Wikipedia:WikiProject Numbers/Guidelines

Guidelines

How far to go?

See also Wikipedia:Notability (numbers).

There are a lot of numbers^{[citation needed]}. Which numbers should get articles and what those articles should say is a rather important question.

Integers: Continuous from −1 to 299. Multiples of 100 from 300 to 900, then multiples of 1000 to 9000. Afterwards, only powers of 10 (from 1 up to 10¹², higher than that only if they have a standard word name and commonly used SI prefix) and numbers with some remarkable mathematical property.
Fractions: Pages for fractions with small denominators, such as 1/2, are acceptable at this point (this is the only such article; articles for 1/3 and 1/4 could be warranted). If needed, redirects for equivalent fractions can be created.
Reals: Important mathematical constants such as e and π.
Imaginaries: i.
Non-numerical entities: NaN, with a possible redirect from Not a Number.
Number bases: Those that are actually used (or have been used in the past) for practical calculations, such as binary, octal, decimal, hexadecimal, vigesimal, and sexagesimal.

Creating a new article

Care should be taken to only create a new article on a number if there is sufficient known information to create an article that consists of more than just "N comes after N − 1 and before N + 1". As a guideline, you ought to know at least three interesting properties of a number. What constitutes interesting can be debated (see Wikipedia:Evaluating how interesting an integer's mathematical property is for one possible way of gauging this), but the point is that the careless creation of number article stubs is to be avoided. Also, and as importantly in many respects, which cultural and scientific properties (or otherwise) can be attributed to the number? For a complete number article, there need-be at least one accompanying important cultural association aside from mathematical properties present. If you only know one interesting mathematical property, consider jotting it down in an article on a near round number. For instance, if you want to write an article on 1050, see if something about it has already been written on it at 1000. That's the point of the series of stubs at the ends of articles like 500 and 7000, to see if there are numbers outside the declared project range that might merit their own article.

So, before creating a new article on a number, go over a checklist:

See if the number has already been written about at an article on a near round number (rounding down, i.e. if searching for the number 455, seek the page 400).
Name at least three interesting and unrelated mathematical properties of the number (or one earth-shatteringly interesting property, such as odd perfect number, or a quasiperfect number of either parity).
Fill out a Docuan table (see below) with the basic properties of the number (factorization, binary representation, etc.)
Understand whether other fields have associations with the number, so as to include whichever philosophical, cultural and scientific links that are relevant.
Follow the template below once you have sufficient information to start a new article, or add onto an existing one.

Assessing mathematical number facts

The following is a proposed Wikipedia policy, guideline, or process. The proposal may still be in development, under discussion, or in the process of gathering consensus for adoption.

The purpose of number articles is to provide an overview of the history, key concepts, properties, and uses of a number. There is an endless supply of true facts about the mathematical properties of a number. There has been considerable WP:Wikidrama about what mathematical facts about a number belong on the page for that number: even if a fact is on topic, it may still not be interesting enough for inclusion (see the amusing interesting number paradox). This section lists several ways one can assess a mathematical number fact. Many facts fail one criterion but pass another.

(WP:NROUTINE) Routine Facts: Routine facts are true for nearly every other number upon a slight modification and are discouraged from inclusion, though they are sometimes acceptable.

Examples that are routine:

On 9: "The aliquot sum of 9 is 4".
On 19: "The Collatz sequence for nine requires nineteen steps to return to one, more than any other number below it. On the other hand, nineteen requires twenty steps, like eighteen. Less than ten thousand, only thirty-one other numbers require nineteen steps to return to one."

Examples that are non-routine:

On 3: "3 is the first odd prime".
On 19: "19 forms a twin prime with 17, a cousin prime with 23, and a sexy prime with 13".

(WP:NOFFTOPIC) Off Topic Facts: Facts on the page for number X should be as much as possible about number X and not about number or object Y, even if X and Y are related. In many cases, it is acceptable to describe the relationship between X and Y, but that doesn't mean that the subject of the article suddenly becomes Y.

Examples that are off topic:

On 5: "The factorial of five 5! = 120 is multiply perfect".
On 5: "A magic constant of 505 is generated by a 10 × 10 normal magic square". (The connection here was, apparently, that 505 contains two 5s in its base 10 representation.)
On 744: "The twentieth prime number is 71, where 31 is the eleventh; in turn, 20 is the eleventh composite number that is also the sixth self-convolution of Fibonacci numbers before 38, which is the prime index of 163."

Examples that are on topic:

On 5: "5 is the first of the three known Wilson primes 5, 13, 563".
On 9: "The aliquot sum of 9 is 4".
On 19: "19 forms a twin prime with 17, a cousin prime with 23, and a sexy prime with 13".

(WP:NCONNECTION) Connection: The existence of a connection between a number and an important or prominent object is usually acceptable.

Examples that are a connection to an important object:

On 5: "In graph theory, all graphs with four or fewer vertices are planar, however, there is a graph with five vertices that is not: $K 5$ , the complete graph with five vertices, where every pair of distinct vertices in a pentagon is joined by unique edges belonging to a pentagram."
On 9: "A polygon with nine sides is called a nonagon".

(WP:NNOPAGE) No Wikipedia Page: If a property is not important enough to have a Wikipedia page, it probably isn't important that the number in question satisfies it. The logical inverse also holds, but is weaker.

(WP:NOEIS WP:NOTOEIS) OEIS: OEIS is considered a reliable source. However, a mathematical fact appearing in OEIS is not by itself a good reason to include it in a Wikipedia article. Wikipedia is not OEIS. OEIS has hundreds of thousands of sequences, most of which do not belong on Wikipedia. A number appearing in an OEIS entry may be worth mentioning if the sequence is famous, beautiful, "core" (of central importance to some topic), or "hard" (which often means that it comes from an unsolved problem).

(WP:OR WP:SYNTH) No Original Research, No Synthesis: Violations of WP:OR and WP:SYNTH should be removed even if they pass all of the previous tests. Most facts need to be stated somewhere other than Wikipedia prior to inclusion.

Template for number articles

The following is a proposed Wikipedia policy, guideline, or process. The proposal may still be in development, under discussion, or in the process of gathering consensus for adoption.

Outline

Each article on a number should consist of at least one of two major sections, the first dealing with the actual mathematical context of the number and the second with non-mathematical properties of the number, such as practical and cultural (including symbolic, and historical) associations of the number. Generally, the article should open with simple mathematical properties of the number and list some simple associated objects (its associated polygon, factors, whether it is a prime, etc.) it should then move onto topics, including more obscure number facts (type of prime), its role in mathematical history and associations with more obscure objects (number of platonic solids, interesting group with n elements, etcetera). Facts that should not be included in a number article include: figurate numbers, arbitrary properties of the number (for example its square or square root), anything having to with a specific base of expression, the aliquot sum, its position in a specific OEIS sequence (unless several works of mathematical literature consider this to be of interest).

Stub template

This template (originally developed by Docu) is a subtractive template; i.e. given a number N that has all relevant mathematical properties (even mutually exclusive ones), including extra-mathematical properties. To use this template, replace the in-line generic statements with appropriate information:

N (number)

N (spell out number in bold) is the natural number following N − 1 and preceding N + 1. It is mainly known culturally (or in mathematics) for X and Y reason.

In mathematics

**Number infobox**
← N − 1 N N + 1 →
← x₀ x₁ x₂ x₃ x₄ N x₆ x₇ x₈ x₉ →
List of numbers ‧ Integers
← y 2y 3y 4y 5y 6y 7y 8y 9y 10y →
Cardinal	en
Ordinal	Nth
Factorization	1 × N (prime) or p_a × p_b × ...
Divisors	1, p_a, p_b, p_c, ..., p_a × p_b, ..., N
Roman numeral	"N"
Binary	"N₂"
...	...
Hexadecimal	"N₁₆"

N is the xth prime number (or composite number), the previous being N − 2y, with which it comprises a twin (or cousin, sexy, ..., for y = 1, 2, 3, ...) prime.

A polygon with N sides is called an n-gon.

N is part of the first few, or part of the last, members of a specific sequence.

N is a Mersenne prime, or a Fermat prime, or a special and well-studied other prime.

There are exactly N of (special groups, platonic solids, or other objects).

There is a prominent mathematical object with N number of subobjects.

Note: there should be links to the relevant articles (which already contain lists of that kind of number).

\hookrightarrow

Use {{Infobox number}} template to generate a formal number infobox that displays basic information.

In Science

N is the atomic number of elementium.

In Popular Culture

N is important in Religion A's sacred texts.

Note: be meticulous to only add information pertinent to the number, without including entries that exclusively reference the numeral(s).

\hookrightarrow

See § Extra-mathematical associations for more information.

See also

The year N A.D.

References

Pencil, Sharp (January 2004). "Integers". Encyclopedia of Things. Open Publishing. Retrieved 2021-01-01.
Eraser, Smooth (January 2022). "Constants". Encyclopedia of Things. Open Publishing. Retrieved 2023-01-01.

Naming compliance

For most cases, articles should be named N (number), with the literal spelling of the numbers redirected accordingly (e.g., Four hundred and ninety-six redirects to 496 (number)).

Numbers deserving their own article that are greater than 999, should have the article title written in digits without any separators between the digits of the integer part. Writing the number with separators may of course be acknowledged in the body of the article. Thus, the article on the taxicab number 1,729 should be 1729 (number), though the article can mention that the number may be written "1,729" or "1.729."

Besides −1, there are no articles on negative integers. Adding information about a negative number therefore can fall under articles representative of numbers' positive, absolute values. One half is the chosen article name for 1⁄2.

Non-mathematical properties

It is preferable to have a stub article than to pad an article with trivial or tenuously related information. Normal Wikipedia policies, and guidelines, should be considered when choosing which content to include. Specifically, any scientific and cultural associations of a number, and otherwise, must be verifiable, and covered with due weight.

A scientific notion referenced in a number article depends on the mathematics of its properties and characteristics, and how substantial they are, as aforementioned. Examples include:

a statement such as, there is theoretical and empirical evidence to suggest that brain computation is organized via power-of-two-based permutation logic,
three soap films meet along a Plateau border at 120 degree angles.

As well as any other scientific fact that is arithmetically, geometrically, or algebraically tied to the number itself, including by statistical significance, and where equalities near almost integer values.

Other associations or attributes

Highly culturally important references to numbers can be included, such as lucky or unlucky numbers (as a form of numerology), as long as there is a direct reference to mathematical properties of the number, even if mystical (i.e. The One in the philosophy of neoplatonism). See the essay Wikipedia:"In popular culture" content for guidance on how to select appropriate cultural references.

What not to include

Do not include content that relates to the article's title only as an identifier, or label, or simple enumeration, or measurement, or as a trivial mention. For example:

Route 66 does not have a significant relationship with the number 66 - rather, the "66" is an identification code.
86 (novel series) is not about the number 86.
The 35 in 35 mm film is a measurement, not a property of, or reference to, the number 35.
The 9 in ISO 9 is a simple enumeration of a series of items, with no significant relationship with the number 9.
The centre-forward in association football wearing the number 9 shirt is a trivial mention of the number 9.

If there is plausible ambiguity between such items and the given string of characters, the place to mention it would be on a disambiguation page for the number.

Finally, do not include other general content in the body of the article that is untied to the number as a mathematical object:

telephone number calling codes,
bus routes,
firearms (i.e. Glock 17),
military and transportation classes of vehicles, aircraft, or otherwise,
album titles or song titles that include a numeral, or books (except for when they deal directly with the mathematics of a number, or reference it thoroughly in some way),
sports jerseys (identified with numbers, or letters and numbers), NASCAR car numbers, etc.,
world records of any sort, aside from records that could be of cultural interest in mathematics, such as enumerating digits of pi by memory, etc.
marketed items, such as bubble gum 5.

Or any notion or item that is not directly relatable to mathematical aspects of the number (in this case, only its numeral is being referenced). If need-be, a hatnote atop the article can be used to link to another article if an important disambiguation is needed. This permits the article to remain focused on information that is primarily number-theoretical.

Citations

Just as with any information in Wikipedia, articles on numbers need to cite sources. (See Wikipedia:Citing sources for general information on citing sources.) Some statements that are easily verified with a pocket calculator might not need citations (e.g., the fact that 2×3 = 6), but anything slightly more difficult to verify does. It is acceptable for a number article to have few citations if the articles to which it links have primary and secondary sourcing. For example, to avoid footnote overkill, an article about a number p that is a certain type of prime does not need citations to background reading about that type of prime.

It is not the place of this project to prescribe a citation format. Until Wikipedia decides on a uniform citation format, number articles may use whatever citation format would be acceptable in a mathematics journal. Consistency within an article is generally preferred.

Web versions of respected professional journals are reliable sources. On the other hand, preprints on the arXiv that have not been peer-reviewed are generally unsuitable for our purposes. The On-Line Encyclopedia of Integer Sequences should be used with care: it is curated by experts and generally accurate, but it is by design rather indiscriminate about what it includes. From the standpoint of serious mathematical literature, some OEIS entries are mere curiosities. Those that are more noteworthy will include references into the literature that include more substantial discussions; consider supplementing citations to the OEIS with direct pointers to the peer-reviewed papers that it cites. MathWorld has a history of being less than reliable, for example by including neologisms that have not become accepted mathematical terminology. It should be avoided.

Edit summaries

Every project member (indeed anyone who edits Wikipedia) is encouraged to write brief but complete edit summaries. (See Wikipedia:Edit summary for advice on writing edit summaries for articles on any topic.)

For articles about numbers, or mathematics in general, it is advisable to use "linear notation" (markup typeset into a single line, without superscripts or subscripts) or pseudocode.

For example, instead of writing "Corrected mathematical formula to sum of reciprocals of squares of factorials instead of sum of reciprocals of factorials of squares, corrected links to Italian, Chinese Wikipedias", you could write "Corrected formula Sum(1/n!^2) instead of Sum(1/n^2!), corrected it:, zh:"

In edit summaries, use the mathematical operators available on the standard keyboard (+, -, *, /, ^) even though a different operator (e.g., ×) would be more appropriate in the article text.

Although Greek letters can technically be used in edit summaries, it is preferable to use the name of the letter spelled out in the English alphabet. For example, "Changed e to pi in formula", "Mu(100) is 0, not 1" (The article text should of course fully avail itself to any applicable Greek letters.)

Some shorthand notations that might be useful:

n, num, #	An arbitrary integer
p	An arbitrary prime number
x, num, #	An arbitrary real number
val	Value
tri; sq, ^2; pentag; hexag; heptag, etc.	Triangular; square; pentagonal; hexagonal; heptagonal, etc.
sum; prod	Sum; product
!; !!; super!, $!; hyper!; ¡!, i!; !sum; 1/!	Factorial; double factorial; superfactorial; hyperfactorial; alternating factorial; factorial sum; reciprocal of factorial
bin; oct; dec; hex	Binary; octal; decimal; hexadecimal
Infobox, Docuan table	The table with binary, hexadecimal representation, factorization and other general data points about the number