Wikipedia:ProyekWiki Matematika/Gaya penulisan

Halaman ini adalah hasil alih bahasa dari subhalaman artikel Wikipedia Bahasa Inggris Manual of Style. Halaman ini berisi panduan untuk menulis dan membuat suntingan yang jelas, ensiklopedik, dan menarik, terkait artikel-artikel matematika; juga penggunaan notasi matematika untuk artikel Wikipedia dan subjek-subjek lainnya. Untuk pedoman penulisan yang tidak dijelaskan pada halaman ini, ikuti pedoman umum dan sub-subhalaman lainnya untuk konsistensi penulisan di Wikipedia.

Struktur

Mungkin hal tersulit ketika menulis artikel Wikipedia mengenai topik matematika tertentu (atau topik apapun pada umumnya), adalah memahami tingkat pengetahuan pembaca. Sebagai contoh, ketika menulis artikel tentang lapangan dalam konteks Aljabar abstrak, apakah sebaiknya mengasumsikan pembaca sudah familiar dengan teori grup? Pendekatan yang umum dalam menulis adalah memulai artikel dengan konsep yang sederhana lalu melanjutkannya dengan pembahasan yg lebih abstrak dan teknis, sama halnya ketika mengikuti suatu seminar

Bagian pembuka

Halaman utama: Wikipedia:Manual of Style/Lead section

Artikel sebaiknya diawali dengan bagian perkenalan, yang bertujuan untuk:

• mendeskripsikan dan mendefinisikan subjek,
• memberikan konteks terkait subjek, dan
• memberikan rangkuman hal-hal penting dari artikel.

Bagian ini, sedapat mungkin dapat dimengerti oleh pembaca awam, sehingga penggunaan istilah dan simbol yang spesifik sebaiknya dihindari. Selain itu, penggunaan formula di paragraf pertama harus dihindari, karena mereka tidak dapat ditampilkan dalm jendela pop-up yang muncul ketika mengarahkan tetikus ke pranala biru.

Secara umum, kalimat pertama perlu berisi judul artikel (atau variasinya) berserta nama-nama alternatifnya, dalam tulisan cetak tebal. Kalimat tersebut juga perlu menyebutkan artikel berisi sebuah topik matematika, kecuali sudah disebutkan pada judul artikel. Aman untuk mengasumsikan pembaca familiar dengan aritmetika, aljabar, geometri, dan mungkin juga sudah mendengar tentang kalkulus, walau kemungkinan besar mereka belum familiar dengannya. Untuk artikel pada subjek-subjek ini, atau subjek yang lebih sederhana, asumsikan pembaca tidak familiar dengan subjek tulisan. Dapat diasumsikan juga pembaca tidak mengetahui topik-topik selain pada subjek tersebut atau yang topik lebih rumit. Kalimat pertama sebaiknya mendefinisikan atau mendeskripsikan subjek secara informal. Sebagai contoh:

Dalam matematika, topologi (Berasal dari Bahasa Yunani bahasa Yunani: τόπος, har. 'tempat', dan bahasa Yunani: λόγος, har. 'ilmu') adalah ilmu yang mempelajari sifat-sifat objek geometri that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing.

In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane.

Bagian pembuka perlu mencakup, jika sesuai:

• sejarah , termasuk nama dan tanggal, terutama jika artikel tidak memiliki bagian "Sejarah". Asal usul nama subjek harus dijelaskan jika tidak jelas dengan sendirinya.
• Sebuah pengantar informal untuk topik, yang bersifat sederhana, dan cocok untuk khalayak umum. Pembaca yang sesuai untuk bagian ini akan berbeda-beda menurut artikelnya, tetapi harus sesederhana mungkin. Pengenalan informal harus secara jelas menyatakan bahwa itu informal, dan hanya dikatakan untuk memperkenalkan pendekatan formal. Sertakan analogi fisik atau geometris atau diagram jika dapat membantu memperkenalkan topik.
• Motivasi atau aplikasi , yang dapat menjelaskan penggunaan topik dan hubungannya dengan bidang matematika lain atau mata pelajaran non-matematika lainnya.

Isi artikel

Pembaca memiliki tingkat pengalaman dan pengetahuan yang berbeda. Jika ragu, artikel harus menentukan notasi yang mereka gunakan. Misalnya, beberapa pembaca akan segera mengenali bahwa Δ ( K ) berarti discriminant of a number field, tetapi yang lain mungkin tidak mengetahui notasi tersebut. Hal ini dapat dibantu oleh tambahan kalimat seperti "... di mana Δ ( K ) adalah discriminant dari lapangan K . "

Sebuah artikel harus menggunakan notasi standar jika memungkinkan, dan notasi yang tidak standar atau tidak umum harus didefinisikan di sebelumnya. Misalnya, jika x ^ n atau x ** n digunakan untuk eksponen alih-alih x ⁿ , artikel harus mendefinisikan notasi ini. Jika sebuah artikel memerlukan notasi yang banyak, pertimbangkan untuk memasukkan notasi-notasi tersebut sebagai daftar berpoin atau memisahkannya menjadi bagian "Notasi".

Artikel tentang objek matematika harus memberikan definisi objek yang tepat, mungkin di bagian "Definisi" setelah bagian motivasi. Sebagai contoh:

Misalkan S dan T adalah ruang topologi, dan misalkan f menjadi fungsi dari S menjadi T . Fungsi f disebut kontinu jika, untuk setiap himpunan terbuka O di T , preimage f   ⁻¹ ( O ) adalah himpunan terbuka di S .

Frasa "definisi formal" dapat membantu menandai definisi sebenarnya dari sebuah konsep bagi pembaca yang tidak terbiasa dengan terminologi akademis; di mana "definisi" berarti definisi formal, dan "bukti" selalu merupakan bukti formal.

When the topic is a theorem, the article should provide a precise statement of the theorem. Sometimes this statement will be in the lead, for example:

Lagrange's theorem, in the mathematics of group theory, states that for any finite group G, the order (number of elements) of every subgroup H of G divides the order of G.

Other times, it may be better to separate the statement into its own section, as for long theorems like the Poincaré–Birkhoff–Witt theorem, or to present multiple equivalent formulations, as for Nakayama's lemma.

Representative examples and applications help to illustrate definitions and theorems and to provide context for why they might be interesting. Shorter examples may fit into the main exposition of the article, such as the discussion at Algebraic number theory § Failure of unique factorization, while others may deserve their own section, as in Chain rule § First example. Multiple related examples may also be given together, as in Adjunction formula § Applications to curves. Occasionally, it is appropriate to give a large number of computationally-flavored examples, as in Lambert W function § Applications. It may also be edifying to list non-examples, which almost-but-not-quite satisfy the definition. In keeping with the purpose and tone of an encyclopedia, examples should be informative rather than instructional (see WP:NOTTEXTBOOK for details).

A picture can really bring home a point, and can often precede the mathematical discussion of a concept. How to create graphs for Wikipedia articles contains some details on how to create graphs and other pictures as well as how to include them in articles.

Formulas tend to repel less mathematical readers, and mathematics articles should take pains to explain (or even replace) them by words if possible.Wahyu {{{1}}}:{{{2}}} In particular, the English words "for all", "exists", and "in" should be preferred to the corresponding symbols ∀, ∃, and ∈. Similarly, definitions should be highlighted with words such as "is defined by" in the text.

If not included in the introduction, a history section can provide additional context and details on the topic's motivation and connections.

Concluding matters

Most mathematical ideas are capable of some form of generalization. If appropriate, such material can be put under a "Generalizations" section. As an example, multiplication of the rational numbers can be generalized to other fields.

It is also generally good to have a "See also" section in an article. The section should link to related subjects, or to pages which could provide more insight into the contents of the article. More details on "See also" sections can be found at Wikipedia:Manual of Style/Layout § "See also" section. Lastly, a well-written and complete article should have a "References" section. This topic is discussed in detail in the section § Including literature and references.

Writing style in mathematics

There are several issues of writing style that are particularly relevant in mathematical writing.

In the interest of clarity, sentences should not begin with a symbol. Do not write:

• Suppose that G is a group. G can be decomposed into cosets, as follows.
• Let H be the corresponding subgroup of G. H is then finite.
• $\pi$ is a mathematical constant.

Instead, write something like:

• A group G may be decomposed into cosets as follows.
• If H is the corresponding subgroup of G, then H is finite.
• The letter $\pi$ denotes a mathematical constant.

Mathematics articles are often written in a conversational style similar to a whiteboard lecture. However, a narrative pedagogical style runs counter to Wikipedia's recommended encyclopedic tone. While opinions vary on the most edifying style, authors should generally strike a balance between bare lists of facts and formulae, and relying too much on addressing the reader directly and referring to "we". Also avoid contentless clichés as Note that, It should be noted that, It must be mentioned that, It must be emphasized that, Consider that, and We see that. There is no use in imploring the reader to take note of each thing being pointed out. Rather than drawing the reader's attention to crucial information buried in the text, try to reorganize and rephrase to put the crucial part first. Templat:SeeAlso

Articles should be as accessible as possible to readers not already familiar with the subject matter. Notations not entirely standard should be properly introduced and explained. Whenever a variable or other symbol is defined by a formula, make sure to say this is a definition introducing a notation, not an equation involving a previously known object. Also identify the nature of the entity being defined. Don't write:

• Multiplying M by u = v − v₀, ...

Instead, write:

• Multiplying M by the vector u defined by u = v − v₀, ...

In definitions, the symbol "=" is preferred over "≡" or ":=".

When defining a term, do not use the phrase "if and only if". For example, instead of

• A function f is even if and only if f(−x) = f(x) for all x

write

• A function f is even if f(−x) = f(x) for all x.

If it is reasonable to do so, rephrase the sentence to avoid the use of the word "if" entirely. For example,

• An even function is a function f such that f(−x) = f(x) for all x.

Avoid, as far as possible, useless phrases such as:

• It is easily seen that ...
• Clearly ...
• Obviously ...

The reader might not find what you write obvious. Instead, try to hint why something must hold, such as:

• It follows directly from this definition that ...
• By a straightforward, if lengthy, algebraic calculation, ...

Articles should avoid common blackboard abbreviations such as wrt (with respect to), wlog (without loss of generality), and iff (if and only if), as well as quantifier symbols ∀ and ∃ instead of for all and there exists. In addition to compromising the encyclopedic tone, these abbreviations are a form of jargon that may confuse the reader.

The plural of formula is either formulae or formulas. Both are acceptable, but an article should be internally consistent. In an already consistent article, editors should refrain from changing one style to another.

Mathematical conventions

Lihat pula: Wikipedia:WikiProject Logic/Standards for notation

A number of conventions have been developed to make Wikipedia's mathematics articles more consistent with each other. These conventions cover choices of terminology, such as the definitions of compact and ring, as well as notation, such as the correct symbols to use for a subset.

These conventions are suggested in order to bring some uniformity between different articles, to aid a reader who moves from one article to another. However, each article may establish its own conventions. For example, an article on a specialized subject might be more clear if written using the conventions common in that area. Thus the act of changing an article from one set of conventions to another should not be undertaken lightly.

Each article should explain its own terminology as if there are no conventions, in order to minimize the chance of confusion. Not only do different articles use different conventions, but Wikipedia's readers come to articles with widely different conventions in mind. These readers will often not be familiar with our conventions, which may differ greatly from the conventions they see outside Wikipedia. Moreover, when our articles are presented in print or on other websites, there may be no simple way for readers to check what conventions have been employed.

Terminology conventions

Natural numbers

"The set of natural numbers" has two common meanings: (0, 1, 2, 3, ...}, which may also be called non-negative integers, and (1, 2, 3, ...}, which may also be called positive integers. Use the sense appropriate to the field to which the subject of the article belongs if the field has a preferred convention. If the sense is unclear, and if it is important whether or not zero is included, consider using one of the alternative phrases rather than natural numbers if the context permits.

Algebra

• A ring is assumed to be associative and unital. A structure satisfying all the ring axioms except the existence of a multiplicative identity is called a rng. There is an exception for rings of operators, such as * algebras, B* algebras, C* algebras, which we do not assume to be unital.
• The ring with one element is called the zero ring.
• A local ring is not assumed noetherian (contra Zariski).
• For Clifford algebras use v² = +Q(v).

Algebraic geometry

• An algebraic variety is assumed to be an irreducible algebraic set.
• A scheme is not assumed to be separated. The term "prescheme" is not used.

Topology

• A compact space is not assumed to be Hausdorff (contra Bourbaki, who uses quasi-compact for our notion of compactness).
• Separation axioms for topological spaces are as described on the separation axiom page.

Miscellaneous

• Directed sets are preordered sets with finite joins, not partial orders as in, e.g., Kelley (General Topology; ISBN 0-387-90125-6).
• A lattice need not be bounded. In a bounded lattice, 0 and 1 are allowed to be equal.
• Elliptic functions are written in ω = half-period style.
• A weight k modular form follows the Serre convention that f(−1/τ) = τ^kf(τ), and q = e^2πiτ.

Notational conventions

• The abstract cyclic group of order n, when written additively, has notation Z_n, or in contexts where there may be confusion with p-adic integers, Z/nZ; when written multiplicatively, e.g. as roots of unity, C_n is used (this does not affect the notation of isometry groups called C_n).
• The standard notation for the abstract dihedral group of order 2n is D_n in geometry and D_2n in finite group theory. There is no good way to reconcile these two conventions, so articles using them should make clear which they are using.
• Bernoulli numbers are denoted by B_n, and are zero for n odd and greater than 1.
• In category theory, write Hom-sets, or morphisms from A to B, as Hom(A,B) rather than Mor(A,B) (and with the implied convention that the category is not a small category unless that is said).
• The semidirect product of groups K and Q should be written K ×_φ Q or Q ×_φ K where K is the normal subgroup and φ : Q → Aut(K) is the homomorphism defining the product. The semidirect product may also be written K ⋊ Q or Q ⋉ K (with the bar on the side of the non-normal subgroup) with or without the φ.
  • The context should clearly state that this is a semidirect product and should state which group is normal.
  • The bar notation is discouraged because it is not supported by all browsers.
  • If the bar notation is used it should be entered as {{unicode|⋉}} (⋉) or {{unicode|⋊}} (⋊) for maximum portability.
• Subset is denoted by $\subseteq$, proper subset by $\subsetneq$. The symbol $\subset$ may be used if the meaning is clear from context, or if it is not important whether it is interpreted as subset or as proper subset (for example, $A\subset B$ might be given as the hypothesis of a theorem whose conclusion is obviously true in the case that $A=B$). All other uses of the $\subset$ symbol should be explicitly explained in the text.
• For a matrix transpose, use superscript non-italic capital letter T: X^T, $X^{\mathrm {T} }$ or $X^{\mathsf {T}}$, and not X^T, $X^{T}$, or $X^{\top }$.
• In a lattice, infima are written as a ∧ b or as a product ab, suprema as a ∨ b or as a sum a + b. In a pure lattice theoretical context the first notation is used, usually without any precedence rules. In a pure engineering or "ideals in a ring" context the second notation is used and multiplication has higher precedence than addition. In any other context the confusion of readers of all backgrounds should be minimized. In an abstract bounded lattice, the smallest and greatest elements are denoted by 0 and 1.
• The scalar or dot product of vectors should be denoted with a centre-dot a ⋅ b, as an inner product ⟨a,b⟩ or (a,b), or as a matrix product a^Tb, never with juxtaposition ab.

Proofs

This is an encyclopedia, not a collection of mathematical texts; but we often want to include proofs to explain a theorem or definition. A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgment; as a rule of thumb, include proofs when they expose or illuminate the concept or idea; don't include them when they serve only to establish the correctness of a result.

Since many readers will want to skip proofs, it is a good idea to set them apart in some way, for instance by giving them a separate section. Additional discussion and guidelines can be found at Wikipedia:WikiProject Mathematics/Proofs.

Algorithms

Lihat pula: Wikipedia:WikiProject Computer science/Manual of style (computer science) § Algorithms

An article about an algorithm may include pseudocode or in some cases source code in some programming language. Wikipedia does not have a standard programming language or languages, and not all readers will understand any particular language even if the language is well-known and easy to read, so consider whether the algorithm could be expressed in some other way. If source code is used always choose a programming language that expresses the algorithm as clearly as possible.

Articles should not include multiple implementations of the same algorithm in different programming languages unless there is encyclopedic interest in each implementation.

Source code should always use syntax highlighting. For example this markup:

<syntaxhighlight lang="Haskell">
  primes = sieve [2..]
  sieve (p : xs) = p : sieve [x | x <- xs, x `mod` p > 0]
</syntaxhighlight>

generates the following:

  primes = sieve [2..]
  sieve (p : xs) = p : sieve [x | x <- xs, x `mod` p > 0]

Including literature and references

It is quite important for an article to have a well-chosen list of references and pointers to the literature. Some reasons for this are the following:

• Wikipedia articles cannot be a substitute for a textbook (that is what Wikibooks is for). Also, often one might want to find out more details (like the proof of a theorem stated in the article).
• Some notions are defined differently depending on context or author. Articles should contain some references that support the given usage.
• Important theorems should cite historical papers as an additional information (not necessarily for looking them up).
• Today many research papers or even books are freely available online and thus virtually just one click away from Wikipedia. Newcomers would greatly profit from having an immediate connection to further discussions of a topic.
• Providing further reading enables other editors to verify and to extend the given information, as well as to discuss the quality of a particular source.

The Wikipedia:Cite sources article has more information on this and also several examples for how the cited literature should look.

Typesetting of mathematical formulae

Lihat pula: Help:Displaying a formula

One may set formulae using LaTeX (the <math> tag, described in the next subsection) or, in certain cases, using other means of formatting that render in HTML; both are acceptable and widely used, except for section headings, which should use HTML only, as LaTeX markup might cause uneven spacing in the table of contents, as well as the appearance of illegible anchor links to sections. Some of the issues presented by using LaTeX or HTML are discussed below.

Large-scale formatting changes to an article or group of articles are likely to be controversial. One should not change formatting boldly from LaTeX to HTML, nor from non-LaTeX to LaTeX without a clear improvement. Proposed changes should generally be discussed on the talk page of the article before implementation. If there is no positive response, or if planned changes affect more than one article, consider notifying an appropriate Wikiproject, such as WikiProject Mathematics for mathematical articles.

For inline formulae, such as a² − b², the community of mathematical editors of English Wikipedia currently has no consensus about preferred formatting; see WP:Rendering math for details.

For a formula on its own line the preferred formatting is the LaTeX markup, with a possible exception for simple strings of Latin letters, digits, common punctuation marks, and arithmetical operators. Even for simple formulae the LaTeX markup might be preferred if required for uniformity within an article.

Using LaTeX markup

Wikipedia allows editors to typeset mathematical formulae in (a subset of) LaTeX markup (see also TeX); the formulae are, for a default reader, translated into PNG images. They may also be rendered as MathML or HTML (using MathJax), depending on user preferences. For more details on this, see Help:Displaying a formula.

The LaTeX formulae can be displayed inline (like this: $\mathbf {x} \in \mathbb {R} ^{2}$), as well as on their own line: $$\int _{0}^{\pi }\sin x\,dx.$$

A frequent method for displaying formulas on their own line has been to indent the line with one or more colons (:). Although this produces the intended visual appearance, it produces invalid html (see Wikipedia:Manual of Style/Accessibility § Indentation). Instead, formulas may be placed on their own line using <math display=block>. For instance, the formula above was typeset using <math display=block>\int_0^\pi \sin x\,dx.</math>.

If you find an article which indents lines with spaces in order to achieve some formula layout effect, you should convert the formula to LaTeX markup.

Having LaTeX-based formulae inline has the following drawbacks:

• The font size can be slightly larger than that of the surrounding text on some browsers, making text containing inline formulae harder to read.
• The download speed of a page is negatively affected if it contains many formulas.

If an inline formula needs to be typeset in LaTeX, often better formatting can be achieved with the \textstyle LaTeX command. By default, LaTeX code is rendered as if it were a displayed equation (not inline), and this can frequently be too big. For example, the formula <math>\sum_{n=1}^\infty 1/n^2 = \pi^2/6</math>, which displays as $\sum _{n=1}^{\infty }1/n^{2}=\pi ^{2}/6$, is too large to be used inline. \textstyle generates a smaller summation sign and moves the limits on the sum to the right side of the summation sign. The code for this is <math>\textstyle\sum_{n=1}^\infty 1/n^2 = \pi^2/6</math>, and it renders as the much more aesthetic $\textstyle \sum _{n=1}^{\infty }1/n^{2}=\pi ^{2}/6$.

HTML-generating formatting, as described below, is adequate for articles that use only simple inline formulae and better for text-only browsers.

Deprecated formatting

Older versions of the MediaWiki software supported displaying simple LaTeX formulae as HTML rather than as an image. Although this is no longer an option, some formulae have formatting in them intended to force them to display as an image, such as an invisible quarter space (\,) added at the end of the formula, or \displaystyle at the beginning. Such formatting can be removed if a formula is edited and need not be added to new formulae.

Alt text

Images generated from LaTeX markup have alt text, which is displayed to visually impaired readers and other readers who cannot see the images. The default alt text is the LaTeX markup that produced the image. You can override this by explicitly specifying an alt attribute for the math element. For example, <math alt="Square root of pi">\sqrt{\pi}</math> generates an image ${\sqrt {\pi }}$ whose alt text is "Square root of pi". Small and easily explained formulas used in less technical articles can benefit from explicitly specified alt text. More complicated formulas, or formulas used in more technical articles, are often better off with the default alt text.

Using HTML

The following sections cover the way of presenting simple inline formulae in HTML, instead of using LaTeX.

Templates supporting HTML formatting are listed in Category:Mathematical formatting templates. Not all templates are recommended for use; in particular, use of the {{frac}} template to format fractions is discouraged in mathematics articles.

Font formatting

By default, regular text is rendered in a sans serif font.

The relationship is defined as ''x'' = −(''y''<sup>2</sup> + 2).

will result in:

The relationship is defined as x = −(y² + 2).

As TeX uses a serif font to display a formula (both as PNG and HTML), you may use the {{math}} template to display your HTML formula in serif as well. Doing so will also ensure that the text within a formula will not line-wrap, and that the font size will closely match the surrounding text in any skin. Note that certain special characters (equal signs, absolute value bars) require special attention.

The relationship is defined as {{math|''x'' {{=}} −(''y''<sup>2</sup> + 2)}}.

will result in:

The relationship is defined as x = −(y² + 2).

Variables

To start with, we generally use italic text for variables, but never for numbers or symbols. You can use ''x'' in the edit box to refer to the variable x. Some prefer using the HTML "variable" tag, <var>, since it provides semantic meaning to the text contained within. Others use the {{mvar}} template to show single variables in a serif typeface, to help distinguish certain characters such as I and l. Which method you choose is entirely up to you, but in order to keep with convention, we recommend the wiki markup method of enclosing the variable name between repeated apostrophe marks. Thus we write:

''x'' = −(''y''<sup>2</sup> + 2) ,

which results in:

x = −(y² + 2) .

While italicizing variables, things like parentheses, digits, equal and plus signs should be kept outside of the double-apostrophed sections. In particular, do not use double apostrophes as if they are <math> tags; they merely denote italics. Descriptive subscripts should not be in italics, because they are not variables. For example, m_foo is the mass of a foo. SI units are never italicized: x = 5 cm.

Functions

Names for standard functions, such as sin and cos, are not in italic font, but we use italic names such as f for functions in other cases; for example when we define the function as in f(x) = sin(x) cos(x).

Sets

Sets are usually written in upper case italics; for example:

A = {x : x > 0}

would be written:

''A'' = {''x'' : ''x'' > 0} .

Greek letters

Italicize lower-case Greek letters when they are variables or constants (in line with the general advice to italicize variables): the example expression λ + y = πr² would then be typeset as:

''&lambda;'' + ''y'' = ''&pi;r''<sup>2</sup>

(It is also possible to enter Greek letters directly.)

For consistency with the (La)TeX style, do not italicize capital Greek letters; n! = Γ(n+1).

Common sets of numbers

Commonly used sets of numbers are typeset in boldface, as in the set of real numbers R. Again, typically we use wiki markup: three apostrophes (''') rather than the HTML <b> tag for making text bold.

Informasi lebih lanjut: § Blackboard bold

Superscripts and subscripts

Halaman utama: Wikipedia:Manual of Style (superscripts and subscripts)

Subscripts and superscripts should be wrapped in <sub> and <sup> tags, respectively, with no other formatting info. Font sizes and such should be entrusted to be handled with stylesheets. For example, to write c₃₊₅, use

''c''<sub>3+5</sub>.

Do not use special characters like ² (²) for squares. This does not combine well with other powers, as the following comparison shows:

1 + x + x² + x³ + x⁴ (with ²) versus

1 + x + x² + x³ + x⁴ (with <sup>2</sup>).

Moreover, the TeX engine used on Wikipedia may format simple superscripts using <sup>...</sup> depending on user preferences. Thus, instead of the image $x^{2}\,$, many users see x². Formulae formatted without using TeX should use the same syntax to maintain the same appearance.

Special symbols

There are list of mathematical symbols, list of mathematical symbols by subject and a list at Wikipedia:Mathematical symbols that may be useful when editing mathematics articles. Almost all mathematical operator symbols have their specific code points in Unicode outside both ASCII and General Punctuation (with notable exception of "+", "=", "|", as well as ",", ":", and three sorts of brackets). As a rule of thumb, specific mathematical symbols shall be used, not similar-looking ASCII or punctuation symbols, even if corresponding glyphs are indistinguishable. The list of mathematical symbols by subject includes markup for LaTeX and HTML, and Unicode code points.

There are two caveats to keep in mind, however.

1. Not all of the symbols in these lists are displayed correctly on all browsers (see Help:Special characters). Although the symbols that correspond to named entities are very likely to be displayed correctly, a significant number of viewers will have problems seeing all the characters listed at Mathematical operators and symbols in Unicode. One way to guarantee that an uncommon symbol is rendered correctly for all readers is to force the symbol to display as an image, using the <math> environment.
2. Not all readers will be familiar with mathematical notation. Thus, to maximize the size of the audience who can read an article, it is better to be conservative in using symbols. For example, writing "a divides b" rather than "a | b" in an elementary article may make it more accessible.

Less-than sign

Although the MediaWiki markup engine is fairly smart about differentiating between unescaped "<" characters that are used to denote the start of an embedded HTML or HTML-like tag and those that are just being used as literal less-than symbols, it is ideal to use < when writing the less-than sign, just like in HTML and XML. For example, to write x < 3, use

''x'' < 3,

not

''x'' < 3.

Multiplication sign

Standard algebraic notation is best for formulae, so two variables q and d being multiplied are best written as qd when presented in a formula. That is, when citing a formula, don't use ×.

However, when explaining the formula for a general audience (not just mathematicians), or giving examples of its application, it is prudent to use the multiplication sign: "×", coded as × in HTML. Do not use the letter "x" to indicate multiplication. For example:

• When dividing 26 by 4, 6 is the quotient and 2 is the remainder, because 26 = 6 × 4 + 2.
• −42 = 9 × (−5) + 3

An alternative to the × markup is the dot operator ⋅ (also encoded <math>\cdot</math> and reachable in the "Math and logic" drop-down list below the edit box), which produces a properly spaced centered dot: "a ⋅ b".

Do not use the ASCII asterisk (*) as a multiplication sign outside of source code. It is not used for this purpose in professionally published mathematics, and most fonts render it in an inappropriate vertical position (above the midline of the text rather than centered on it). For the dot operator, do not use punctuation symbols, such as a simple interpunct · (the choice offered in the "Wiki markup" drop-down list below the edit box), as in many fonts it does not kern properly. The use of U+2022 • bullet as an operator symbol is also discouraged except in abstract contexts (e.g. to denote an unspecified operator).

Minus sign

The correct encoding of the minus sign "−" is different from all varieties of hyphen "-‐‑", as well as from en-dash "–". To really get a minus sign, use the "minus" character "−" (reachable via selecting "Math and logic" in the drop-down list below the edit box or using {{subst:minus}}) or use the "−" entity.

Square brackets

Square brackets have two problems; they can occasionally cause problems with wiki markup, and editors sometimes 'fix' the brackets in asymmetrical intervals to make them symmetrical. The nowiki tag can be used as a general solution to problems like this, as in <nowiki>]</nowiki> to have the ] treated as literal text.

The use of intervals for the range or domain of a function is very common. A solution which makes the reason for the different brackets around an interval more plain is to use one of the templates {{open-closed}}, {{closed-open}}, {{open-open}}, {{closed-closed}}. For instance:

{{open-closed|−π, π}}

produces

(−π, π].

These templates use the {{math}} template to avoid line breaks and use the TeX font.

Function symbol

There is a special Unicode symbol, U+0192 ƒ latin small letter f with hook (HTML: ƒ ƒ), sometimes used as the Florin currency symbol. As of December 2010, this character is not interpreted correctly by screen readers such as JAWS and NonVisual Desktop Access. An italicized letter f should be used instead.

Radical symbol

The radical symbol √ can be used when written on its own, but when part of a larger expression, can be problematic. {{radic}} is the best way to write such expressions in HTML, but the result is unattractive due to the hole between the overline and the radical symbol in many web browsers:

√9, ³√27

This method should be avoided whenever technically possible to do so. Instead, use <math>...</math> tags and \sqrt{}, even if inline. For example:

${\sqrt {9}},{\sqrt[{3}]{27}}$

Because of Mediawiki bug Templat:Phab, <math>...</math> markup is incompatible with the Media Viewer (used for full-screen image viewing on mobile devices), so until that is fixed, the {{radic}} method or √ with no overline should be used in image captions.

The use of √ with no overline is acceptable for simple expressions, as long as the operand is unambiguous.

Explanation of symbols in formulae

A list such as:

Example 1: The foocity is given by

$\mathbf {F} =\mathbf {b} \times a\mathbf {r} ,$

where

• $\mathbf {b}$ is the barness vector,
• $a$ is the bazness coefficient,
• $\mathbf {r}$ is the quuxance vector.

should be written as prose:Wahyu {{{1}}}:{{{2}}}

Example 2: The foocity is given by

$\mathbf {F} =\mathbf {b} \times a\mathbf {r} ,$

where $\mathbf {b}$ is the barness vector, $a$ is the bazness coefficient, and $\mathbf {r}$ is the quuxance vector.

An exception would be if some of the definitions are very long (for example, as in Heat equation), but, even in this case, each definition should end with a comma or semicolon, and the last one should end with a period if it terminates a sentence.

Punctuation after formulae

Just as in mathematics publications, a sentence which ends with a formula must have a period at the end of the formula. This equally applies to displayed formulae (that is, formulae that take up a line by themselves). Similarly, if the conventional punctuation rules would require a question mark, comma, semicolon, or other punctuation at that place, the formula must have that punctuation at the end.

If the formula is written in LaTeX, that is, surrounded by the <math> and </math> tags, then the punctuation should also be inside the tags, because otherwise the puctuation could wrap to a new line if the formula is at the edge of the browser window. Alternatively—since the previous result can be unaesthetic, especially for inlined formulae presented as an image whose baseline does not line up with that of the running text—the punctuation can be placed after the </math> tag and then the whole formula (including the punctuation) can be enclosed with the {{nowrap}} template, as in This shows that {{nowrap|<math>\tfrac{1}{2} = 0.5</math>.}}.

Font usage

Multi-letter names

Functions that have multi-letter names should always be in an upright font. The most well-known functions—trigonometric functions, logarithms, etc.—can be written without parentheses for as long as the result does not become ambiguous. For example:

$2\sin x$   (parentheses may be omitted here, as the argument consists of a single term only; typeset from <math>2\sin x</math>)

$2\sin(x+1)$ (parentheses are required to clarify the intended argument)

but not

$2sinx$   (incorrect—typeset from <math>2sin x</math>).

Note: For potential pitfalls of forms not understood consistently across the board, see order of operations and implied multiplication; if there is any risk that a term could become ambiguous for our readership, use parentheses.

When operator (function) names do not have a pre-defined abbreviation, we may use \operatorname:

$2\operatorname {csch} x$   (typeset from <math>2\operatorname{csch}x</math>).

$a\operatorname {tr} (A)$   (typeset from <math>a\operatorname{tr}(A)</math>).

\operatorname includes correct spacing that would not be present with other means such as \rm:

$2{\rm {sin}}x$   (incorrect—typeset from <math>2{\rm sin} x</math>).

Special care is needed with subscripted labels to distinguish the purpose of the subscript (as this is a common error): variables and constants in subscripts should be italic, while textual labels should be in normal text font (Roman, upright). For example:

$x_{\text{this one}}=y_{\text{that one}}$   (correct—typeset from <math> x_\text{this one} = y_\text{that one}</math>),

and

$\sum _{i=1}^{n}{y_{i}^{2}}$   (correct—typeset from <math>\sum_{i=1}^n { y_i^2 }</math>),

but not

$r=x_{predicted}-x_{observed}$   (incorrect—typeset from <math>r = x_{predicted} - x_{observed}</math>).

For several years this manual recommended \mbox as a workaround for lack of \text, but this is now considered undesirable. See An opinion: Why you should never use \mbox within Wikipedia.

Roman versus italic

For single-letter variables, constants, and operators such as the differential, imaginary unit, and Euler's number, Wikipedia articles usually use an italic font. One writes

$\int _{0}^{\pi }\sin x\,dx,$   (typeset from <math>\int_0^\pi \sin x \, dx ,</math>—note the thin space (\,) before dx),

${\frac {dz}{dx}}={\frac {dz}{dy}}\cdot {\frac {dy}{dx}},$   (typeset from <math>\frac{dz}{dx} = \frac{dz}{dy} \cdot \frac{dy}{dx} ,</math>),

$x+iy,$   (typeset from <math>x+iy,</math>), and

$e^{i\theta }.$   (typeset from <math>e^{i\theta} .</math>).

Some authors prefer to use an upright (Roman) font, as in d, i, and e, and other authors use Roman boldface, as in i. Changes from one style to another should be done only to make an article consistent with itself. Formatting changes should not be made solely to make articles consistent with each other, nor to make articles conform to a particular style guide or standards body. It is inappropriate for an editor to go through articles doing mass changes from one style to another. When there is dispute over the correct style to use, follow the same principles as MOS:STYLERET.

Generally, one way to determine which usage is appropriate on Wikipedia is to look at prevalence in reliable sources in addition to relevant style guides, per WP:WEIGHT. For example, the ISO 80000-2 recommends that the mathematical constant e should be typeset in an upright Roman font: e. But this guide is rarely followed in reliable mathematical sources, and it is contradicted by other style guides, like Donald Knuth's TeXbook. This makes the more common practice to use an italic face for the constant e.

Blackboard bold

Blackboard bold typeface was never used in traditional typography. It has been introduced for easier distinguishing boldface from ordinary face on a blackboard. It is presently used in mathematical printing for denoting some constant objects in a way that cannot be confused with other uses of boldface.

Nowadays, blackboard bold is very commonly used for denoting standard number systems ($\mathbb {N} ,$ $\mathbb {Z} ,$ $\mathbb {Q} ,$ $\mathbb {R} ,$ $\mathbb {C} ,$ $\mathbb {H} ,$ $\mathbb {F} _{q},$ $\mathbb {Z} _{p},$ $\mathbb {Q} _{p}$). The advantage of these notations, is that they can be used without being redefined in texts that are not specifically about them. Other uses of blackboard bold are less common, and are generally not commonly accepted. Some authors still use usual boldface for denoting standard number systems.

A particular concern for the use of blackboard bold on Wikipedia is that the Unicode symbols for blackboard bold characters are not supported by all systems, or that font substitution on browsers often render these symbols in discordant fonts. The use of Unicode characters for blackboard bold is discouraged in English Wikipedia. Instead, the LaTeX rendering (for example <math>\mathbb{Z}</math>) or the standard boldface must be used. As with all such choices, each article should be consistent with itself, and editors should not change articles from one choice of typeface to another, except for consistency. Again, when there is dispute, follow MOS:STYLERET.

Fractions

Lihat pula: Wikipedia:Manual of Style/Dates and numbers § Fractions

In mathematics articles, fractions should always be written either with a horizontal fraction bar (as in $\textstyle {\frac {1}{2}}$), or with a forward slash and with the baseline of the numbers aligned with the baseline of the surrounding text (as in 1/2). The use of {{frac}} (such as ½) is discouraged in mathematics articles. The use of Unicode symbols (such as ½) is discouraged entirely, for accessibility reasons among others. Metric units are given in decimal fractions (e.g., 5.2 cm); non-metric units can be either type of fraction, but the fraction style should be consistent throughout the article.

Graphs and diagrams

The angle CAB is α.
The length of CA is b.

Lihat pula: Wikipedia:How to create charts for Wikipedia articles

There is no general agreement on what fonts to use in graphs and diagrams. In geometrical diagrams points are normally labelled using upper case letters, sides with lower case and angles with lower case Greek letters.

Recent geometry books tend to use an italic serif font in diagrams as in $A$ for a point. This allows easy use in LaTeX markup. However, older books tend to use upright letters as in $\mathrm {A}$ and many diagrams in Wikipedia use sans-serif upright A instead. Graphs in books tend to use LaTeX conventions, but yet again there are wide variations.

For ease of reference diagrams and graphs should use the same conventions as the text that refers to them. If there is a better illustration with a different convention, though, the better illustration should normally be used.

See also

Help for those writing a formula

• Help:Displaying a formula
• Wikipedia:Mathematical symbols
• Wikipedia:Rendering math

General information

• Wikipedia:WikiProject Mathematics
• Wikipedia:Scientific citation guidelines—advice on providing references for mathematical and scientific articles

Further reading

A style guide specifically written for mathematics:

• Higham, Nicholas J. (1998), Handbook of Writing for the Mathematical Sciences (edisi ke-second), SIAM (Society for Industrial and Applied Mathematics), ISBN 0-89871-420-6 .

More style guidance:

• Halmos, P.R. (1970), "How to Write Mathematics", Enseignements Mathématiques, 16: 123–152, doi:10.5169/seals-43857 . Reprinted in ISBN 0821800558

Some finer points of typography are discussed in:

• Knuth, Donald E. (1984), The TeXbook, Reading, Massachusetts: Addison-Wesley, ISBN 0-201-13448-9 .

General style manuals often include advice on mathematics, including

• University of Chicago Press Staff, ed. (2010), The Chicago Manual of Style (edisi ke-16th), University of Chicago Press, ISBN 9780226104201