Talk:Parity of zero

message: Could someone please clarify what the graphic :File:NuerkFigure4.svg is meant to convey? 173.75.159.152 (talk) 11:01, 13 April 2010 (UTC)
replies: text: It's a scaling analysis of response times. See the footnote or the image description page for more details. Melchoir (talk) 19:59, 13 April 2010 (UTC)
replies: text: Well, the image caption says that much.  But what does it mean?  The image description fails to indicate the significance of the lines and the apparently random distribution of numbers in the oval.  173.75.159.152 (talk) 23:02, 13 April 2010 (UTC)
replies: text: Good point. I've now answered this question in additions to the caption footnote and the Commons description. Melchoir (talk) 03:26, 14 April 2010 (UTC)
replies: text: Much better, thanks.  173.75.151.23 (talk) 00:37, 15 April 2010 (UTC)
replies: text: No prob! Melchoir (talk) 01:27, 15 April 2010 (UTC)
thread_title:  Inscrutable graphic 

message: Recently the following interesting exchange took place at WPM, between editors Mdcq and PrimeHunter:
:Two thirds of elementary teacher candidates thought zero was odd? Eek! Surely that can't be right? Dmcq (talk) 16:18, 19 April 2010 (UTC)
replies: text: That is not quite what the article says. It says about two thirds answered "False" to "Zero is an even number." I guess most of them thought it was neither even nor odd. It's bad but I'm willing to believe it. I would have been less willing to believe that two thirds thought zero was odd. PrimeHunter (talk) 23:00, 19 April 2010 (UTC)

text: No, I don't recall ever seeing excluded middle mentioned in the literature. This is probably because it's an orthogonal issue. Classical logic is perfectly comfortable saying that 0 is neither positive nor negative; that 1 is neither prime nor composite; that 1/3 is neither even nor odd. Melchoir (talk) 19:09, 20 April 2010 (UTC)
replies: text: I expect the teachers think 0 is not even because you cannot divide it into two SMALLER groups with the same number of elements.  The way parity would be typically taught is in terms of a pile of candies that you can (or cannot) divvy up between two children, with each naturally getting less than the full pile.  If that's the definition, then 0 is not even.  What do you think?  Tkuvho (talk) 10:14, 21 April 2010 (UTC)
replies: text: There is one child in one of the articles, I think by Ball, who says something that leads the author to surmise that he is looking for a number N < 0 such that N + N = 0. There's no evidence that this belief is common, let alone universal. Melchoir (talk) 18:05, 21 April 2010 (UTC)
thread_title:  included middle 

message: I'm removing this as OR. It's all true, but it's still not defensible at FAC. I do intend for the basic idea to be represented in the "Basic explanations" section. Melchoir (talk) 19:16, 25 July 2010 (UTC)
thread_title:  Removed "The empty set" 

message: In connection with the suggestion to prove the even parity of zero by means of the fixed point-free involution of the empty set given by the empty function: has it occurred to anybody that the empty function can be shown to be an odd function?  Namely, for every x in the domain, it satisfies f(-x)=-f(x).  Truly odd :)  Tkuvho (talk) 08:59, 26 July 2010 (UTC)
replies: text: Heh. :) You know, in the course of researching this article, I've come to hate even and odd functions. They introduce so much noise into web search results! You get all these hits that look like a source is saying that 0 is both even and odd, or neither even nor odd. Then you follow the source, and no, it was talking about a function named theta, or capital-O, or the zero function on the real numbers. Bastards. Melchoir (talk) 09:25, 26 July 2010 (UTC)
thread_title:  semi-arbitrary section 

message: Just for the record, I've come to agree with . It's relevant and correct to describe 0 as "the sum of an integer with itself", but it's also unnecessary and misleading. Melchoir (talk) 05:06, 25 February 2012 (UTC)
thread_title:  Sum of an integer with itself 

message: For the history section, does anyone know beliefs about the parity of zero in the 1800s?  I ask this because Froebel's Education of Man instructs schoolmasters to teach that 1 is not an even number nor an odd number.  Two is discussed as even, then three as odd, etc.  The current article makes it sound as though the issue of 1 not having parity was resolved after the Greeks adopted 1 as a number, but the concept obviously lingered in European minds through the 1800s.  
This observation also makes me question the inability to date the parity of zero.  I noticed Chase (1849) hidden in the references, and I think this information should be portrayed in the history content.  
The statement about one historian's opinion about Greeks not knowing zero is misleading because even after ancient Greeks became aware of zero, they still had objections with the number 1 for various reasons.
 
Thelema418 (talk) 17:08, 18 June 2012 (UTC)
replies: text: Chase (1849) was once in the main body text, but it was moved into the footnotes with , in response to feedback at Wikipedia:Peer review/Evenness of zero/archive1. To avoid rehashing the reasoning, it would be great if you could take a look at that link, and then you can follow up here if you still think a change is warranted. Melchoir (talk) 07:17, 25 June 2012 (UTC)
thread_title:  History Issues 

message: I'm moving this content here from the Further Reading section of the article. The following sources have something to say about the parity of zero, but they couldn't be worked into the article for one reason or another. Melchoir (talk) 04:47, 31 July 2013 (UTC)
thread_title:  Old Further Reading section 

message: It is odd. I mean, what other number is the sum of itself with itself? What other number is both positive and negative? What other integer number has the same factorial as its successor?
Since this makes zero odd, it makes it the only number that is both even and odd, which in turn makes it even odder.
David Olivier (talk) 10:18, 29 August 2013 (UTC)
replies: text: How do any of those three things you've stated make it odd? To my knowledge, no other odd number has any of those characteristics. OrganicsLRO 10:55, 29 August 2013 (UTC)
replies: text: Well, that's true! That only makes it odder still! David Olivier (talk) 11:02, 29 August 2013 (UTC)
replies: text: That's wordplay, isn't it. --benlisquareT•C•E 11:20, 29 August 2013 (UTC)
replies: text: That's indeed what it appears to be.  (For what it's worth, what I find most odd about the number zero is that any human ever in the history of humanity failed to innately realise it was even, always even, and nothing but even.  That, to me, is supremely odd.)  allixpeeke (talk) 05:36, 11 March 2017 (UTC)
thread_title: I think that zero is odd.

message: In the introduction of this article it is stated "zero shares all the properties that characterize even numbers: 0 is divisible by 2..." and " Not only is 0 divisible by 2, it is divisible by every integer. "
This seemed highly dubious to me, and after some research, the Wikipedia article "Division by zero" states that " In ordinary (real number) arithmetic, there is no number which, multiplied by 0, gives a (a≠0), and so division by zero is undefined". " Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a /0 is contained in George Berkeley's criticism of infinitesimal calculus in The Analyst ("ghosts of departed quantities").[citation needed]
There is a clear fallacy in one of these statements / articles and must be corrected at once. 
--DragonFly31 (talk) 16:14, 29 August 2013 (UTC)
replies: text: Whether it is possible to divide by zero is irrelevant to the question of whether zero can be divided by other numbers. It seems like you are drawing a link between two unconnected things. MartinPoulter (talk) 16:28, 29 August 2013 (UTC)
replies: text: I changed it to "divisible by every positive integer." Pedantry satisfied. Ntsimp (talk) 16:38, 29 August 2013 (UTC)
replies: text: Is there such a thing as pedantry in mathematics? I guess another debate for another dayDragonFly31 (talk) 13:48, 3 September 2013 (UTC)

text: This is not a problem. 0 is divisible by 0 under the standard definition of a divisor. For m | n, the definition only needs there to be an integer for which mk = n, and certainly for m = n = 0 any integer works. Sometimes a proviso that k be nonzero is made, but then the result is that 0 is only divisible by 0. No matter how you look at it, 0 divides 0 by this definition, although I agree that the standard terminology is a bit confusing for this case. I am also not sure how to read this into DragonFly31's OP, which seems to confuse "0 is divisible by 2" (true) with "2 is divisible by 0" (false), but it is true that there is a little wrinkle here for 0 being divisible by 0. Double sharp (talk) 02:42, 20 December 2017 (UTC)
thread_title: Divisibility by 2 (of zero)

message: Regarding these two edits  , would it work to replace "sum of an integer (0) with itself" with "sum of an integer with itself (0 + 0)" or similar? Melchoir (talk) 16:48, 29 August 2013 (UTC)
thread_title:  Sum of an integer with itself 

message: This Wikipedia article says it is positive, but the "Zero" Wikipedia page states that zero is neither positive nor negative.  ??  — Preceding unsigned comment added by 64.211.112.98 (talk) 17:45, 29 August 2013 (UTC)
replies: text: Er, which part of this article are you referring to? A quotation would help. Melchoir (talk) 17:47, 29 August 2013 (UTC)

text: When grafted, zero is the point at which negativity meets positivity.  allixpeeke (talk) 06:55, 11 March 2017 (UTC)
thread_title: Is zero positive?

message: Ib the section 'Everyday Contexts", I see this: "Around the year 2000, media outlets noted a pair of unusual milestones: "1999/11/19" was the last calendar date composed of all odd digits that would occur for a very long time..."  That doesn't make sense. This must be a typo for "1999/11/29" and I am correcting it..  70.114.146.227 (talk) 20:19, 29 August 2013 (UTC)
replies: text: The 2 in "29" is an even digit, not an odd digit. Melchoir (talk) 20:32, 29 August 2013 (UTC)

text: Twenty-nine is a number, not a digit.  allixpeeke (talk) 06:57, 11 March 2017 (UTC)
replies: text: It is NOT a typo. 2 is even. Already we have one useless article about 0 being even. Do we need an article on why 2 is even? Then 4? Then 6? And so on forever? I really wish that you could all just use your logic. 2A00:23C7:5882:8201:A92D:B524:90B0:715 (talk) 16:57, 1 March 2023 (UTC)
thread_title: Calendar date

message: "zero is an integer multiple of 2, namely 0 × 2, so zero is even." A classic example of an unstated assumption. This is only true if zero is assumed to be an integer which, luckily, it is.67.170.238.175 (talk) 21:52, 29 August 2013 (UTC)
thread_title:  Why Zero is Even 

message: It's impressive that a statement of the trivial and obvious can have 75 references. Next time someone complains about the difficulty of finding references for their article, I shall refer them here. Maproom (talk) 21:58, 29 August 2013 (UTC)
replies: text: The Monty Hall problem is trivial too, and yet, lots of people get it wrong. The same is true for the evenness of 0. That means that these are useful problems for math education. MvH (talk) 14:10, 12 February 2014 (UTC)
thread_title:  References 

message: I'm not sure that I understand . Replacing the word "namely" with "specifically" makes the sentence harder to read. What's the point? Melchoir (talk) 21:59, 29 August 2013 (UTC)
replies: text: "Namely" is wrong - it is not followed by its name. Maproom (talk) 22:12, 29 August 2013 (UTC)
replies: text: Hmm, that's not quite a slam-dunk case. A formal multiple of 2 is precisely an arithmetic expression of the form N × 2, which is a name that happens to signify the number formed by multiplying N by 2. It's not the canonical name of that number, but it's a valid one. Either way, you were right to call it pedantic. :-P Is the distinction all that important in this context? Melchoir (talk) 22:30, 29 August 2013 (UTC)

text: ...Actually, the more I think about this, the less sure I am. Does anyone else have an opinion? Melchoir (talk) 22:41, 29 August 2013 (UTC)
replies: text: Nothing much is at stake, but wouldn't "since" work perfectly well, and enhance readability because it has one syllable rather than five? MartinPoulter (talk) 21:20, 4 September 2013 (UTC)
replies: text: How would that work? Replacing just the one word would read, "it is an integer multiple of 2, since 0 × 2", which doesn't make sense. I suppose you could say "since it is", but that's awkward in the context. Melchoir (talk) 23:34, 4 September 2013 (UTC)
replies: text: Yes, I was mistaken. I was thinking "since 0 x 2 = 0". "specifically 0 x 2" is the most correct and elegant. MartinPoulter (talk) 08:00, 5 September 2013 (UTC)
thread_title:  Is specifically better than namely? 

message: # A pair consists of two elements. 
# Dividing a number by two, we find the number of pairs.
# Zero elements, resulting zero pairs.
The number Zero is neither odd nor even.    
Zero parity
--Gvitalie (talk) 07:40, 17 October 2015 (UTC)
replies: text: This is not a matter of opinion. You're just wrong. Double sharp (talk) 14:28, 11 January 2017 (UTC)
thread_title:  Could we include some different opinion regarding zero parity? 

message: A recent attempt to say that zero is neither odd nor even comes from a misinterpretation from the gambling world. The 0 that appears on a roulette table is just a symbol, it is not a number. Casino owners need to be very clear on this point since their profits depend upon it. If someone bets on evens and a 0 comes up, the casino owners will not give a payoff. This is justified by the statement that 0 is a transnumeral, that is, it is beyond numbers, i.e., it is not a number. Since it is not a number, it can not be even (or odd for that matter). Similarly we have 00 as a transnumeral on Vegas tables. In the same way, 0 is not red or black (usually it is placed on a green background), but this doesn't really cause any problems because this is a visual property and few would argue that there should be a payoff for 0. --Bill Cherowitzo  (talk) 22:24, 31 May 2017 (UTC)
thread_title:  Roulette tables 

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thread_title:  External links modified 

message: Isn't this article relevant to be mentioned in a see also section? I'm not a mathematician but it seems like a related concept.-occono (talk) 12:20, 16 June 2018 (UTC)
replies: text: Outside of the fact that the word "zero" appears in both titles, I see no connection between these articles. The division by zero article sheds no light on the parity question and a *See also* section is supposed to direct a reader to related articles for an expansion of the topic. --Bill Cherowitzo  (talk) 18:26, 16 June 2018 (UTC)
replies: text: A redirect for this article is evenness of zero. Evenness means whether a number can be divided by two. Division by zero concerns the notion of dividing by zero. So Zero can be divided by two, but nothing can be divided by Zero. Seems like it's a related topic of division and multiplication of zero to me? :S --occono (talk) 21:23, 16 June 2018 (UTC)
replies: text: I agree with Bill's comment: Division by zero does not expand on Parity of zero.  Both articles do expand on the base subject Zero though, and indeed, the former article is rightfully listed in its See also, and the latter is directly wikilinked in the article. But here we don't need to mention the other article. - DVdm (talk) 21:50, 16 June 2018 (UTC)
thread_title:  Division by Zero 

message: It seems so, so absurd that anybody in the history of humanity would ever think about zero as anything but even and only even. There are all sorts of arguments that zero is even. 0 divided by 2 is 0 (an integer). It is actually the most even number since you can divide it forever and you never get a decimal number. I think this page should be deleted. Why should Wikipedia have a page just about some bullsh*t that some stupid children say? 2A00:23C7:5882:8201:1B:E11:8CC4:81D6 (talk) 16:17, 20 December 2022 (UTC)
replies: text: The short answer: see Parity of zero#References and Parity of zero#Bibliography. And Religion. - DVdm (talk) 17:17, 20 December 2022 (UTC)

text: Yes. This article is absolutely wrong. 188.208.126.106 (talk) 05:53, 24 December 2022 (UTC)
thread_title:  How the actual f*ck did anyone in the history of humanity think zero is not even or both even and odd? (Nomination for deletion) 

message: No, we cannot group zero elements in group of two elements, therefore number zero is neither odd nor even. 188.208.127.146 (talk) 09:54, 20 February 2023 (UTC)
replies: text: Yes we can; we can group zero elements into zero groups of two elements :-) Lokys dar Vienas (talk) 02:16, 25 February 2023 (UTC)
replies: text: We cannot group zero elements in groups with two elements in group. 188.208.127.94 (talk) 07:44, 12 March 2023 (UTC)
replies: text: We certainly can, such that the number of such groups is an integer. MartinPoulter (talk) 20:45, 12 March 2023 (UTC)
replies: text:  This is off-topic here per wp:talk page guidelines. - DVdm (talk) 21:28, 12 March 2023 (UTC)

text: If we have zero groups, how many elements are in zero group? 188.208.126.99 (talk) 05:31, 16 March 2023 (UTC)
thread_title:  Can we group the zero elements into groups of two elements? 

message: They were restored with edit summary "Undid revision 1132064612 by Lokys dar Vienas (talk) Sourced material was removed with insufficient justification". In fact the justification was pretty sufficient:
*curprev 02:48, 7 January 2023‎ Lokys dar Vienas talk contribs‎  45,176 bytes −11,162‎  →‎Mathematical contexts: not about zero but about parity in general undo Tag: Reverted
*curprev 02:47, 7 January 2023‎ Lokys dar Vienas talk contribs‎  56,338 bytes −3,051‎  →‎Defining parity: rm OR 
I restored my deletion with a reworded justification: " original research of WP:SYNTH type: the deleted text and source within do not discuss the article subject, i.e., parity of zero "
If you disagree,pleaase presentn your agrumments here, in article talk page. Lokys dar Vienas (talk) 20:20, 1 May 2023 (UTC)
replies: text: It's alarming that you present the above edit summaries as though they were "pretty sufficient" justification. It's not clear to me how those edit summaries relate to the edits they are supposed to summarise. You didn't present an argument on the Talk page before, or subsequent to, making these drastic changes. I shall set out why the article should have stayed the way it was. First of all, you removed substantial sourced material from an article that has passed Featured Article review. That needs a very good case to be made; a Featured Article is a community decision resulting from careful and detailed reading of the article. For your specific edits, you claim the material removed in this edit is "not about zero" but it plainly does include arguments as to why zero is even, which are clearly on topic for this article. Even if, hypothetically, we were only talking about material that explains parity in general, that would clearly belong in the article because in explaining the article topic we have to set out what parity is and how it is decided. The material you have removed as "original research" is sourced to Caldwell and Xiong 2012, Gowers 2002, Partee 1978, and Stewart 2001. If you think the article goes beyond those sources or misrepresents those sources, then you should set out your argument: we need a fuller justification than "rm OR". MartinPoulter (talk) 20:59, 1 May 2023 (UTC)
thread_title:  Deleted pieces 

message: Why do people go to this talk page trying to say that 0 is neither even nor odd?? Georgia guy (talk) 15:42, 1 July 2023 (UTC)
replies: text: Its the same person trolling and wasting the time of whoever responds to them. All the IPs come from the same range, 188.208... and originate in the same country. —CX Zoom[he/him] (let's talk • {C•X}) 17:57, 1 July 2023 (UTC)
thread_title:  Serious question