find out.  Quote:
 
December 27th, 2016, 04:23 AM  #27 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,142 Thanks: 158 
If you restrict yourself to the imaginary axis exclusively trichotomy holds. So $i > 0$ is positive , $i<0$ is negative. Trichotomy fails when you go to ordered pairs $a + bi$ Where both $a$ , $b$ are non zero real numbers Lol , there is no ordering of ordered pairs (in the usual sense) Last edited by agentredlum; December 27th, 2016 at 04:26 AM. 
December 27th, 2016, 07:11 AM  #28 
Member Joined: Jan 2014 Posts: 86 Thanks: 4 
Jeff your analogy with the elephant is not comparable with the original and instead a better analogy would be "the elephant is not alive nor dead" and in science fiction those are called "deadalive". If we see that i is like a fiction of mathematics the "both positive and negative" part is not such a stretch considering accepting i in the first place.
Last edited by Tau; December 27th, 2016 at 07:17 AM. 
December 27th, 2016, 07:57 AM  #29 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,398 Thanks: 2105 Math Focus: Mainly analysis and algebra 
The point is that $i$ does not exist except as embedded in the conplex plane, which is a numbering system of ordered pairs. These ordered pairs do not a total ordering analogous to the total ordering of the real numbers viewed on the real number line. The real numbers, embedded in the complex plane are not subject to such a total ordering either. On the complex plane, positive and negative have no meaning because the ordering does not exist which allows one to relate the numbers to zero. The standard definitions of positive and negative refer to the standard ordering relation on the real number line. Since $i$ is not on that number line, the terms do not apply to that number. You are telling us that the colour blue smells more bitter than the colour black. 
December 27th, 2016, 07:58 AM  #30 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,398 Thanks: 2105 Math Focus: Mainly analysis and algebra  

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