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Numbers

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	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
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Semi-protected edit request on 23 December 2023

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insert the citation:" in through scholarly works written in Arabic.[citation needed]" Insert: ^[1] MPBWM (talk) 21:24, 23 December 2023 (UTC)[reply]

Not done: The provided source is not in Arabic. Spintendo 22:41, 27 December 2023 (UTC)[reply]

@Spintendo: the source does not have to be in Arabic, the citation needed relates to the transmission of the numeral via Arabic texts. @MPBWM: the reference you provided is not in English so I've been unable to verify where the relevant information is. Do you have a page number? Or an English language source? Polyamorph (talk) 10:46, 28 December 2023 (UTC)[reply]

References

^ Eves, Howard (2011). Introdução à história da matemática. Graduate Texts in Mathematics. Vol. 164 (5 ed.). Editora UNICAMP. p. 41. ISBN 978-8526806573.

Smallest Difference?

"Additionally, 1 is the smallest possible difference between two distinct natural numbers." 3-4 = -1

-1<1 2003:CA:E70B:F500:ACDE:4B1D:9525:6ED1 (talk) 15:56, 18 January 2024 (UTC)[reply]

You should read between the lines that "1 is the smallest possible absolute difference". i.e. the difference between 3 and 4 is |3-4| = |4-3| = 1. Dhrm77 (talk) 19:02, 18 January 2024 (UTC)[reply]

Facts about the number 1

This is a section to discuss various facts about the number one, whether (and how) they should be included, and hopefully, seek consensus on the issue. Allan Nonymous (talk) 14:40, 8 August 2024 (UTC)[reply]

I am happy to go through the article line by line if need be. Polyamorph (talk) 18:45, 8 August 2024 (UTC)[reply]

We should do this for all the articles in question, I believe. I will be removing my own SYNTH for all articles I was involved in, which should conclude after a couple of days. For this article, I think most points are valid frankly, they are very tacit and precise, as well as sourced. Radlrb (talk) 21:08, 8 August 2024 (UTC)[reply]

"Mathematically, the number 1 has unique properties and significance."

Redundant sentence, yes, we know 1 is special, its in the lede. We can remove this here

"In normal arithmetic (algebra), the number 1 is the first natural number after 0 (zero) and can be used to make up all other integers (e.g... etc.)." While correct, the way this is phrased is slightly incorrect, this is a fact about the successor function and the succession of numbers. I have rewritten this to that effect. Allan Nonymous (talk) 14:12, 9 August 2024 (UTC)[reply]

Why are you not waiting for a response first? I thought you said you were going to stop editing until there was a consensus reached, in WP:WP Numbers for guidelines to be established, and here for each point needing discussion. Polyamorph asked you that he can go line by line. Radlrb (talk) 14:41, 9 August 2024 (UTC)[reply]

The lead is meant to summarise the article contents, so one would expect content present in the article to be present in the lead. That said, I don't have an issue removing that first sentence. I have modified your revised sentence relating to the succession of numbers so that it fits better as the first sentence of the paragraph. For this I feel it is important to mention that it succeeds 0. Polyamorph (talk) 15:12, 9 August 2024 (UTC)[reply]

The latter part, that it follows 0, is indeed fundamental. Thank you for returning that point, it felt a bit vacuous without it. 0 and 1 are adjacent, and with remarkably dissimilar and similar properties, so it is important to mention their juxtaposition in the set of natural numbers. Radlrb (talk) 16:18, 9 August 2024 (UTC)[reply]

A number following another number isn't really "fundamental" in fact, almost no fact about a number is fundamental (which is an important part of group theory). Is it due? Maybe, I would say no, per the emerging guideline at NROUTINE (as 2 follows 1, etc.) Allan Nonymous (talk) 17:53, 9 August 2024 (UTC)[reply]

It is fundamental in that it is first, the very beginning of countability, which needs to be mentioned so that an understanding of the distinction between N_0 and N^+1 can be introduced, and the "disambiguity" that comes from this, where different authors make use of either different definition in different ways depending on contexts. Secondly, because their properties are soo powerful individually, the proximity between them makes it more remarkable than that from between for instance, 100001 and 100000. Radlrb (talk) 20:29, 9 August 2024 (UTC)[reply]

1 being the first or 2nd element of the naturals is already discussed everywhere else, however, this fact might actually qualify on being a basic fact. Allan Nonymous (talk) 20:35, 9 August 2024 (UTC)[reply]

"1 is the only natural number that is neither composite (a number with more than two distinct positive divisors) nor prime (a number with exactly two distinct positive divisors) with respect to division." is redundant with prior discussions of the primality of one, which cover this topic and are mentioned here.

"The product of 0 numbers (the empty product) is 1 and the factorial 0! evaluates to 1, as a special case of the empty product." This is about 0!, and should probably be paired with facts about 1!. In general, this, and facts about 1 being the first of many sequences should be rewritten as "By convention, 1 is the start of several sequences."

"Any number multiplied or divided by 1 remains unchanged. This makes it a mathematical unit, and for this reason, 1 is often called unity." The etymology is unsourced, and it looks like this sentence means to say a different thing. What is meant to be said here is that 1 is the identity under multiplication in the real numbers.

"Consequently, if is a multiplicative function, then must be equal to 1." this is NOFFTOPIC. Removing

"This distinctive feature leads to 1 being is its own factorial, its own square and square root, its own cube and cube root, and so forth." Given there is nos source, this is WP:OR. Removing.

"By definition, 1 is the magnitude, absolute value, or norm of a unit complex number, unit vector, and a unit matrix (more usually called an identity matrix)." This is clunky phrasing of the concept, given that magnitude, absolute value and norm are all norms.

"1 is the multiplicative identity of the integers, real numbers, and complex numbers." This is correct, but true because each of these sets of numbers extends the integers, since we have already discussed the multiplicative identity above, it is redundant. If someone wants to describe why 1 is also the multiplicative identity of these sets (as well as quotient fields, among others), feel free to do so but that should probably belong somewhere further down in the article. Allan Nonymous (talk) 18:14, 9 August 2024 (UTC)[reply]

I haven't had a chance to review these comments yet (and I'm about to hit the sack) but I've reverted your changes because you did not have agreement to remove the content. You have to give us a chance to actually read your comments and respond before removing content in mainspace. By continuing to delete content before getting consensus is simply a continuation of the same disruptive pattern that you have been warned for. I am expecting this page to be edit protected shortly. (@Daniel Case and Johnuniq: pinging two admins familiar with this case for their independent assessment.) Polyamorph (talk) 21:18, 9 August 2024 (UTC)[reply]

I really wish you would engage with the edits made rather than reverting them, but, to be perfectly honest, it is your choice as to how you wish to respond. Either way, now that you've reverted, I hope you can address the rationale behind the edits. Allan Nonymous (talk) 22:09, 9 August 2024 (UTC)[reply]

Just stop deleting content. You don't have consensus and have been warned many times to stop. When I have engaged with your edits directly in mainspace, you have reverted my changes anyway. So stick to your agreement to stop editing and discuss. This means wait for a response before going ahead and implementating your deletions. Polyamorph (talk) 07:01, 10 August 2024 (UTC)[reply]

@Beland: as an admin who is actively helping mediate the current disputes across numbers articles. Your perspective would be welcome. Polyamorph (talk) 07:15, 10 August 2024 (UTC)[reply]

Short version is a blunt but bedrock cliche: It's probably best to comment on content, and not the behavior of other editors.

Long version is a smattering of responses to specific events and general advice which might be useful to anyone in this discussion:

The edit history will remember everything that is removed, and you can always look at a previous version. It doesn't have to be put back in the article in order to be reviewed. It seems unhelpful to revert a removal without giving an actual objection on the merits, especially if you are in fact intending to look through the removed content in detail and ponder the reasons given. After a dispute has been identified, edits, including reverts, should generally be trying to make progress. Instead of putting everything back blindly, it would be more helpful to only put back what you actually have a content-based reason to keep, and explain that reason as much as possible. It's also helpful, instead of just restoring the same text again, to put up a new version that responds to the concerns expressed by the remover, for example with better sourcing if the objection was "original research" or "NOTOEIS".

Personally, I try not to unilaterally repeatedly undo the changes someone else has made (whether adding or removing), especially if they are exactly the same material, unless there's a clear policy violation like unsourced material in a BLP or something. Even if it's an NPOV violation, I can usually live with the "wrong" version for a few days while it's under discussion by adding a problem tag to the article to highlight the dispute for readers.

People do need to work with others to resolve conflicts and build consensus, but I don't find procedural objections to be particularly helpful. Often if I do A people will complain that I need to do B first. Then other times I'll do B, and people will complain I need to do A first. This isn't a bureaucracy, it's a community of volunteers. I think instead of trying to force other people into our own way of doing things, it's better just to be happy that someone is actually paying attention to articles and trying to build a better encyclopedia and try to make progress from whatever most recent starting point they've given you. For reasonable requests, though, I do often indulge people in whatever procedure they are demanding, because this tends to make them less unhappy and more cooperative, and removes a lot of excuses for saying "no". It does sloooow things down, though, and generally I'm an impatient person, so it takes a bit of effort and is quite frustrating when we end up getting slowly to the same place I thought I should have been allowed to get to quickly. There are also times when an in-depth back-and-forth makes for better-sourced, more neutral, clearer, more informative, or just generally better content, and that's the benefit of having other people question my work and make me defend it.

If there's not an obvious way to make progress by refining content (for example if the dispute is whether or not a fact is important enough to include) then the way to make progress is discussion. I think the time to go back to making edits is when the discussion has either concluded, or reached a point where redrafting to address others' concerns is useful. If the discussion is stalled, I usually hold off on jamming my preferred version back in until I can get another editor to sanity-check my arguments and make sure I'm not in the wrong or at least not in the minority of editors. (Wikipedia:Third opinion is very helpful for that on low-traffic articles, but in this case there are plenty of watchers who will no doubt chime in or could be summoned from the WikiProject discussion.)

Not sure why everyone has gotten so emotionally involved, but this is just a list of facts about numbers. Yes, our articles should be clutter-free, but readers will be able to cope for a day or two by skimming past some boring parts if needed. Having a few facts gone for a day or two that we later decide to restore isn't going to ruin anyone's day. If they are looking for a specific fact, kind of by the definition of no original research, if it's something we're supposed to have here, they should be able to look it up somewhere else. If I need to get some sleep before slogging through some dense content and saying something intelligent about it, I'd consider just leaving things a mess overnight and going to do that. I know I'm more thoughtful and less prickly after a good night's rest, and much better at handling a complicated negotiation, and my brain will work on it overnight anyway and I might have some better ideas in the morning. -- Beland (talk) 08:59, 10 August 2024 (UTC)[reply]

In mathematics section

I have created a sandbox at Talk:1/Draft 1. I suggest we can edit this collaboratively, justifying each edit with detailed edit summaries or here if necessary. Once we arrive at a version we can all agree on then we can request a history merge into mainspace. I suggest we focus on the In mathematics section since this is the most contested. Polyamorph (talk) 14:36, 10 August 2024 (UTC)[reply]

Answering some of the points noted in the section above:

"1 is the only natural number that is neither composite (a number with more than two distinct positive divisors) nor prime (a number with exactly two distinct positive divisors) with respect to division." is redundant with prior discussions of the primality of one, which cover this topic and are mentioned here. - agree that if this is covered in the subsection "Primality". Polyamorph (talk) 17:03, 10 August 2024 (UTC)[reply]
"Any number multiplied or divided by 1 remains unchanged. This makes it a mathematical unit, and for this reason, 1 is often called unity." The etymology is unsourced, and it looks like this sentence means to say a different thing. What is meant to be said here is that 1 is the identity under multiplication in the real numbers. - since unity is an often used synonym of 1, it should be explained. But I agree this etymology does not seem correct and needs revising.
"Consequently, if is a multiplicative function, then must be equal to 1." this is NOFFTOPIC. Removing - not off topic, but it is duplicating detail already provided on the multiplicative identity.
"This distinctive feature leads to 1 being is its own factorial, its own square and square root, its own cube and cube root, and so forth." Given there is nos source, this is WP:OR. Removing. - I have added a source.
"1 is the multiplicative identity of the integers, real numbers, and complex numbers." This is correct, but true because each of these sets of numbers extends the integers, since we have already discussed the multiplicative identity above, it is redundant. If someone wants to describe why 1 is also the multiplicative identity of these sets (as well as quotient fields, among others), feel free to do so but that should probably belong somewhere further down in the article. - I don't see where the redundancy is/was (it's mentioned in the lead but since the lead is a summary of the article contents then it is expected to reproduce some of the main text. I've merged this into the top of the section.

Polyamorph (talk) 17:03, 10 August 2024 (UTC)[reply]

[1] Eves, Howard (2011). Introdução à história da matemática. Graduate Texts in Mathematics. Vol. 164 (5 ed.). Editora UNICAMP. p. 41. ISBN 978-8526806573.

[1]