Talk:Transreal number

message: from the same page the bbc article is at:
Given the, er, light-hearted mathematical debate Dr Anderson's theory has generated, we're delighted to announce he will join us on Tuesday 12 December to answer questions and discuss some of the criticisms levelled against his theory of nullity. You will be able to hear in more detail from Dr Anderson on this page later on Tuesday. Many thanks for your comments.
update:
:Maybe some people on here will try to ask him to clear some stuff up for them. Make sure you visit the BBC site on tuesday if you're interested. fintler 23:59, 11 December 2006 (UTC)
thread_title: BBC Q&A Session on Dec 12, 2006

message: okay, my formal training in mathematics is limited, but can anyone see a reason that the axioms would not be attackable by the standard problem with resolving division by zero to signed infinity?
namely, if 1/0=\infty then:
\infty = 1/0 = 1/(-1 * 0) = -1 * (1/0) = -1 * \infty = -\infty
it looks to me like all of those steps are legit within his axioms (he preserves commutativity and allows multiplication of infinity by negatives to produce negative infinity). yet, this also contradicts his definition of \infty != -\infty
any takers? --Frank duff 17:43, 7 December 2006 (UTC)
replies: text: I agree with you. \infty as a “transreal number” is exactly the same as -\infty and has nothing to do with \infty as in the limit value. This article needs heavy justification. In fact 1/0 no longer equals (-1*1)/(-1*0) with the set of axioms given in the paper. Sam Hocevar 18:13, 7 December 2006 (UTC)
replies: text:  really? it seems to me that given associativity [A12], commutativity [A13] and his definition of division [A17], then 1/0 must equal (-1*1)/(-1*0). i have to admit though, it's been a long time since i did this sort of proof from axiom. --Frank duff 18:30, 7 December 2006 (UTC)

text: For this to work I think you need to prove that a^{-1} * b^{-1} = (a * b)^{-1} 88.108.28.16 18:38, 7 December 2006 (UTC)
thread_title:  axioms of the transreal numbers 

message: We had a series of articles on this topic that were deleted only a week or two ago, as hoax/unscientific nonsense.  Complaints then, as now, are that: 1) Concept seems to be a kludgy reinvention of Conway's star,  2) insufficient context w.r.t. IEEE definitions of NaN. 3) Nebulous claims -- e.g. "might help with projective geometry". I'm disapponted to see this on slashdot, and the recreation of the aricle. linas 19:22, 7 December 2006 (UTC)
replies: text: Yes, the projective geometry claim is totally ludicrous. I’m removing it. Sam Hocevar 20:07, 7 December 2006 (UTC)
thread_title:  Deleted article 

message: How does "transreal arithmetic" with \pm\infty and \Phi differ from standard IEEE floating point math?
In standard floating point math, the same axioms hold, if we simply replace \Phi with NaN:
* 1 \div 0 = \infty
* 0 \div 0 = NaN
* \infty \times 0 = NaN
* \infty - \infty = NaN
* NaN + a = NaN
* NaN \times a = NaN
So, how is transreal arithmetic anything other than a restatement of IEEE floating-point arithmetic???
Moxfyre 19:29, 7 December 2006 (UTC)
replies: text: That wasn't a comprehensive list of the axioms but just a few illustrative identities. But, for example, in IEEE, NaN != NaN but in transreal, \Phi = \Phi. Eliot 19:46, 7 December 2006 (UTC)
replies: text:  Hmmm... okay.  Transreal arithmetic doesn't seem to introduce any more internal consistency than IEEE floating point, in my opinion.  (I've looked at the original sources now.)  I don't get how a floating-point library based on Transreal arithmetic would be any more robust or useful.  It would just have slightly different quirks in the corner cases.  Moxfyre 20:01, 7 December 2006 (UTC)
replies: text:  Look at the paper, the conclusion has an explanation of what he's hoping to achieve with this. It seems that he found NaN to be a limitation in some other research and decided to try to create a way around it. Eliot 20:19, 7 December 2006 (UTC)

text: It seems to me that he made a slight change to the IEEE standard and is trying to introduce it into mainstream math.  I personally prefer NaN over nullity because NaN means that the result is undefined.  This is a very useful concept.  By switching to nullity, any two previously undefined values are now equal to each other.  This is contrary to limit theory. 71.36.13.85 20:02, 7 December 2006 (UTC)
replies: text:  Exactly. If we want to throw all of analysis out the window, then transreal arithmetic is fine. Otherwise, we're stuck with the real numbers. --King Bee 20:09, 7 December 2006 (UTC)
thread_title:  How is this any different from IEEE floating point? 

message: As a description of a mathematical formalism, I don't see why there is anything wrong with this article.  Whether or not that formalism is useful is really not significant -- quite a few are not (e.g. Sedenions) but are still worth mentioning.  However, this article needs to state in more unambiguous terms that this is a specific formalism promoted by  a specific matematician, and isn't widely used. --Hpa 21:32, 7 December 2006 (UTC)
thread_title:  A description of a mathematical formalism 

message: First of all sorry for not using that fancy math-mode but:
0/0 = (0-0)/0 = 0/0 - 0/0 = nullity - nullity = 0 iff nullity = nullity.
Can someonte tell me were the above goes wrong? Poktirity 22:14, 7 December 2006 (UTC)
replies: text: I had a look at the axioms an according to A9 nullity = - nullity.
Then 2*nullity = nullity doesn't it?Poktirity 22:38, 7 December 2006 (UTC)
replies: text:  That’s correct. Sam Hocevar 02:13, 8 December 2006 (UTC)
thread_title:  (0-0)/0 = ??? 

message: The "theory" can be explained as an introduction of a new "value" that are assigned to 
undefined computations made on the extended real line, and does just the same as 
the normal NaN computation does, exept NaN!=NaN, but nullity==nullity. 
This is just a clean? workaround a try-catch statement. Are there any real applications with this theory? —The preceding unsigned comment was added by Paxinum (talk • contribs) 23:34, 7 December 2006 (UTC)
replies: text: The theory has defined several other "things", seeing as it accepts limits as accurate calculations.T.Stokke 14:47, 11 March 2007 (UTC)
thread_title:  Much fuss about nothing? 

message: I was looking through Perspex Machine IX: Transreal Analysis and I found this, [E 8], on page 5:
\ln{-x}=\Phi:-x<\Phi
But, google says otherwise: ln(-1)=Pi*i.
I think this just reiterates the fact that \Phi is just am overglorified symbol for error. -Exomnium 02:03, 9 December 2006 (UTC)
replies: text: You're mixing incompatible mathematical systems.  Traditional complex arithmetic depends on the real numbers being a field over addition and multiplication.  The transreals do not form a field, so you need to re-formulate complex math to deal with them. --Carnildo 04:29, 9 December 2006 (UTC)

text: Looking at it further, you're also misreading what he wrote.  What the statement means is "If the results of taking the natural log of a number are constrained to the transreals, then the result of taking the natural log of a negative number is \Phi".  It's just like taking the natural log of a negative number in the reals: if your results are constrained to the real numbers, then the result is undefined. --Carnildo 04:36, 9 December 2006 (UTC)
replies: text: They're not incompatible, at least according to him. From Axioms of Transreal Arithmetic, "Having obtained the transreal numbers the complex, quaternion, and octonion numbers can be extended to total systems of arithmetic by replacing the components of these numbers with transreal numbers." And reformulating complex math is destructive of the purpose of transreal arithmetic, "they are supposed to produce the same result as standard arithmetic for all calculations where standard arithmetic defines a result." Where did you get that quote from? If he really said that, it's tantamount to him admitting that nullity is an over glorified undefined. -Exomnium 00:52, 10 December 2006 (UTC)
replies: text: These are transreal numbers, not transcomplex. I don't see how you can say they are inconsistent, seeing as ln(-1) is not defined in standard real numbers. And it does not say that \ln{-x}=\Phi:-x<\Phi it says \ln{-x}=\Phi:-x<0, since nullity (\Phi) lies off the number line, you can't have a number smaller than it.T.Stokke 14:45, 11 March 2007 (UTC)
thread_title:  Transreal numbers are inconsistent with Complex numbers 

message: I didn't make the change, but I support it.  Other editors have effectively merged the transreal number into the James Anderson article anyway.  Lunch 18:07, 15 December 2006 (UTC)
thread_title:  redirect to NaN vs. redirect to James Anderson