Talk:James A. D. W. Anderson

message: :This is not new. There already was a NaN ages ago. --Soyweiser 13:07, 7 December 2006 (UTC)
replies: text: And what the Flying F is Transreal analysis in mathematics, as far as I can see the author of the new NaN made that up to. Don't really consider that to be proper academic research now is it? --Soyweiser 13:30, 7 December 2006 (UTC)
replies: text: He came up with a name for his idea, I don't see a problem with that. It separates it from stuff that already exists. It uses NaN only in passing, it has nothing to do with it directly, take a look at the paper. It notes the existance of proofs explaining 0^0 -> 0/0 = DNE. fintler 13:39, 7 December 2006 (UTC)
replies: text:  Well Sadly I don't have the time right now to read another paper. So I'll believe you about the 0^0 -> 0/0 = DNE part. (There where some comments on the /. page about the transreal analysis and the paper, some strange things that could indicate work that still has to be done on the papers.) But the problem was already solved (at least partially then) and it doesn't justify all the media attention. --Soyweiser 13:50, 7 December 2006 (UTC)
thread_title: Publications Discussion

message: Giving Anderson the title of mathematician in my opinion is inaccurate given that his academic background is in Computer Science and his "mathematical" publications are not from any established mathematical journal. 65.246.47.233 18:20, 7 December 2006 (UTC)
replies: text: I agree on that one. --Soyweiser 19:16, 7 December 2006 (UTC)
replies: text:  I also agree. Also candidate for deletion? Lee-Jon 23:09, 7 December 2006 (UTC)
replies: text:  Candidate for deletion? A nope, It is a current event, and it is someone who stirred up some commotion, so in that regard I do think it should have its place in wikipedia. Soyweiser —The preceding unsigned comment was added by 195.169.215.154 (talk) 00:10, 8 December 2006 (UTC)

text: Fifteen minutes of fame (or infamy) doesn't qualify one for an encyclopedia article, IMHO.  Lunch 00:19, 8 December 2006 (UTC)
replies: text: Another vote for deletion, he doesn't have any credite published papers Masiosare 00:23, 8 December 2006 (UTC)
replies: text:  This deletion process is going all wrong. The guys page gets deleted, while the wierd math is staying. How are people going to see that this math ain't normal math? --Soyweiser 04:10, 11 December 2006 (UTC)
thread_title: Mathematician?

message: We need to distinguish equality from definitions;  for example, Φ = −Φ is analogous to -NaN is defined to be NaN, even though they're not "equal".  NaN is NaN, although they don't compare as equal.  I'm not sure how to do this.  — Arthur Rubin |  (talk) 14:53, 15 December 2006 (UTC)
replies: text: If you really need to show that -NaN is NaN but that -NaN ≠ NaN, then say -NaN := NaN (read as negative NaN is defined to be NaN). Welbog 16:47, 15 December 2006 (UTC)
replies: text:  As one Dave Korn points out in response to this BBC article, the only difference between nullity and NaN is that nullity compares as equal to itself while NaN does not; but then by the axiom, \Phi-\Phi=\Phi, so even though nullity is equal to itself, the difference between it and itself does not vanish -- thus the statement that it "is equal to itself" has no real meaning. -- Thomas —The preceding unsigned comment was added by Tkoeppe (talk • contribs) 18:44, 15 December 2006 (UTC)
replies: text: A more sophisticated way to view this is to treat = as an equivalence relation. For IEEE numbers (NaN) this relation is not reflexive, for transreals (\Phi) it is. There are pros and cons to each treatment. --Salix alba (talk) 19:00, 15 December 2006 (UTC)
thread_title:  Transreal arithmetic table... 

message: I am merging the content of the above talk page here, since the content is already merged. Somebody may consider removing that talk page later. AbelCheung 23:31, 5 January 2007 (UTC)
thread_title:  [[Talk:Transreal number]] merged here 

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)

text: Just noticed, James has covered a bit about this himself. His PerspexMachineVIII.pdf [T81] says, (a \times b)^{-1} = a^{-1} \times b^{-1} for many cases of a, b, but not when one of them is zero and another is negative number. This means \left(\frac{0}{-1}\right)^{-1} \ne \frac{0^{-1}}{(-1)^{-1}}, and implies \left(\frac{0}{-1}\right)^{-1} \ne \frac{-1}{0}. Yet fractions like \frac{1}{0} - \frac{1}{0} = \frac{1-1}{0} can be conveniently used. Funny. AbelCheung 02:53, 6 January 2007 (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)

text: His point was to make a complete arithmetic, you take two numbers a and b, use the mathematical operators +,-,*,/ and get the number c as an answer. no matter what you do, as long as you use the mathematical operators and two numbers you get a number as an answer. in IEEE floating point you dont always get a number as an answer. —The preceding unsigned comment was added by T.Stokke (talk • contribs) 22:42, 14 March 2007 (UTC)
replies: text: Sometimes in IEEE floating point, you get NaN, which acts the same as \Phi.  — Arthur Rubin |  (talk) 22:46, 14 March 2007 (UTC)
replies: text:  The difference is NaN is defined by computers as a completely unique kind of variable in that it doesn't necessarily equal itself.  Phi, on the other hand, would be a completely typical variable that does.  This is definitely less messy, especially from a programming standpoint.  Most likely, the effect of this on computing will be minor and long-term, but regardless of its trivality, the result is something arguably more stable than IEEE float.  It does introduce new problems, but there are overall fewer problems in general. 76.93.65.34 (talk) 10:20, 19 November 2008 (UTC)
replies: text: Even worse, it 0*NaN is NaN, but 0*[(0/0)]=0, if we're going to define this Phi thing by (0/0). 129.93.161.205 (talk) 17:46, 29 June 2023 (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: 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)
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)
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 

message: • A machine proof of the consistency of transreal arithmetic has been released. 
• Real arithmetic is partial and allows considerable freedom to chose continuity constraints in real analysis. Transreal arithmetic is total and allows correspondingly less freedom to choose continuity constraints in transreal analysis. However, I know of no case where this reduction in freedom prevents transreal analysis from obtaining a solution. Furthermore, I conjecture that transreal arithmetic obstructs all and only the cases of continuity that are problematical in real analysis. I suggest that it is useful to have this obstruction because it forces machine proofs of  transreal or real analysis to deal explicitly with these cases which might otherwise be missed erroneously. So far as I know, any desired continuity constraint that is valid in real analysis can be imposed on transreal analysis by defining an auxiliary function. Thus, there is no loss in expressive power by adopting transreal analysis, but there is a gain in the security of machine proof. I regard this as useful.
• I am continuing to assess claims to prior invention. Initially, I check the equivalence of the systems. So far, no prior system has proved to be equivalent to transreal arithmetic. I then check the mathematical scope of the other system to understand how it relates to the problem of developing a total arithmetic that is consistent with standard topology, geometry, and analysis. I then seek to understand the motivation for the other system. Where the author(s) are contactable, I engage in a correspondence to get these issues clear. Finally, I draw up conclusions on how the systems relate. This takes some time. If I do find a case of prior invention I will acknowledge that fact. (I will also note close cases, there is only one so far, to save others the trouble of conducting these comparisons, and to highlight similar work. For the avoidance of doubt, I would not have considered this one case to be similar had there not been repeated claims in favour of it.) James A.D.W. Anderson 15:04, 9 January 2007 (UTC)
thread_title:  Second reply to critics giving some verifiable facts and some opinion 

message: This section should be removed, or at least summarized in a few sentences.  We don't need to summarize all of Dr. Anderson's works into his article here.  It's too much detail for an article about Dr. Anderson.  An article for Transreal Arithmetic was removed for being not notable enough, and not having any secondary sources for this seems proof enough.  If anyone wants to summarize this section, feel free to do so, otherwise I will likely delete all of it except for the first two paragraphs. Vir4030 17:16, 15 January 2007 (UTC)
replies: text: Wikinews articles are not reliable sources since they are self-published wiki articles.  I am restoring the cleanup and source tags to the article.  This article needs cleanup. Vir4030 15:21, 16 January 2007 (UTC)
replies: text: Oops - perhaps I should have put my comments in the above section here instead.  At the expense of being repetitive, I think I'll say it again though: this section has no references other than to Dr. Anderson's papers.  The Wikinews article is not a "reliable" technical source of information on transreal numbers.  Lunch 21:30, 16 January 2007 (UTC)
thread_title:  Transreal Arithmetic Section 

message: Transreals and  wheels are different things. Transreal numbers are defined on the set of real numbers, augmented with three strictly transreal numbers: negative infinity, positive infinity, and nullity. Wheels are defined variously on an integral domain and/or a commutative ring, augmented with at least two objects: infinity, and  bottom. These sets are always different because transreals have minus infinity is less than infinity, whereas wheels have minus infinity equals infinity. This leads to a difference in the operations of addition and subtraction, and the property of distributivity, amongst other differences.
The transreal numbers preserve all of the properties of real numbers and extend some of  these properties to the strictly transreal numbers. Wheels do not preserve all of the properties of real numbers. For example, the transreals preserve ordering of the reals so that the sentence “0 < 1” is true, whereas wheels do not preserve ordering so this sentence is undefined. As a second example, the sentence “0/0 = nullity” is a true sentence in transreals describing a property of the real number zero. The corresponding sentence in wheels, “0/0 = bottom,” does not describe a property of the real number zero, it describes a property of the zero element of an integral domain and/or a commutative ring, as the case may be.
IEEE float is dangerous because the specification that NaN is not equal to itself breaks a cultural stereotype. This is illustrated in the fragment of pseudocode, “statement_1; if x = y then statement_2 else statement_3 endif.” Suppose that statement_1 calculates x and y as identical quotients. If the code is executed in integer arithmetic and involves a division by zero in statement_1 then statement_1 raises an exception, otherwise statement_2 is executed. In no case is statement_3 executed. Now, if the code is executed in floating point arithmetic and statement_1 involves a division by zero then statement_1 may or may not raise an exception, depending on how flags are set in the processor. If no exception is raised in this case then statement_3 is executed; but if there is no division by zero in statement_1 then statement_2 is executed. Thus, the behaviour of conditional tests is radically different when a modular change to code is made that converts integer to floating point arithmetic. This is just one example. There are many possible examples of how breaking this cultural stereotype results in erroneous computer code, and it is hard for programmers to find such errors because their cultural stereotypes make it difficult to conceive of such cases.
The transreals, wheels, and floating point arithmetic are all methods of obtaining  total functions. If a computer program uses only total functions then it will execute in every case, but if it uses partial functions, such as the functions of real arithmetic, then it may fail in some cases.
(The article asks for citations relating to my biography. I will supply third-party citations that list the required information where I know of these, but it will take some time to collate this information. All of the biographical information can be verified under the Freedom of Information Act by asking a question, in writing, of the Universities in question.) —The preceding unsigned comment was added by James A.D.W. Anderson (talk • contribs) 18:54, 15 January 2007 (UTC)
replies: text:  You seem to misunderstand the function of a talk page. It most specifically is where Dr. A. should discuss what appear to be inaccuracies in the article. Also, you call Dr. Anderson's posts here 'haranguing' despite that he's nicer than most other posters. You're trolling. 24.82.203.201 (talk) 09:47, 26 January 2008 (UTC)

text: Actually, it is much more important for information to be neutral, not autobiographical. Furthermore, how would these catalogues of university staff be primary or "original" research, anyway? mike4ty4 05:42, 18 June 2007 (UTC)
thread_title:  Third Reply to Critics Giving Verifiable Facts 

message: Uncle G, I've said it before above, but I'm not sure you've read my comments so I'll say it again.  The Wikinews article that you keep mentioning does not address the technical merits of transreal numbers.  Wikinews is not a computer science or mathematics research journal.  As the section "Transreal numbers" currently stands, it is a summary of Dr. Anderson's papers.  It appears to be a fine summary, but -- again -- it is a summary of Dr. Anderson's work alone.  The Wikinews article is not a reliable source on this matter.  I think other editors agree with me here.  Lunch 20:51, 25 January 2007 (UTC)
replies: text: To me the tags seem partially pointless. We are pretty certain that we have all the sources for the article so there is no use in a tag which asks for more sources. Self-published is not an acurate description as they have been reviewed (lightly) and published by a third party. On one of the other JA related articles I briefly created a custom template anlong the lines of: This work has appeared in published journals, however they are not fully peer-review so do not meet normal wikipedia criteria for reliable sources. Something along this line may be a suitable compremise. --Salix alba (talk) 23:41, 25 January 2007 (UTC)
replies: text: Thank you, Salix, for that thoughful comment.  That seems like a reasonable compromise and signals that, hey, there's really only one source on transreals.  Lunch 02:06, 28 January 2007 (UTC)
thread_title:  wikinews as a source on transreal numbers 

message: I see that this talk page is full of misunderstandings about transreal numbers, and the article is almost 49% about Transreal numbers, 49% IEEE floating point and 2% about James himself.
Honestly there should be created 1 article about James Anderson himself, and 1 article about transreal arithmetics.  —The preceding unsigned comment was added by T.Stokke (talk • contribs) 22:59, March 31, 2007  (UTC)
:James Anderson's theories are covered in the article, and I cannot distinguish between transreal numbers and IEEE floating point in any (trans)real sense.  — Arthur Rubin |  (talk) 03:58, 1 April 2007 (UTC)
replies: text: There is a very obvious difference. The IEEE standard requires 0*NaN to be NaN whereas clearly 0*[(0/0)] = 0 in the L'Hopital sense. 129.93.161.205 (talk) 17:51, 29 June 2023 (UTC)
thread_title:  Misunderstandings and article accuracy 

message: The second two limits in the box on the right are wrong.
you cannot evaluate x/0 as x -> 0+
163.1.148.48 15:45, 2 May 2007 (UTC)
replies: text: Changed x/0 to 1/x, for the moment.  That might be the intent.  — Arthur Rubin |  (talk) 16:36, 2 May 2007 (UTC)
thread_title:  The limits in the box on the right... 

message: I do not yet have a source for this, but the BBC report was not only shown on South Today, as I remember seeing this, and I live in an area where South Today is not broadcast  —Preceding unsigned comment added by 86.161.138.219 (talk) 10:02, 10 December 2007 (UTC)
thread_title: BBC

message: I mean, did he publish a single article about the EXACT application of this? He mentions that a pacemaker might fail if it reached an exception while having 0 dividing 0. As one of the "Further Readings" state, with transreal numbers, what can you actually do if you get an answer of nullity? If he does state actual applications for this, it's VERY IMPORTANT that someone add them to the article. --68.161.190.195 (talk) 19:07, 13 December 2007 (UTC)
replies: text: We don't need to note whether or not they're useful, only that he claims they're useful, and that claim is reported.  Personally, I agree that none of his concepts (at least as reported here and in the references here) are useful, but I'm afraid being "useful" is not a requirement for the subject of a Wikipedia article.  — Arthur Rubin |  (talk) 19:27, 13 December 2007 (UTC)
replies: text: However, if you're going to have an article about a concept which has notability, potential usefulness is vital in the article, provided it exists. --68.161.190.195 (talk) 09:40, 14 December 2007 (UTC)
replies: text: Actually, I think that should be: provided there are sources that document it. Otherwise it is original research which is not game for Wikipedia regardless of whether or not it "exists". mike4ty4 (talk) 08:50, 17 December 2007 (UTC)

text: Wikipedia is not the place to make claims about things, only to journalistically and neutrally report on claims that have already been made -- no original research is one of the core principles of Wikipedia. Furthermore, although I know this ain't relevant, I just have to say, the software for pacemakers better darned be fault-tolerant and be able to catch and handle the exception if generated in a way that will allow it to continue to run! If I was running the company making the thing, I'd fire the programmer if I found out they hadn't implemented a proper exception handler! mike4ty4 (talk) 08:50, 17 December 2007 (UTC)
replies: text: "If he does state actual applications for this..." Why are you people nitpicking over each of my posts in succession as if I knew nothing of how Wikipedia works, rather than JUST ADMITTING THAT YOU DON'T KNOW? --68.161.190.195 (talk) 06:52, 18 December 2007 (UTC)

text: I decide to have a look at what Anderson has been up of late and found a blog Transreal Computing - The Elevator Pitch. Apparently they are developing a parallel computer which use transreal arithmetic  in the processing units. If this actually gets built, I see no reason why this system could not be built in a chip, then it could be said that Transreal numbers are useful. --Salix alba (talk) 11:30, 17 December 2007 (UTC)
replies: text: It could be said that they are used. Whether or not they are useful--whether or not they would have been better off using IEEE floating point--would still be up in the air.--Prosfilaes (talk) 14:13, 23 January 2008 (UTC)
thread_title:  Transreal numbers are not useful 

message: It's really criminal and inhumane that they let this nullity-guy 'teach' to mostly acritical, defenseless children. If he's such a tough guy, why doesn't he submit to Nature? They a have a 'dequackination' review board always striving for more blood. The parents of these pupils should sue.  --Quackinator  —Preceding unsigned comment added by 89.152.242.155 (talk) 07:02, 23 January 2008 (UTC)
replies: text: I tend to agree, but this has little to do with editing the article, and probably should be deleted.  — Arthur Rubin |  (talk) 14:04, 23 January 2008 (UTC)
thread_title:  Stupid MF 

message: Dear Mister Anderson,
Your introduction of "nuillity" is old news to the logic community, we usually use the symbol
called \bottom in standard LaTeX to denote the undefined, and I know of no papers which treat the stuff your theory is made of, since it is a very easy excersise for undergraduates to verify by induction on the build-up of terms, that any term containing an occurrence of the constant for nullity, will be provably equivalent to nullity.
In contrast the introduction of complex numbers proved invaluable to many fields of mathematics. I am not an expert on the subject (complex analysis), but the simple identity
i^2=-1 should suffice as an example. Does everyone see the difference? i actually makes new computations possible. One ventures out into the complex plane—and imporantly—returns to the real line. In Anderson's model however, once you go to nullity, there is no coming back. Calling the undefined a number is actually a historically erroneous use of the term number, which usually is reserved for solutions of
equations in a field (and their extenstions). One cannot, and this is an easily provable fact, find a multiplicative inverse for 0 in a field.
In fact, in more theoretically and abstractly flavoured mathematics, division as such do not even enjoy an independent status as an operation on numbers. To divide by n is formally considered as shorthand for the operation to multiply by the multiplicative inverse n^{-1}.
Since it is an axiom of the theory of fields that
\forall x\left(0\cdot x=0\right) (read for all elements x of a field,
it is true that x multiplied by zero equals zero), and since
the axiom for mulitplicative inverses state x^{-1} of x satisfies \forall x\left(x\neq 0\to\exists x^{-1}x\cdot x^{-1}=1\right), it is evident that the only field where division by zero is possible, is the field with exactly one element 0, i.e. 0=1. Note that this last axiom does not state that there is no inverse for 0, only that by defintion, in a field, every nonzero element has an inverse. That 0 does not have an inverse, is a logical consequence of other axioms, and the assumption that 0\neq 1. In fact, there is one unique field where 0 has an inverse: the trivial field with one element.
In this case we have \frac{0}{0}=0. But, recall, that we also have
0=1, so this field is rather uninteresting. (Not inconsistent though, the use of
0=1 as the canonical inconsistency is only sound on the implicit assumption that the theory in question implies nontriviality).
Best Mathias  —Preceding unsigned comment added by 80.212.86.168 (talk) 22:45, 8 February 2008 (UTC)
thread_title:  The theory is void (as in empty) 

message: According to his website "perspex" stands for "perspective simplex", whatever that means. Perhaps that should be included in the article, so people don't get a mental picture of some sort of magic Wonkavator made of acrylic glass. Salvar (talk) 12:06, 1 June 2009 (UTC)
thread_title:  Perspex? 

message: I believe the 2nd AfD established notability.  Is there reason to believe consensus has changed?  — Arthur Rubin  (talk) 15:56, 23 January 2011 (UTC)
thread_title:  Notablility 

message: I'm going by the axioms stated in this paper of his. http://www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf By A15, nullity * a = nullity for any a. By A16, infinity * 0 = nullity. Letting a = nullity, A15 tells us that nullity * nullity = nullity. This means that nullity * nullity = infinity * 0. Dividing both sides by 0 and applying A17 as well as A12, we get nullity * nullity * 0^(-1) = infinity. By A15, this simplifies to nullity * 0^(-1) = infinity, which simplifies by another application of A15 to nullity = infinity. This contradicts his axioms. Q.E.D.  — Preceding unsigned comment added by 99.241.98.119 (talk) 02:11, 14 July 2011 (UTC)
replies: text: When you divide both sides by 0, you're assuming that 0/0 = 1, when it does not.  Correcting your mistake, we have (after dividing by zero) Φ*Φ*0-1 = ∞*Φ, which (by A15) simplifies to Φ = Φ, which is a tautology.  — Preceding unsigned comment added by Ianmathwiz7 (talk • contribs) 03:16, 10 September 2011 (UTC)
thread_title:  A disproof 

message: Transreal arithmetic is discussed in a recent history of mathematics book. See http://www.bookofparagon.com/News/News_00039.htm I had no contact with the author prior to publication. James Anderson - the subject of this page.  — Preceding unsigned comment added by 134.225.31.99 (talk) 11:42, 1 October 2013 (UTC)
thread_title:  Transreal arithmetic in a history of mathematics book 

message: I am the subject of this wiki. The wiki says that I have published two papers on division by zero but there are more publications than this, two of which won best-paper prizes. See: http://www.bookofparagon.com/Pages/Papers.htm
There is a Google+ group on transmathematics here: https://plus.google.com/communities/103261551046378190173  — Preceding unsigned comment added by 109.147.66.221 (talk) 19:59, 6 June 2018 (UTC)
thread_title:  FYI There are more than two publications on transreal arithmetic 

message: I am the subject of this page.
I established the Transmathematica journal https://www.transmathematica.org in 2017. You might want to put this in the external links section of the page.
I retired from Reading University with effect from New Year's Eve, 2019.
86.178.110.164 (talk) 16:00, 8 January 2020 (UTC)
thread_title:  FYI - Retired from University 2019, established journal 2017 

message: I am the subject of this article. I removed a libellous comment and replaced it with a true statement of fact. This is your second warning - DO NOT LIBEL ME AGAIN.
I have corrected false statements about IEEE floating-point arithmetic. These are matters of fact, which you can check by consulting the IEEE standards or the Wikipedia pages about them. Specifically, there is a multitude of NaNs none of which is equal to any NaN. Evaluating NaN = NaN is either FALSE or ERROR, depending on context switches.
The article makes several false statements about transreal arithmetic. These are matters of fact, which can be checked in peer reviewed papers. Is an editor happy for me, the subject of this article, to correct these matters of fact?
SERIOUSLY - DO NOT LIBEL ME AGAIN
James A.D.W. Anderson (talk) 11:37, 28 October 2022 (UTC)
replies: text: I have corrected typos, made the text consistent, clarified the result of an IEEE floating-point operation that has multiple NaN arguments, and replaced unsupported and false statements about transreal arithmetic with true statements supported by existing references or an informal proof. James A.D.W. Anderson (talk) 11:25, 29 October 2022 (UTC)
thread_title:  Edited libellous comment and corrected false statements about IEEE floating-point arithmetic 

message: I am the subject of this article so am not permitted to make biographical edits. I therefore propose that someone else should consider making the following additions to improve the article.
Add a note that I am the Editor in Chief of the Transmathematica journal - https://transmathematica.org - so that readers can easily find papers on total systems, including transreal arithmetic, written by multiple authors.
Add a link to my Google Scholar page - https://scholar.google.co.uk/citations?user=IPoHbOoAAAAJ&hl=en - so that readers can quickly find my publications and other papers that cite them. This will allow readers to more easily assess the range, value, and increasing acceptance of transreal arithmetic and of the other transnumber systems (currently transcomplex and transquaternion numbers).
Note that I was a Fellow of the British Computer Society and remain a lifetime member of the AAAI.
James A.D.W. Anderson (talk) 11:42, 29 October 2022 (UTC)
thread_title:  Proposal to improve this article 

message: I am the subject of this page. The description of my academic and employment history is missing significant detail. Here is the detail from a source that is relatively easy to check.
Book:
J.A.D.W. Anderson, “Pop-11 Comes of Age: the advancement of an AI programming language,” Ellis Horwood, 1989.
There is a biography inside the back cover which reads as follows.
“Graduating with a B.Sc. (Hons) in Experimental Psychology from the University of Sussex in 1980, James Anderson held the post of research assistant in Engineering and Applied Sciences at Sussex University (1982-1983); and from 1983 to 1987 he held the same position in the Department of Electrical and Electronic Engineering at Plymouth Polytechnic. Previous to his current position as Lecturer in the Department of Computer Science at Reading University, Mr Anderson held a research fellowship in that department (1987 to March 1989). He is Chairman of the Poplog and Pop Languages User Group.”
James A.D.W. Anderson (talk) 14:38, 3 November 2022 (UTC)
thread_title:  FYI