2757:. 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.
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familiar with the subjects of arithmetic, algebra, geometry, and that they may have heard of calculus, but are likely unfamiliar with it. For articles that are on these subjects, or on simpler subjects, it can be assumed that the reader is not familiar with the aforementioned subjects. A reader can be assumed to be ignorant of any topics outside of that scope or more advanced topics.
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2858:. Knowledge 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.
38:
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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,
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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
6247:
tags, then the punctuation should also be inside the tags, because otherwise the punctuation 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
1907:
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
Knowledge's readers come to articles with widely different conventions in mind. These readers will often not be
3816:
tags results in line wrapping points that allow wrapping between it and adjacent text (typically punctuation). Including such text within the tags to avoid this wrapping results in its font being discordant with other text. This can be remedied by wrapping the LaTeX markup in a suitable template
1452:
Mathematics articles are often written in a conversational style similar to a whiteboard lecture. However, a narrative pedagogical style runs counter to
Knowledge's recommended encyclopedic tone. While opinions vary on the most edifying style, authors should generally strike a balance between bare
6235:
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,
984:
In general, the lead sentence should include the article title, or some variation thereof, in bold along with any alternate names, also in bold. The lead sentence should state that the article is about a topic in mathematics, unless the title already does so. It is safe to assume that a reader is
1321:
Formulas tend to repel less mathematical readers, and mathematics articles should take pains to explain (or even replace) them by words if possible. In particular, the
English words "for all", "exists", and "in" should be preferred to the corresponding symbols ∀, ∃, and ∈. Similarly, definitions
956:
The lead should, as much as possible, be accessible to a general reader, so specialized terminology and symbols should be avoided. Formulas should appear in the first paragraph only if necessary, since they will not be displayed in the preview that pops up when hovering over a link. For having
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This is an encyclopedia and 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,
1903:
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
1073:
to the topic, without rigor, suitable for a general audience. The appropriate audience for the overview will vary by article, but it should be as basic as reasonable. The informal introduction should clearly state that it is informal, and that it is only stated to introduce the formal approach.
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A particular concern for the use of blackboard bold on
Knowledge is that the Unicode symbols for blackboard bold characters are not supported by all systems, and font substitution in browsers often renders these symbols in discordant fonts. The use of Unicode characters for blackboard bold is
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letter style originated in the 1960s to distinguish bold letters from ordinary letters on a blackboard or using a typewriter; in professionally typeset documents, bold fonts were used for the same purpose. Since then, blackboard bold has gradually gained currency, and is now commonly used in
4227:
is undesirable for readers because it will render in a sans serif font; this is especially confusing when other articles or sections render the same variables or equations in a serif font. Descriptive subscripts should not be in italics, because they are not variables. For example,
5571:. 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
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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.
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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
5348:
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
1945:. 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
7837:) or standard bold fonts should 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 to maintain internal consistency. When there is dispute, follow
1908:
familiar with our conventions, which may differ greatly from the conventions they see outside
Knowledge. 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.
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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:
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6281:
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:
1341:
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
3059:, and arithmetical operators. Even for simple formulae the LaTeX markup might be preferred if required for uniformity within an article. For readability, it is also strongly preferred not to mix HTML and LaTeX markup in the same expression.
907:
and for the use of mathematical notation in
Knowledge articles on other subjects. For matters of style not treated on this subpage, follow the main Manual of Style and its other subpages to achieve consistency of style throughout Knowledge.
1477:. 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.
1278:
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
8153:
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.
1333:
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
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2837:
164:
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1218:
The phrase "formal definition" may help to flag the actual definition of a concept for readers unfamiliar with academic terminology, in which "definition" means formal definition, and a "proof" is always a formal proof.
2947:
Today many research papers or even books are freely available online and thus virtually just one click away from
Knowledge. Newcomers would greatly profit from having an immediate connection to further discussions of a
8104:
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.
7119:
3868:, 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
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6002:
9052:
676:
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5092:
of neighboring characters, which is typical when used as a prefix or infix operator, or a standalone character. Usage should be consistent across articles covering the same subfield of mathematics; see
3189:
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
4919:
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 "
6654:
916:
Probably the hardest part of writing a
Knowledge article on a mathematical topic, and generally any Knowledge article, is addressing a reader's level of knowledge. For example, when writing about a
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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
3960:
template so they display in a serif font 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
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551:
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4207:
While italicizing variables, things like parentheses, digits, equal and plus signs should be kept outside of the double-apostrophed sections. Using double apostrophes for math content instead of
2824:
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
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1892:
A number of conventions have been developed to make
Knowledge's mathematics articles more consistent with each other. These conventions cover choices of terminology, such as the definitions of
6878:
6996:
3185:
6749:
2930:, it is essential for article content to have inline citations, and thus to have a well-chosen list of references and pointers to the literature. Some reasons for this are the following:
7903:
6520:
6467:
5900:
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and related articles attempt to cover both unital rings and non-unital rings: they do not consistently implement this interpretation. This attempt to cover multiple meanings violates
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601:
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Readers have differing levels of experience and knowledge. When in doubt, articles should define the notation they use. For example, some readers will immediately recognize that Δ(
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9135:
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1139:) should define the notations. If an article requires extensive notation, consider introducing the notation as a bulleted list or separating it into a section titled "Notation".
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Articles should not include multiple implementations of the same algorithm in different programming languages unless there is encyclopedic interest in each implementation.
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1066:, including names and dates, especially if the article does not have a "History" section. The origin of the subject's name should be explained if it is not self-evident.
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5835:) 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:
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before implementation. If there is no positive response, or if planned changes affect more than one article, consider notifying an appropriate
Wikiproject, such as
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1878:. Both are acceptable, but an article should be internally consistent. In an already consistent article, editors should refrain from changing one style to another.
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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
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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
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629:
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346:
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Generally, one way to determine which usage is appropriate on Knowledge is to look at prevalence in reliable sources in addition to relevant style guides, per
4622:) and its adjacent characters should be avoided at present, since these characters are not yet universally supported and may have an inconsistent appearance.
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also helps some spell checkers and screen readers treat math markup properly. Note that certain special characters (equal signs, absolute value bars) require
9285:
654:
504:
142:
9011:
8755:
8642:
7871:
6209:, for example). In any case, each definition should end with a comma or semicolon, and the last one should end with a period if it terminates a sentence.
5612:"–". 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
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259:
226:
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and many diagrams in Knowledge use sans-serif upright A instead. Graphs in books tend to use LaTeX conventions, but yet again there are wide variations.
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Italicize lower-case Greek letters when they are variables or constants (in line with the general advice to italicize variables): the example expression
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Use standard notation when possible. If an article requires non-standard or uncommon notation, they should be defined. For example, an article that uses
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373:
329:
70:
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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.
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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.
1222:
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:
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8662:
8657:
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8591:
8517:
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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.
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8195:
2825:
738:
586:
341:
196:
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Square brackets have two problems; they can occasionally cause problems with wiki markup, and editors sometimes 'fix' the brackets in asymmetrical
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are intended for compatibility with legacy character sets, and Unicode-capable environments (like Knowledge) should use the Greek letters instead (
3459:
8868:
8863:
8647:
8632:
8569:
5338:
4885:
4853:
3191:
2517:
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,
928:? A general approach to writing an article is to start simple and then move towards more abstract and technical subjects later on in the article.
482:
477:
231:
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149:
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tags, respectively, with no other formatting info. Font sizes and such should be entrusted to be handled with stylesheets. For example, to write
8714:
3253:
The font size can be slightly larger than that of the surrounding text on some browsers, making text containing inline formulae harder to read.
2281:
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.
937:
306:
4099:
templates (which will set a serif font but not italics), use the wikitext markup of double apostrophes to make variables italic. For example:
1904:
conventions common in that area. Thus the act of changing an article from one set of conventions to another should not be undertaken lightly.
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8832:
8596:
7038:
1453:
lists of facts and formulae, and relying too much on addressing the reader directly and referring to "we". Also avoid contentless clichés as
1325:
If not included in the introduction, a history section can provide additional context and details on the topic's motivation and connections.
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176:
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renders exponents lower, especially under square roots, often resulting in a smaller square root which fits better in inline text: compare
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728:
444:
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385:
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Some notions are defined differently depending on context or author. Articles should contain some references that support the given usage.
7850:), which is more common anyway. If absolutely necessary (e.g. when discussing the notation itself), use the Unicode character (e.g. 𝟙).
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9210:
9037:
8601:
8574:
8324:
This style, adopted by Knowledge, is shared by Higham (1998), Halmos (1970), the Chicago Manual of Style, and many mathematics journals.
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which should use HTML only, as LaTeX markup might cause uneven spacing in the table of contents, as well as the appearance of illegible
837:
832:
661:
181:
154:
5072:, and is typical when used as a postfix. This character also appears on keyboards, and is thus easier to type and search for. Example:
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9150:
8678:
8652:
8545:
855:
266:
236:
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8606:
8487:
8462:
8401:
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5575:(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
3024:
2131:
732:
186:
46:
6093:
5963:
3019:
from LaTeX to HTML, nor from non-LaTeX to LaTeX without a clear improvement. Proposed changes should generally be discussed on the
3015:
Large-scale formatting changes to an article or group of articles are likely to be controversial. One should not change formatting
1346:. Lastly, a well-written and complete article should have a "References" section. This topic is discussed in detail in the section
1295:. It may also be edifying to list non-examples, which almost-but-not-quite satisfy the definition. In keeping with the purpose and
4903:
are very likely to be displayed correctly, a significant number of viewers will have problems seeing all the characters listed at
9275:
8817:
8802:
8797:
8719:
8709:
8693:
5914:
markup is incompatible with the Media Viewer (used for full-screen image viewing on mobile devices), so until that is fixed, the
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should provide an exact definition of the object, perhaps in a "Definition" section after section(s) of motivation. For example:
1084:, which can illuminate the use of the topic and its connections to other areas of mathematics or other non-mathematical subjects.
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7292:. Changes from one style to another should be done only to make an article consistent with itself. Formatting changes should
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468:
380:
336:
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the formula for a general audience (not just mathematicians), or giving examples of its application, it is prudent to use the
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8807:
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8240:
8173:
4857:
4257:
812:
424:
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1768:. In addition to compromising the encyclopedic tone, these abbreviations are a form of jargon that may confuse the reader.
8510:
7318:. But this guide is rarely followed in reliable mathematical sources, and it is contradicted by other style guides, like
3576:
9190:
7942:); non-metric units can be either type of fraction, but the fraction style should be consistent throughout the article.
4849:
3040:, the community of mathematical editors of English Knowledge currently has no consensus about preferred formatting; see
2865:
1487:
not an equation involving a previously known object. Also identify the nature of the entity being defined. Don't write:
817:
7848:, LaTeX blackboard bold currently does not work with numerals. Use bold instead (e.g. {{math|'''1'''}} or <math: -->
4554:
tag for making text bold. Bold notation has been largely replaced by blackboard bold, which may be encoded in LaTeX as
8812:
4968:
429:
351:
3267:
If an inline formula needs to be typeset in LaTeX, keep the height down by using text-style or horizontal fractions:
3101:
2944:
Important theorems should cite historical papers as an additional information (not necessarily for looking them up).
1101:, but others will never have encountered the notation. The latter group will be helped by an aside like "...where Δ(
8683:
3056:
271:
58:
8277:"-" as a valid representation of the minus sign. Except situations where "-" has to represent the minus sign in a
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8526:
8168:
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3092:
3076:
3052:
2995:
2938:
is for). Also, often one might want to find out more details (like the proof of a theorem stated in the article).
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50:
17:
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5589:
as an operator symbol is also discouraged except in abstract contexts (e.g. to denote an unspecified operator).
126:
9145:
9140:
9130:
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7909:
and with the baseline of the numbers aligned with the baseline of the surrounding text (as in 1/2). The use of
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5778:
3856:
at the beginning. Such formatting can be removed if a formula is edited and need not be added to new formulae.
3041:
787:
782:
772:
7879:
4081:
template to enclose a simple mention of a variable by name. This helps distinguish certain characters such as
7366:
Today, either blackboard bold or ordinary bold letters can be used interchangeably to represent the standard
4071:
Use italic text for variables, but never for numbers or symbols. To ensure an italic serif typeface, use the
1651:
If it is reasonable to do so, rephrase the sentence to avoid the use of the word "if" entirely. For example,
1318:
contains some details on how to create graphs and other pictures as well as how to include them in articles.
7363:
mathematical printing to denote certain common objects in a style distinct from other uses of bold letters.
6490:
6443:
5866:
4896:
1970:. A structure satisfying all the ring axioms except the existence of a multiplicative identity is called a
1280:
1267:
Other times, it may be better to separate the statement into its own section, as for long theorems like the
5927:
The use of √ with no overline is acceptable for simple expressions, as long as the operand is unambiguous.
3914:
The following sections cover the way of presenting simple inline formulae in HTML, instead of using LaTeX.
942:
Articles should start with a short introductory section, called the "lead". The purpose of the lead is to
9125:
8128:
for a point. This allows easy use in LaTeX markup. However, older books tend to use upright letters as in
6424:
5678:
5633:
5486:
3709:
2956:
2435:
The context should clearly state that this is a semidirect product and should state which group is normal.
1167:
767:
7876:
In mathematics articles, fractions should always be written either with a horizontal fraction bar (as in
6236:
comma, semicolon, or other punctuation at that place, the formula must have that punctuation at the end.
2959:
article has more information on this and also several examples for how the cited literature should look.
1314:
A picture can really bring home a point, and can often precede the mathematical discussion of a concept.
903:
contains guidelines for writing and editing clear, encyclopedic, attractive, and interesting articles on
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For simple fractional subscripts or superscripts, the horizontal style is visually the least confusing:
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to make them symmetrical. The nowiki tag can be used as a general solution to problems like this, as in
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23:
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1291:. Occasionally, it is appropriate to give a large number of computationally-flavored examples, as in
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827:
802:
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708:
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4822:. Formulae formatted without using TeX should use the same syntax to maintain the same appearance.
3884:
3803:, is adequate for articles that use only simple inline formulae and better for text-only browsers.
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generates a smaller summation symbol and moves the limits to its right side. The rewritten formula
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might be given as the hypothesis of a theorem whose conclusion is obviously true in the case that
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There are several issues of writing style that are particularly relevant in mathematical writing.
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for a variable. Upright fonts are sometimes used for standard, nearly universal constants, as in
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6013:
5936:
5815:√ can be used when written on its own, but when part of a larger expression, can be problematic.
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5088:(∗) for subscripts and when the bottom of the character should roughly align with the
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4711:) for squares. This does not combine well with other powers, as the following comparison shows:
3263:
is fixed, it will not work in image captions when readers click through to see full-size images.
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132:
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6314:(parentheses may be omitted here, as the argument consists of a single term only; typeset from
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2460:
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9155:
8484:
8459:
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6427:; if there is any risk that a term could become ambiguous for our readership, use parentheses.
5773:. As of December 2010, this character is not interpreted correctly by screen readers such as
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2015:
921:
128:
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4907:. One way to guarantee that an uncommon symbol is rendered correctly for all readers is to
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5047:
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2720:
2665:
2301:
2138:
2073:
2001:
1926:
8384:
7854:
5906:
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font to display a formula (whether as SVG or HTML). HTML math expressions should use the
3260:
7962:
6419:
Note: For potential pitfalls of forms not understood consistently across the board, see
5544:
and reachable in the "Math and logic" drop-down list below the edit box or via template
5033:
is appropriate; do not use the ASCII apostrophe (') or double quote (") in these cases.
3321:
2546:
8351:
8220:
6936:
6248:
does not line up with that of the running text—the punctuation can be placed after the
5918:
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2798:
2337:
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1967:
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When defining a term, do not use the phrase "if and only if". For example, instead of
1296:
1027:
1001:
872:
8111:
8023:
7998:
6162:
6037:
3012:
to sections. Some of the issues presented by using LaTeX or HTML are discussed below.
2838:
Knowledge:WikiProject Computer science/Manual of style (computer science) § Algorithms
1074:
Include a physical or geometric analogy or diagram if it can help introduce the topic.
957:
formulae displayed when hovering, they must be written in raw html (without templates
9269:
8266:
8243:, not a well-known language so generally not a good choice when showing an algorithm.
8009:
7990:
7912:
7367:
6206:
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Commonly used sets of numbers are typeset in boldface, as in the set of real numbers
4221:
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2088:
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2069:
2048:
1971:
971:
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tag and then the whole formula (including the punctuation) can be enclosed with the
1386:
In the interest of clarity, sentences should not begin with a symbol. Do not write:
8451:
8274:
8252:
7838:
7827:
discouraged in English Knowledge; instead, either the LaTeX rendering (for example
7702:
7606:
7319:
7298:
6431:
When operator (function) names do not have a pre-defined abbreviation, we may use
5855:
This method should be avoided whenever technically possible to do so. Instead, use
5514:
4988:
4984:
4895:
Not all of the symbols in these lists are displayed correctly on all browsers (see
3051:
the preferred formatting is the LaTeX markup, with a possible exception for simple
2405:
2203:
2162:
2108:
1796:
1723:
1718:
1713:
1580:
1491:
1474:
1470:
1466:
1462:
1458:
1454:
1403:
1390:
1238:
1234:
961:
925:
7845:
5353:
when writing the less-than sign, just like in HTML and XML. For example, to write
4880:(with notable exception of "+", "=", "|", as well as ",", ":", and three sorts of
979:). In the latter case the LaTeX source is displayed without the tags <math: -->
57:
It is a generally accepted standard that editors should attempt to follow, though
5073:
4980:
4976:
3256:
The download speed of a page is negatively affected if it contains many formulas.
1828:
1812:
1742:
1737:
1655:
1617:
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988:
The lead sentence should informally define or describe the subject. For example:
8478:
8416:
8334:
8278:
8270:
5770:
5568:
5069:
4767:
Moreover, the TeX engine used on Knowledge may format simple superscripts using
2851:
2761:
1963:
1230:
993:
904:
9234:
7823:). Font preferences vary from one mathematical author or publisher to another.
6083:
should be written as prose, to avoid using more vertical space than necessary:
130:
8291:
7670:
7326:. This makes the more common practice to use an italic face for the constant
6932:
5604:
The correct encoding of the minus sign "−" is different from all varieties of
5275:
4865:
3940:
3527:{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {\pi ^{2}}{6}}.}
2847:
1997:
1983:
1979:
1284:
4991:. (The only exception is when discussing the Unicode characters themselves.)
8394:
8338:
8224:
6545:
includes correct spacing that would not be present with other means such as
5494:
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for functions in other cases; for example when we define the function as in
2935:
2843:
2593:
2438:
The bar notation is discouraged because it is not supported by all browsers.
1990:
1975:
1481:
3067:
Knowledge allows editors to typeset mathematical formulae in (a subset of)
2141:
need not be bounded. In a bounded lattice, 0 and 1 are allowed to be equal.
8072:
7938:
reasons among others. Metric units are given in decimal fractions (e.g.,
7308:. For example, the ISO 80000-2 recommends that the mathematical constant
2428:(with the bar on the side of the non-normal subgroup) with or without the
8108:
Recent geometry books tend to use an italic serif font in diagrams as in
5564:
5490:
5185:
5094:
2309:
1249:
1198:
1187:
8432:
8281:(including wiki code), it should not be seen in a rendered page, though.
8198:—advice on providing references for mathematical and scientific articles
7266:
Some authors prefer to use an upright (Roman) font for operators, as in
7114:{\displaystyle {\frac {dz}{dx}}={\frac {dz}{dy}}\cdot {\frac {dy}{dx}},}
5339:
Knowledge:Manual of Style/Abbreviations § Unicode abbreviation ligatures
1900:, as well as notation, such as the correct symbols to use for a subset.
7928:
4881:
4869:
4611:
4238:
3921:. Not all templates are recommended for use; in particular, use of the
3088:
2934:
Knowledge articles cannot be a substitute for a textbook (that is what
2872:
primes = sieve sieve (p : xs) = p : sieve </syntaxhighlight: -->
2305:
2008:
1729:
The reader might not find what you write obvious. Instead, try to hint
1052:
8354:(¼, ½, and ¾) work with screen readers, but others, like ⅐, might not.
6205:
An exception would be if some of the definitions are very long (as in
1322:
should be highlighted with words such as "is defined by" in the text.
8472:
General style manuals often include advice on mathematics, including
8389:(second ed.), SIAM (Society for Industrial and Applied Mathematics),
5605:
3931:
template to format fractions is discouraged in mathematics articles.
3080:
2454:
5592:
Metric units often embed the notion of multiplication and division.
5585:
5438:
Standard algebraic notation is best for formulae, so two variables
1760:(if and only if), as well as quantifier symbols ∀ and ∃ instead of
8495:
8071:
6931:
For single-letter variables, constants, and operators such as the
5229:
for set substraction. (Either Unicode character can be used where
5189:
4873:
3949:
3068:
5596:
endorses the half-high dot (⋅) or a bare space for this purpose.
2408:
defining the product. The semidirect product may also be written
2094:
Separation axioms for topological spaces are as described on the
2058:
is not assumed to be separated. The term "prescheme" is not used.
5609:
5593:
3249:
Having LaTeX-based formulae inline has the following drawbacks:
3091:), depending on user preferences. For more details on this, see
3084:
8499:
6239:
If the formula is written in LaTeX, that is, surrounded by the
5924:
method or √ with no overline should be used in image captions.
1795:
when verbalizing quantifiers since it is ambiguous. Instead of
9236:
6127:{\displaystyle \mathbf {F} =\mathbf {b} \times a\mathbf {r} ,}
5997:{\displaystyle \mathbf {F} =\mathbf {b} \times a\mathbf {r} ,}
3072:
2336:) (and with the implied convention that the category is not a
1748:
Articles should avoid common blackboard abbreviations such as
1287:. Multiple related examples may also be given together, as in
924:, is it best to assume that a reader is already familiar with
133:
32:
8253:
Unicode Technical Report #25: Unicode Support for Mathematics
5274:(which on some systems is too small and can be confused with
4888:
includes markup for LaTeX and HTML, and Unicode code points.
4301:
Sets are usually written in upper case italics; for example:
6943:, Knowledge articles usually use an italic font. One writes
5053:
can be useful to prevent overlap with italicized characters.
3827:. Take care of some necessary substitutions documented for
1743:
By a straightforward, if lengthy, algebraic calculation, ...
6920:
An opinion: Why you should never use \mbox within Knowledge
6366:(parentheses are required to clarify the intended argument)
5330:, which on some systems renders as two separate characters.
3194:). Instead, formulas may be placed on their own line using
3075:); the formulae are, for a default reader, translated into
7816:{\displaystyle \mathbb {H} ^{i}(X,\Omega _{X}^{\bullet })}
4536:. Again, typically we use wiki markup: three apostrophes (
4268:, are not in italic font, but we use italic names such as
8302:
Knowledge talk:WikiProject Mathematics/Archive 68#ƒ or f?
4971:(ASCII) letters should be used instead of the equivalent
1569:
In definitions, the symbol "=" is preferred over "≡" or "
1281:
Algebraic number theory § Failure of unique factorization
1271:, or to present multiple equivalent formulations, as for
7605:) and for certain other mathematical objects, including
5552:), which produces a symmetrically spaced centered dot: "
5481:. Do not use the letter "x" to indicate multiplication.
1974:. There is an exception for rings of operators, such as
1347:
8237:
7872:
Knowledge:Manual of Style/Dates and numbers § Fractions
7349:
6649:{\displaystyle x_{\text{this one}}=y_{\text{that one}}}
6226:
5944:
5802:
5744:
5429:
4953:
4937:" in an elementary article may make it more accessible.
4839:
4638:
Knowledge:Manual of Style (superscripts and subscripts)
4446:
For consistency with the LaTeX style, do not italicize
3098:
The LaTeX formulae can be displayed inline (like this:
2985:
2978:
1857:
1782:
1700:
1560:
1374:
1367:
102:
95:
88:
7927:) is discouraged in mathematics articles. The use of
7883:
4816:
will be an image, and for others it will be HTML like
3817:(optionally excluding the adjacent punctuation), e.g.
3757:
3579:
3286:
8134:
8114:
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Knowledge:How to create charts for Knowledge articles
8035:
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Knowledge:Manual of Style/Accessibility § Indentation
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2606:
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2483:
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Knowledge:Manual of Style/Layout § "See also" section
8375:
A style guide specifically written for mathematics:
5727:
template to avoid line breaks and use the TeX font.
4789:
depending on user preferences. Thus, for some users
4470:
According to the Unicode Consortium, the characters
3917:Templates supporting HTML formatting are listed in
3643:{\textstyle \sum _{n=1}^{\infty }1/n^{2}=\pi ^{2}/6}
3215:. For instance, the formula above was typeset using
2441:
If the bar notation is used it should be entered as
2219:, or in contexts where there may be confusion with
1709:
Avoid, as far as possible, useless phrases such as:
1283:, while others may deserve their own section, as in
9224:
9118:
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3398:
3371:
3349:
3313:
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3218:
3195:
1059:The lead section should include, when appropriate:
8446:Some finer points of typography are discussed in:
8142:
8120:
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7661:
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2708:
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2621:
2589:symbol should be explicitly explained in the text.
2581:
2561:
2535:
2509:
2489:
2469:
1888:Knowledge:WikiProject Logic/Standards for notation
952:and summarize the article's most important points.
8386:Handbook of Writing for the Mathematical Sciences
4860:may be useful when editing mathematics articles.
4642:Superscripts and subscripts should be wrapped in
3823:, or by replacing the tags with a template, e.g.
1738:It follows directly from this definition that ...
1015:, 'study') is concerned with the properties of a
5860:tags and \sqrt{}, even if inline. For example:
3128:{\displaystyle \mathbf {x} \in \mathbb {R} ^{2}}
8477:University of Chicago Press Staff, ed. (2010),
7270:, for the differential operator, as opposed to
6917:, but this is now considered undesirable. See
4995:For when to use or not use Roman numerals, see
2764:of vectors should be denoted with a centre-dot
2596:, use superscript non-italic capital letter T:
2247:is used (this does not affect the notation of
8511:
7862:markup should not be used in image captions.
5234:markup cannot be used for technical reasons.)
4905:Mathematical operators and symbols in Unicode
3454:is too large to be used inline, rendering as
3370:Often better formatting can be achieved with
2922:Including citations and literature references
880:
8:
8363:Not all fractions are available precomposed.
7314:should be typeset in an upright Roman font:
6873:{\displaystyle r=x_{predicted}-x_{observed}}
1034:, crumpling and bending, but not tearing or
9136:Categories, lists, and navigation templates
6991:{\displaystyle \int _{0}^{\pi }\sin x\,dx,}
5450:when presented in a formula. That is, when
4997:Knowledge:Manual of Style/Dates and numbers
4899:). Although the symbols that correspond to
3180:{\displaystyle \int _{0}^{\pi }\sin x\,dx.}
1316:How to create graphs for Knowledge articles
1289:Adjunction formula § Applications to curves
1010:
1004:
778:Categories, lists, and navigation templates
8518:
8504:
8496:
8458:, Reading, Massachusetts: Addison-Wesley,
7286:; other authors use Roman boldface, as in
6909:For several years this manual recommended
6744:{\displaystyle \sum _{i=1}^{n}{y_{i}^{2}}}
3939:By default, regular text is rendered in a
3919:Category:Mathematical formatting templates
1430:may be decomposed into cosets, as follows.
1399:can be decomposed into cosets, as follows.
887:
873:
403:
367:
114:
8483:(16th ed.), University of Chicago Press,
8337:before the punctuation instead, but it's
8135:
8133:
8113:
8044:
8040:
8034:
7969:
7964:
7934:(such as ½) is discouraged entirely, for
7898:{\displaystyle \textstyle {\frac {1}{2}}}
7884:
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7804:
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2482:
2462:
2237:; when written multiplicatively, e.g. as
2213:, when written additively, has notation Z
1843:, depending on what you wish to express.
8196:Knowledge:Scientific citation guidelines
5567:(*) as a multiplication sign outside of
5068:when the character should render like a
4862:Almost all mathematical operator symbols
4518:). This is also required for "micro" by
3864:Images generated from LaTeX markup have
2826:Knowledge:WikiProject Mathematics/Proofs
1989:The ring with one element is called the
8208:
6977:
6515:{\displaystyle a\operatorname {tr} (A)}
6462:{\displaystyle 2\operatorname {csch} x}
5895:{\displaystyle {\sqrt {9}},{\sqrt{27}}}
5641:to have the ] treated as literal text.
5188:) in mathematical expressions, because
4909:force the symbol to display as an image
4886:list of mathematical symbols by subject
4854:list of mathematical symbols by subject
3166:
2871:<syntaxhighlight lang="Haskell": -->
2260:The standard notation for the abstract
1299:of an encyclopedia, examples should be
467:
117:
24:Knowledge:Manual of Style (mathematics)
6264:This shows that {{nowrap|<math: -->
4987:, and not precomposed characters like
4973:Unicode characters in the U+21XX range
3852:) added at the end of the formula, or
3652:which fits much better inline. Adding
3000:One may set formulae using LaTeX (the
2642:
1986:, which we do not assume to be unital.
949:provide context regarding the subject,
938:Knowledge:Manual of Style/Lead section
69:. When in doubt, discuss first on the
5446:being multiplied are best written as
5290:(which on some systems is too large).
5190:tilde has other mathematical meanings
3878:<math alt="Square root of pi": -->
3743:{\displaystyle {\sqrt {x^{2}+y^{2}}}}
3079:images. They may also be rendered as
1348:§ Including literature and references
1135:to denote exponentiation (instead of
49:is a part of the English Knowledge's
7:
8419:(1970), "How to Write Mathematics",
8333:It is technically possible to use a
5203:... \smallsetminus ...</math: -->
4626:
2963:Typesetting of mathematical formulae
977:), or in LaTeX (inside <math: -->
9286:Knowledge Manual of Style (science)
8021:
7996:
7858:
6087:Example 2: The foocity is given by
5957:Example 1: The foocity is given by
5910:
5856:
5753:There is a special Unicode symbol,
5230:
4912:
4701:Do not use special characters like
3944:
3001:
8136:
7796:
7701:, the additive and multiplicative
6570:
6567:
6564:
5931:Explanation of symbols in formulae
3788:{\textstyle {\sqrt {x^{2}+y^{2}}}}
3596:
3479:
2701:
2613:
2165:follows the Serre convention that
1756:(without loss of generality), and
1055:to three given circles in a plane.
31:
8264:Note that, aside of <math: -->
8191:Knowledge:WikiProject Mathematics
7570:{\displaystyle \mathbb {Z} _{p},}
7539:{\displaystyle \mathbb {F} _{q},}
4129:is a value on the horizontal axis
4117:is a value on the horizontal axis
3135:), as well as on their own line:
1439:be the corresponding subgroup of
1408:be the corresponding subgroup of
1293:Lambert W function § Applications
1051:is to construct circles that are
65:edit to this page should reflect
9248:
9247:
8163:Help for those writing a formula
7756:{\displaystyle \mathbb {G} _{m}}
7727:{\displaystyle \mathbb {G} _{a}}
7694:{\displaystyle \mathbb {A} _{K}}
7662:{\displaystyle \mathbb {P} ^{n}}
7630:{\displaystyle \mathbb {A} ^{n}}
7598:{\displaystyle \mathbb {Q} _{p}}
6265:\tfrac{1}{2} = 0.5</math: -->
6187:
6179:is the bazness coefficient, and
6145:
6117:
6106:
6098:
6064:
6018:
5987:
5976:
5968:
3303:{\displaystyle {\tfrac {1}{2}}x}
3106:
2622:{\displaystyle X^{\mathrm {T} }}
946:describe and define the subject,
36:
5198:... \setminus ...</math: -->
4051:The relationship is defined as
3992:The relationship is defined as
3800:
3799:HTML-generating formatting, as
2651:{\displaystyle X^{\mathsf {T}}}
1421:Instead, write something like:
8174:Knowledge:Mathematical symbols
7810:
7786:
6509:
6503:
6353:
6341:
5763:LATIN SMALL LETTER F WITH HOOK
4858:Knowledge:Mathematical symbols
4439:(It is also possible to enter
3898:{\displaystyle {\sqrt {\pi }}}
2864:Source code should always use
1733:something must hold, such as:
1269:Poincaré–Birkhoff–Witt theorem
1248:(number of elements) of every
1099:discriminant of a number field
1:
9053:References and external links
7508:{\displaystyle \mathbb {H} ,}
7484:{\displaystyle \mathbb {C} ,}
7460:{\displaystyle \mathbb {R} ,}
7436:{\displaystyle \mathbb {Q} ,}
7412:{\displaystyle \mathbb {Z} ,}
7388:{\displaystyle \mathbb {N} ,}
7239:{\displaystyle e^{i\theta }.}
6581:{\displaystyle 2{\rm {sin}}x}
5180:to mean "approximately" (and
4603:{\displaystyle \mathbb {R} .}
3391:tag, which translates to the
3030:For inline formulae, such as
677:References and external links
8339:seldom respected by browsers
8255:, §2.5 Duplicated Characters
8143:{\displaystyle \mathrm {A} }
6913:as a workaround for lack of
6194:{\displaystyle \mathbf {r} }
6152:{\displaystyle \mathbf {b} }
6071:{\displaystyle \mathbf {r} }
6025:{\displaystyle \mathbf {b} }
5296:... \ngtr ...</math: -->
4850:list of mathematical symbols
3683:<math display=inline: -->
3542:<math display=inline: -->
2449:(⋊) for maximum portability.
1354:Writing style in mathematics
8906:Specific naming conventions
8480:The Chicago Manual of Style
8421:Enseignements Mathématiques
6054:is the bazness coefficient,
5240:... \circ ...</math: -->
4632:Superscripts and subscripts
4618:(plain text ℝ or math font
3367:is too tall to fit inline.
3217:<math display=block: -->
3027:for mathematical articles.
2868:. For example this markup:
2807:, never with juxtaposition
2490:{\displaystyle \subsetneq }
2389:is the normal subgroup and
1929:" has two common meanings:
532:Specific naming conventions
9302:
8585:Organizing by subject area
8097:
7869:
7339:
6359:{\displaystyle 2\sin(x+1)}
6216:
6213:Punctuation after formulae
5934:
5792:
5734:
5608:"-‐‑", as well as from en-
5419:
5336:
4994:
4943:
4829:
4635:
4624:
4516:GREEK CAPITAL LETTER OMEGA
4388:would then be typeset by:
3055:of Latin letters, digits,
2993:
2968:
2926:Per the Knowledge policy,
2835:
2536:{\displaystyle A\subset B}
2470:{\displaystyle \subseteq }
1885:
1847:
1772:
1714:It is easily seen that ...
1690:
1550:
1479:
1467:It must be emphasized that
1357:
1285:Chain rule § First example
935:
78:
9243:
9211:Wikimedia sister projects
8533:
8221:WP:DICT#Major differences
8169:Help:Displaying a formula
5905:Because of Mediawiki bug
5769:), sometimes used as the
4402:''λ'' + ''y''
3093:Help:Displaying a formula
2996:Help:Displaying a formula
2875:generates the following:
2709:{\displaystyle X^{\top }}
2569:). All other uses of the
1941:which may also be called
1933:which may also be called
1463:It must be mentioned that
1019:that are preserved under
1011:
1005:
833:Wikimedia sister projects
18:Knowledge:Manual of Style
8236:This example, from here
8179:Knowledge:Rendering math
7830:\mathbb{Z}</math: -->
6201:is the quuxance vector.
5785:should be used instead.
5781:. An italicized letter
5779:NonVisual Desktop Access
5717:These templates use the
5473:in HTML or accessed via
3943:font. The TeX markup of
3879:\sqrt{\pi}</math: -->
3057:common punctuation marks
3021:talk page of the article
2877:
2723:, infima are written as
2582:{\displaystyle \subset }
2510:{\displaystyle \subset }
2447:{{unicode|⋊}}
2443:{{unicode|⋉}}
1949:if the context permits.
1882:Mathematical conventions
1045:Euclidean plane geometry
9276:WikiProject Mathematics
8395:10.1137/1.9780898719550
8057:{\displaystyle x^{1/2}}
7297:the same principles as
6307:{\displaystyle 2\sin x}
6159:is the barness vector,
6078:is the quuxance vector.
4897:Help:Special characters
4542:) rather than the HTML
3025:WikiProject Mathematics
2297:odd and greater than 1.
2115:with finite joins, not
1912:Terminology conventions
1459:It should be noted that
8144:
8122:
8095:
8058:
7981:
7899:
7849:\bold{1}</math: -->
7817:
7757:
7728:
7695:
7663:
7631:
7599:
7571:
7540:
7509:
7485:
7461:
7437:
7413:
7389:
7240:
7200:
7115:
7023:—note the thin space (
6992:
6874:
6751:(correct—typeset from
6745:
6723:
6656:(correct—typeset from
6650:
6582:
6516:
6463:
6425:implied multiplication
6399:
6360:
6308:
6203:
6195:
6173:
6153:
6128:
6081:
6072:
6048:
6032:is the barness vector,
6026:
5998:
5896:
5771:Florin currency symbol
5312:
5311:{\displaystyle \ngtr }
5256:
5255:{\displaystyle \circ }
4810:
4604:
4526:Common sets of numbers
4241:are never italicized:
4237:is the mass of a foo.
3899:
3876:element. For example,
3789:
3744:
3644:
3600:
3528:
3483:
3340:
3304:
3181:
3129:
2957:Knowledge:Cite sources
2710:
2683:
2652:
2623:
2583:
2563:
2537:
2511:
2491:
2471:
2197:Notational conventions
1265:
1237:, states that for any
1216:
1057:
1040:
8843:Writing about fiction
8411:More style guidance:
8145:
8123:
8075:
8059:
8027:x^{1/2}</math: -->
7982:
7949:in abstract algebra:
7945:Only "/" is used for
7932:precomposed fractions
7905:), or with a forward
7900:
7818:
7758:
7729:
7696:
7664:
7632:
7600:
7572:
7541:
7510:
7486:
7462:
7438:
7414:
7390:
7241:
7201:
7199:{\displaystyle x+iy,}
7116:
6993:
6875:
6746:
6703:
6651:
6583:
6517:
6464:
6400:
6398:{\displaystyle 2sinx}
6361:
6309:
6196:
6174:
6154:
6129:
6085:
6073:
6049:
6027:
5999:
5955:
5897:
5563:Do not use the ASCII
5454:a formula, don't use
5313:
5257:
5097:for a canonical list.
4811:
4809:{\displaystyle x^{2}}
4625:Further information:
4610:However, the special
4605:
4504:GREEK SMALL LETTER MU
4450:Greek letters; e.g.
3900:
3841:Deprecated formatting
3819:({{nobr|<math: -->
3790:
3745:
3645:
3580:
3529:
3463:
3341:
3305:
3182:
3130:
2711:
2684:
2682:{\displaystyle X^{T}}
2653:
2624:
2584:
2564:
2538:
2512:
2492:
2472:
2340:unless that is said).
2072:is not assumed to be
1935:non-negative integers
1259:divides the order of
1224:
1148:
1071:informal introduction
1064:Historical motivation
1041:
990:
460:Writing about fiction
165:Organizing by subject
119:Manual of Style (MoS)
59:occasional exceptions
9186:Talk page guidelines
8874:Stringed instruments
8580:Disambiguation pages
8132:
8112:
8033:
7963:
7880:
7771:
7738:
7709:
7676:
7644:
7612:
7580:
7549:
7518:
7494:
7470:
7446:
7422:
7398:
7374:
7217:
7178:
7039:
6950:
6793:
6700:
6620:
6556:
6491:
6444:
6412:2sin x</math: -->
6377:
6329:
6289:
6183:
6163:
6141:
6094:
6060:
6038:
6014:
5964:
5867:
5302:
5246:
5095:Asterisk#Mathematics
4864:have their specific
4793:
4614:characters, such as
4589:
3885:
3755:
3710:
3577:
3460:
3322:
3282:
3139:
3102:
2856:programming language
2842:An article about an
2693:
2666:
2633:
2604:
2573:
2547:
2521:
2501:
2481:
2461:
2044:is assumed to be an
1210:) is an open set in
1049:Apollonius's problem
932:Article introduction
899:This subpage of the
813:Talk page guidelines
488:Stringed instruments
160:Disambiguation pages
8991:Trinidad and Tobago
8921:France (and French)
8916:China (and Chinese)
8433:10.5169/seals-43857
8381:Higham, Nicholas J.
8185:General information
8068:Graphs and diagrams
8002:R / A</math: -->
7980:{\displaystyle R/A}
7809:
7209:x+iy,</math: -->
6967:
6927:Roman versus italic
6739:
6421:order of operations
5467:multiplication sign
5416:Multiplication sign
4878:General Punctuation
4585:, which renders as
3881:generates an image
3339:{\displaystyle x/2}
3156:
2866:syntax highlighting
2562:{\displaystyle A=B}
2477:, proper subset by
2293:, and are zero for
1752:(with respect to),
1144:mathematical object
1142:An article about a
617:Trinidad and Tobago
552:France (and French)
542:China (and Chinese)
9191:Template namespace
8290:Latin Extended-B,
8217:ring (mathematics)
8140:
8118:
8096:
8054:
7977:
7895:
7894:
7813:
7795:
7753:
7724:
7691:
7659:
7627:
7595:
7567:
7536:
7505:
7481:
7457:
7433:
7409:
7385:
7236:
7196:
7111:
7021:dx ,</math: -->
6988:
6978:
6953:
6870:
6741:
6725:
6646:
6578:
6512:
6459:
6395:
6356:
6304:
6277:Multi-letter names
6191:
6169:
6149:
6124:
6068:
6044:
6022:
5994:
5945:MOS:EXPLAINSYMBOLS
5892:
5509:An alternative to
5504:−42 = 9 × (−5) + 3
5489:26 by 4, 6 is the
5308:
5252:
4916:with LaTeX markup.
4806:
4600:
4324:would be written:
4258:standard functions
3895:
3872:attribute for the
3785:
3740:
3640:
3524:
3336:
3300:
3295:
3177:
3167:
3142:
3125:
3063:Using LaTeX markup
2706:
2679:
2648:
2619:
2579:
2559:
2533:
2507:
2487:
2467:
2355:should be written
2345:semidirect product
2328:) rather than Mor(
2145:Elliptic functions
2087:for our notion of
2035:Algebraic geometry
1931:{0, 1, 2, 3, ...},
1561:MOS:MATH#DEFSYMBOL
1329:Concluding matters
1227:Lagrange's theorem
1160:topological spaces
980:and </math: -->
920:in the context of
818:Template namespace
762:Related guidelines
9263:
9262:
9201:Understandability
9063:Structure drawing
9012:Latter Day Saints
8813:Lyrics and poetry
8756:Stand-alone lists
8643:Dates and numbers
8121:{\displaystyle A}
7892:
7860:...</math: -->
7106:
7083:
7060:
6643:
6630:
6536:(A)</math: -->
6172:{\displaystyle a}
6047:{\displaystyle a}
5912:...</math: -->
5890:
5875:
5858:...</math: -->
5639:]</nowiki: -->
5232:...</math: -->
5086:ASTERISK OPERATOR
4914:...</math: -->
4627:§ Blackboard bold
3986:special attention
3946:...</math: -->
3893:
3825:({{tmath|1=...}})
3820:...</math: -->
3814:...</math: -->
3783:
3738:
3519:
3499:
3294:
3071:markup (see also
3042:WP:Rendering math
3006:section headings,
2850:or in some cases
2285:Bernoulli numbers
2274:in geometry and D
2042:algebraic variety
2016:Clifford algebras
1962:is assumed to be
1943:positive integers
978:...</math: -->
897:
896:
823:Understandability
753:
752:
687:Structure drawing
642:Latter Day Saints
495:
494:
430:Lyrics and poetry
352:Stand-alone lists
227:Dates and numbers
113:
112:
22:(Redirected from
9293:
9281:Knowledge how-to
9251:
9250:
9237:
9161:Military history
9070:Computer science
9043:Compound classes
8890:Military history
8520:
8513:
8506:
8497:
8492:
8467:
8452:Knuth, Donald E.
8435:
8406:
8364:
8361:
8355:
8348:
8342:
8331:
8325:
8322:
8316:
8313:October 2020 RfC
8310:
8304:
8299:
8293:
8288:
8282:
8271:parser functions
8262:
8256:
8250:
8244:
8234:
8228:
8213:
8149:
8147:
8146:
8141:
8139:
8127:
8125:
8124:
8119:
8093:
8089:
8083:
8079:
8063:
8061:
8060:
8055:
8053:
8052:
8048:
8028:
8019:
8015:
8013:1/2</sup: -->
8003:
7994:
7993:|''R'' / ''A''}}
7986:
7984:
7983:
7978:
7973:
7958:
7947:quotient objects
7941:
7926:
7925:
7921:
7916:
7904:
7902:
7901:
7896:
7893:
7885:
7861:
7836:
7835:\Z</math: -->
7831:
7822:
7820:
7819:
7814:
7808:
7803:
7785:
7784:
7779:
7762:
7760:
7759:
7754:
7752:
7751:
7746:
7733:
7731:
7730:
7725:
7723:
7722:
7717:
7700:
7698:
7697:
7692:
7690:
7689:
7684:
7668:
7666:
7665:
7660:
7658:
7657:
7652:
7639:projective space
7636:
7634:
7633:
7628:
7626:
7625:
7620:
7604:
7602:
7601:
7596:
7594:
7593:
7588:
7576:
7574:
7573:
7568:
7563:
7562:
7557:
7545:
7543:
7542:
7537:
7532:
7531:
7526:
7514:
7512:
7511:
7506:
7501:
7490:
7488:
7487:
7482:
7477:
7466:
7464:
7463:
7458:
7453:
7442:
7440:
7439:
7434:
7429:
7418:
7416:
7415:
7410:
7405:
7394:
7392:
7391:
7386:
7381:
7352:
7331:
7317:
7313:
7290:
7285:
7281:
7277:
7273:
7269:
7261:
7259:
7256:
7252:
7245:
7243:
7242:
7237:
7232:
7231:
7210:
7205:
7203:
7202:
7197:
7171:
7169:
7165:
7161:
7158:
7155:
7152:
7148:
7144:
7141:
7137:
7133:
7129:
7126:
7120:
7118:
7117:
7112:
7107:
7105:
7097:
7089:
7084:
7082:
7074:
7066:
7061:
7059:
7051:
7043:
7032:
7028:
7027:
7022:
7020:
7016:
7013:
7010:
7006:
7003:
6997:
6995:
6994:
6989:
6966:
6961:
6916:
6912:
6904:
6902:
6898:
6894:
6890:
6879:
6877:
6876:
6871:
6869:
6868:
6835:
6834:
6781:
6779:
6775:
6771:
6767:
6763:
6759:
6756:
6750:
6748:
6747:
6742:
6740:
6738:
6733:
6722:
6717:
6688:
6686:
6682:
6679:
6676:
6672:
6668:
6665:
6662:
6655:
6653:
6652:
6647:
6645:
6644:
6641:
6632:
6631:
6628:
6607:
6605:
6601:
6598:
6587:
6585:
6584:
6579:
6574:
6573:
6548:
6544:
6537:
6535:
6531:
6528:
6521:
6519:
6518:
6513:
6484:
6482:
6478:
6475:
6468:
6466:
6465:
6460:
6436:
6435:
6413:
6404:
6402:
6401:
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6365:
6363:
6362:
6357:
6322:
6320:
6313:
6311:
6310:
6305:
6267:
6262:template, as in
6261:
6255:
6251:
6246:
6242:
6229:
6200:
6198:
6197:
6192:
6190:
6178:
6176:
6175:
6170:
6158:
6156:
6155:
6150:
6148:
6133:
6131:
6130:
6125:
6120:
6109:
6101:
6077:
6075:
6074:
6069:
6067:
6053:
6051:
6050:
6045:
6031:
6029:
6028:
6023:
6021:
6003:
6001:
6000:
5995:
5990:
5979:
5971:
5947:
5923:
5917:
5913:
5901:
5899:
5898:
5893:
5891:
5889:
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5876:
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5859:
5851:
5850:
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5843:
5834:
5828:
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5818:
5805:
5784:
5768:
5764:
5761:
5758:
5757:
5747:
5726:
5720:
5712:
5702:
5701:
5697:
5694:
5691:
5684:. For instance:
5683:
5677:
5673:
5667:
5663:
5657:
5653:
5647:
5640:
5623:
5619:
5588:
5583:
5580:
5579:
5574:
5551:
5543:
5542:
5539:
5536:
5533:
5530:
5527:
5524:
5519:
5512:
5505:
5500:
5480:
5472:
5469:: "×", coded as
5457:
5432:
5410:
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5405:
5402:
5399:
5396:
5384:
5383:
5379:
5376:
5373:
5370:
5367:
5359:
5352:
5329:
5328:NOT GREATER-THAN
5326:
5323:
5322:
5317:
5315:
5314:
5309:
5297:
5289:
5286:
5283:
5282:
5273:
5270:
5267:
5266:
5261:
5259:
5258:
5253:
5241:
5233:
5228:
5225:
5222:
5221:
5216:
5213:
5210:
5209:
5204:
5199:
5183:
5175:
5172:
5169:
5168:
5163:
5160:
5157:
5156:
5149:
5146:
5143:
5142:
5137:
5134:
5131:
5130:
5123:
5120:
5117:
5116:
5111:
5108:
5105:
5104:
5087:
5084:
5081:
5080:
5075:
5067:
5064:
5061:
5060:
5052:
5046:
5042:
5036:
5028:
5025:
5022:
5021:
5016:
5013:
5010:
5009:
4990:
4986:
4982:
4978:
4956:
4936:
4915:
4856:and the list at
4842:
4821:
4815:
4813:
4812:
4807:
4805:
4804:
4788:
4787:
4784:
4781:
4777:
4774:
4771:
4762:
4757:
4736:
4732:
4710:
4706:
4696:
4695:
4691:
4688:
4684:
4681:
4678:
4675:
4672:
4669:
4666:
4658:
4649:
4645:
4621:
4617:
4609:
4607:
4606:
4601:
4596:
4584:
4583:
4580:
4577:
4574:
4570:
4567:
4564:
4561:
4558:
4553:
4552:
4549:
4546:
4541:
4540:
4535:
4517:
4514:
4511:
4510:
4505:
4502:
4499:
4498:
4493:
4490:
4487:
4486:
4481:
4478:
4475:
4474:
4467:
4465:
4436:
4435:
4431:
4428:
4424:
4421:
4418:
4415:
4412:
4409:
4406:
4403:
4400:
4397:
4394:
4387:
4364:
4362:
4357:
4353:
4349:
4346:
4343:
4340:
4337:
4334:
4331:
4319:
4293:
4291:
4271:
4267:
4263:
4247:
4236:
4226:
4220:
4216:
4210:
4203:
4186:
4185:
4181:
4178:
4175:
4171:
4168:
4165:
4162:
4158:
4155:
4152:
4149:
4146:
4143:
4140:
4128:
4118:
4116:
4112:
4109:
4106:
4098:
4092:
4088:
4084:
4080:
4074:
4061:
4047:will result in:
4042:
4041:
4037:
4034:
4031:
4027:
4024:
4021:
4018:
4014:
4011:
4008:
4005:
4002:
3999:
3996:
3983:
3977:
3973:
3967:
3959:
3947:
3930:
3924:
3904:
3902:
3901:
3896:
3894:
3889:
3880:
3875:
3871:
3855:
3851:
3836:
3830:
3826:
3822:
3815:
3796:, respectively.
3795:
3794:
3792:
3791:
3786:
3784:
3782:
3781:
3769:
3768:
3759:
3749:
3747:
3746:
3741:
3739:
3737:
3736:
3724:
3723:
3714:
3706:which render as
3705:
3703:
3702:
3698:
3694:
3690:
3687:
3680:
3678:
3677:
3673:
3669:
3665:
3662:
3655:
3651:
3649:
3647:
3646:
3641:
3636:
3631:
3630:
3618:
3617:
3608:
3599:
3594:
3571:
3569:
3567:
3564:
3560:
3556:
3553:
3549:
3546:
3539:
3533:
3531:
3530:
3525:
3520:
3515:
3514:
3505:
3500:
3498:
3497:
3485:
3482:
3477:
3453:
3451:
3450:
3446:
3442:
3439:
3436:
3433:
3429:
3425:
3421:
3417:
3414:
3411:
3408:
3404:
3401:
3394:
3390:
3389:
3386:
3383:
3380:
3377:
3374:
3366:
3364:
3363:
3359:
3355:
3352:
3345:
3343:
3342:
3337:
3332:
3317:
3315:
3309:
3307:
3306:
3301:
3296:
3287:
3277:
3275:
3273:
3242:
3240:
3238:
3234:
3231:
3228:
3224:
3221:
3214:
3213:
3210:
3207:
3204:
3201:
3198:
3186:
3184:
3183:
3178:
3155:
3150:
3134:
3132:
3131:
3126:
3124:
3123:
3118:
3109:
3039:
3003:
2988:
2981:
2917:
2914:
2911:
2908:
2905:
2902:
2899:
2896:
2893:
2890:
2887:
2884:
2881:
2788:
2773:
2756:
2746:
2733:or as a product
2732:
2715:
2713:
2712:
2707:
2705:
2704:
2688:
2686:
2685:
2680:
2678:
2677:
2657:
2655:
2654:
2649:
2647:
2646:
2645:
2628:
2626:
2625:
2620:
2618:
2617:
2616:
2588:
2586:
2585:
2580:
2568:
2566:
2565:
2560:
2542:
2540:
2539:
2534:
2516:
2514:
2513:
2508:
2496:
2494:
2493:
2488:
2476:
2474:
2473:
2468:
2448:
2444:
2427:
2417:
2403:
2384:
2369:
2287:are denoted by B
2125:General Topology
2096:separation axiom
1940:
1932:
1860:
1842:
1826:
1810:
1785:
1744:
1739:
1725:
1720:
1715:
1703:
1701:MOS:MATH#OBVIOUS
1685:
1647:
1609:
1563:
1545:
1516:Instead, write:
1512:
1476:
1472:
1468:
1464:
1460:
1456:
1448:
1431:
1417:
1400:
1377:
1370:
1273:Nakayama's lemma
1205:
1017:geometric object
1014:
1013:
1008:
1007:
976:
970:
966:
960:
922:abstract algebra
889:
882:
875:
694:Computer science
667:Compound classes
512:Military history
404:
368:
134:
115:
105:
98:
91:
40:
39:
33:
27:
9301:
9300:
9296:
9295:
9294:
9292:
9291:
9290:
9266:
9265:
9264:
9259:
9239:
9238:
9233:
9220:
9114:
9079:
9016:
8995:
8894:
8878:
8847:
8793:Anime and manga
8781:
8760:
8729:
8725:Trivia sections
8698:
8684:Image placement
8667:
8663:Titles of works
8658:Text formatting
8621:
8612:Self-references
8592:Gender identity
8558:
8529:
8527:Manual of Style
8524:
8490:
8476:
8465:
8450:
8436:. Reprinted in
8415:
8404:
8379:
8373:
8371:Further reading
8368:
8367:
8362:
8358:
8349:
8345:
8332:
8328:
8323:
8319:
8311:
8307:
8300:
8296:
8289:
8285:
8263:
8259:
8251:
8247:
8235:
8231:
8214:
8210:
8205:
8187:
8165:
8160:
8130:
8129:
8110:
8109:
8102:
8091:
8087:
8081:
8077:
8070:
8036:
8031:
8030:
8017:
8007:
7988:
7961:
7960:
7950:
7939:
7923:
7919:
7918:
7910:
7878:
7877:
7874:
7868:
7846:a rendering bug
7833:
7828:
7774:
7769:
7768:
7765:hypercohomology
7741:
7736:
7735:
7712:
7707:
7706:
7679:
7674:
7673:
7647:
7642:
7641:
7615:
7610:
7609:
7583:
7578:
7577:
7552:
7547:
7546:
7521:
7516:
7515:
7492:
7491:
7468:
7467:
7444:
7443:
7420:
7419:
7396:
7395:
7372:
7371:
7360:blackboard bold
7356:
7355:
7348:
7344:
7338:
7336:Blackboard bold
7327:
7315:
7309:
7288:
7283:
7279:
7275:
7271:
7267:
7260:.</math: -->
7257:
7254:
7250:
7220:
7215:
7214:
7176:
7175:
7170:,</math: -->
7167:
7163:
7159:
7156:
7153:
7150:
7146:
7142:
7139:
7135:
7131:
7127:
7124:
7098:
7090:
7075:
7067:
7052:
7044:
7037:
7036:
7025:
7018:
7014:
7011:
7008:
7004:
7001:
6948:
6947:
6929:
6914:
6910:
6900:
6896:
6892:
6888:
6839:
6802:
6791:
6790:
6777:
6773:
6769:
6765:
6761:
6757:
6754:
6698:
6697:
6684:
6680:
6677:
6674:
6670:
6666:
6663:
6660:
6636:
6623:
6618:
6617:
6606:x</math: -->
6603:
6599:
6596:
6554:
6553:
6546:
6542:
6533:
6529:
6526:
6489:
6488:
6483:x</math: -->
6480:
6476:
6473:
6442:
6441:
6433:
6375:
6374:
6327:
6326:
6321:x</math: -->
6318:
6287:
6286:
6279:
6274:
6263:
6259:
6253:
6249:
6244:
6240:
6233:
6232:
6225:
6221:
6215:
6181:
6180:
6161:
6160:
6139:
6138:
6092:
6091:
6058:
6057:
6036:
6035:
6012:
6011:
5962:
5961:
5951:
5950:
5943:
5939:
5933:
5921:
5915:
5865:
5864:
5848:
5846:
5841:
5839:
5832:
5826:
5825:(often seen as
5822:
5816:
5809:
5808:
5801:
5797:
5791:
5782:
5766:
5762:
5759:
5755:
5754:
5751:
5750:
5743:
5739:
5733:
5731:Function symbol
5724:
5718:
5710:
5699:
5695:
5692:
5689:
5681:
5675:
5671:
5665:
5661:
5655:
5651:
5645:
5638:<nowiki: -->
5637:
5630:
5628:Square brackets
5621:
5613:
5602:
5584:
5581:
5577:
5576:
5572:
5545:
5540:
5537:
5534:
5531:
5528:
5525:
5522:
5517:
5510:
5503:
5499:26 = 6 × 4 + 2.
5498:
5474:
5470:
5455:
5436:
5435:
5428:
5424:
5418:
5407:
5403:
5400:
5397:
5394:
5381:
5377:
5374:
5371:
5368:
5365:
5354:
5350:
5346:
5341:
5327:
5324:
5320:
5319:
5300:
5299:
5294:
5287:
5284:
5280:
5279:
5271:
5268:
5264:
5263:
5244:
5243:
5238:
5227:REVERSE SOLIDUS
5226:
5223:
5219:
5218:
5214:
5211:
5207:
5206:
5201:
5196:
5181:
5173:
5170:
5166:
5165:
5161:
5158:
5154:
5153:
5147:
5144:
5140:
5139:
5135:
5132:
5128:
5127:
5121:
5118:
5114:
5113:
5109:
5106:
5102:
5101:
5085:
5082:
5078:
5077:
5065:
5062:
5058:
5057:
5050:
5044:
5040:
5034:
5026:
5023:
5019:
5018:
5014:
5011:
5007:
5006:
5000:
4975:. For example,
4960:
4959:
4952:
4948:
4928:
4927:" rather than "
4846:
4845:
4840:MOS:MATHSPECIAL
4838:
4834:
4828:
4826:Special symbols
4817:
4796:
4791:
4790:
4785:
4782:
4779:
4775:
4772:
4769:
4759:
4740:
4734:
4715:
4708:
4702:
4692:
4689:
4686:
4682:
4679:
4676:
4673:
4670:
4667:
4664:
4657:
4651:
4647:
4643:
4640:
4634:
4629:
4619:
4615:
4587:
4586:
4581:
4578:
4575:
4572:
4568:
4565:
4562:
4559:
4556:
4550:
4547:
4544:
4538:
4531:
4528:
4520:MOS:UNITSYMBOLS
4515:
4512:
4508:
4507:
4503:
4500:
4496:
4495:
4491:
4488:
4484:
4483:
4479:
4476:
4472:
4471:
4452:
4451:
4432:
4429:
4426:
4422:
4419:
4416:
4413:
4410:
4407:
4404:
4401:
4398:
4395:
4392:
4375:
4372:
4360:
4355:
4351:
4347:
4344:
4341:
4338:
4335:
4332:
4329:
4305:
4299:
4274:
4273:
4269:
4265:
4261:
4254:
4242:
4235:
4229:
4224:
4218:
4214:
4208:
4194:
4183:
4179:
4176:
4173:
4169:
4166:
4163:
4160:
4156:
4153:
4150:
4147:
4144:
4141:
4138:
4126:
4114:
4110:
4107:
4104:
4096:
4090:
4086:
4082:
4078:
4072:
4069:
4052:
4039:
4035:
4032:
4029:
4025:
4022:
4019:
4016:
4012:
4009:
4006:
4003:
4000:
3997:
3994:
3981:
3975:
3971:
3965:
3953:
3937:
3935:Font formatting
3928:
3922:
3912:
3883:
3882:
3877:
3873:
3869:
3862:
3853:
3849:
3843:
3834:
3828:
3824:
3818:
3812:
3811:Directly using
3809:
3801:described below
3773:
3760:
3753:
3752:
3751:
3728:
3715:
3708:
3707:
3700:
3696:
3692:
3688:
3685:
3682:
3675:
3671:
3667:
3663:
3660:
3657:
3622:
3609:
3575:
3574:
3573:
3565:
3562:
3558:
3554:
3551:
3547:
3544:
3541:
3537:
3534:
3506:
3489:
3458:
3457:
3448:
3444:
3440:
3437:
3434:
3431:
3427:
3423:
3419:
3415:
3412:
3409:
3406:
3402:
3399:
3396:
3392:
3387:
3384:
3381:
3378:
3375:
3372:
3361:
3357:
3353:
3350:
3347:
3320:
3319:
3311:
3280:
3279:
3271:
3268:
3236:
3232:
3229:
3226:
3222:
3219:
3216:
3211:
3208:
3205:
3202:
3199:
3196:
3137:
3136:
3113:
3100:
3099:
3065:
3049:on its own line
3031:
2998:
2992:
2991:
2984:
2977:
2973:
2965:
2924:
2919:
2918:
2915:
2912:
2909:
2906:
2903:
2900:
2897:
2894:
2891:
2888:
2885:
2882:
2879:
2873:
2840:
2834:
2818:
2778:
2765:
2748:
2738:
2724:
2696:
2691:
2690:
2669:
2664:
2663:
2636:
2631:
2630:
2607:
2602:
2601:
2571:
2570:
2545:
2544:
2519:
2518:
2499:
2498:
2479:
2478:
2459:
2458:
2446:
2442:
2419:
2409:
2390:
2380:
2371:
2365:
2356:
2302:category theory
2292:
2280:
2273:
2256:
2249:isometry groups
2246:
2218:
2199:
2147:are written in
2113:preordered sets
2105:
2065:
2037:
2000:is not assumed
1955:
1947:natural numbers
1939:{1, 2, 3, ...},
1938:
1930:
1927:natural numbers
1919:
1917:Natural numbers
1914:
1890:
1884:
1864:
1863:
1858:MOS:MATH#PLURAL
1856:
1852:
1789:
1788:
1781:
1777:
1707:
1706:
1699:
1695:
1589:if and only if
1567:
1566:
1559:
1555:
1543:
1510:
1484:
1416:is then finite.
1381:
1380:
1373:
1366:
1362:
1356:
1331:
1201:
1091:
1009:, 'place', and
974:
968:
964:
958:
940:
934:
914:
901:Manual of Style
893:
843:
842:
763:
755:
754:
749:
748:
724:
714:
713:
657:
647:
646:
632:
622:
621:
527:
517:
516:
507:
497:
496:
410:Anime and manga
401:
391:
390:
376:
365:
357:
356:
332:
322:
321:
317:Trivia sections
297:
287:
286:
272:Image placement
262:
252:
251:
247:Titles of works
242:Text formatting
212:
202:
201:
192:Self-references
172:Gender identity
145:
135:
129:
109:
108:
101:
94:
87:
83:
75:
74:
61:may apply. Any
51:Manual of Style
37:
29:
28:
21:
20:
12:
11:
5:
9299:
9297:
9289:
9288:
9283:
9278:
9268:
9267:
9261:
9260:
9258:
9257:
9244:
9241:
9240:
9231:
9229:
9228:
9226:
9222:
9221:
9219:
9218:
9213:
9208:
9203:
9198:
9193:
9188:
9183:
9178:
9173:
9168:
9163:
9158:
9153:
9148:
9146:Citing sources
9143:
9141:Categorization
9138:
9133:
9131:Article titles
9128:
9122:
9120:
9116:
9115:
9113:
9112:
9111:
9110:
9103:Figure skating
9100:
9099:
9098:
9087:
9085:
9081:
9080:
9078:
9077:
9072:
9067:
9066:
9065:
9060:
9055:
9050:
9045:
9035:
9030:
9024:
9022:
9018:
9017:
9015:
9014:
9009:
9003:
9001:
8997:
8996:
8994:
8993:
8988:
8983:
8978:
8973:
8968:
8963:
8958:
8953:
8948:
8943:
8938:
8933:
8928:
8923:
8918:
8913:
8908:
8902:
8900:
8896:
8895:
8893:
8892:
8886:
8884:
8880:
8879:
8877:
8876:
8871:
8866:
8861:
8855:
8853:
8849:
8848:
8846:
8845:
8840:
8835:
8830:
8825:
8820:
8815:
8810:
8805:
8800:
8795:
8789:
8787:
8783:
8782:
8780:
8779:
8774:
8768:
8766:
8762:
8761:
8759:
8758:
8753:
8751:Road junctions
8748:
8746:Lists of works
8743:
8737:
8735:
8731:
8730:
8728:
8727:
8722:
8717:
8712:
8706:
8704:
8700:
8699:
8697:
8696:
8691:
8686:
8681:
8675:
8673:
8669:
8668:
8666:
8665:
8660:
8655:
8650:
8645:
8640:
8638:Capitalization
8635:
8629:
8627:
8623:
8622:
8620:
8619:
8617:Words to watch
8614:
8609:
8604:
8599:
8594:
8589:
8588:
8587:
8577:
8572:
8566:
8564:
8560:
8559:
8557:
8556:
8549:
8542:
8534:
8531:
8530:
8525:
8523:
8522:
8515:
8508:
8500:
8494:
8493:
8488:
8470:
8469:
8463:
8444:
8443:
8409:
8408:
8402:
8372:
8369:
8366:
8365:
8356:
8352:ISO/IEC 8859-1
8350:Characters in
8343:
8326:
8317:
8305:
8294:
8283:
8257:
8245:
8229:
8207:
8206:
8204:
8201:
8200:
8199:
8193:
8186:
8183:
8182:
8181:
8176:
8171:
8164:
8161:
8159:
8156:
8138:
8117:
8086:The length of
8085:
8069:
8066:
8051:
8047:
8043:
8039:
8012:|x<sup: -->
7976:
7972:
7968:
7891:
7888:
7867:
7864:
7812:
7807:
7802:
7798:
7794:
7791:
7788:
7783:
7778:
7750:
7745:
7721:
7716:
7688:
7683:
7656:
7651:
7624:
7619:
7592:
7587:
7566:
7561:
7556:
7535:
7530:
7525:
7504:
7500:
7480:
7476:
7456:
7452:
7432:
7428:
7408:
7404:
7384:
7380:
7368:number systems
7354:
7353:
7345:
7340:
7337:
7334:
7264:
7263:
7246:(typeset from
7235:
7230:
7227:
7223:
7212:
7206:(typeset from
7195:
7192:
7189:
7186:
7183:
7173:
7121:(typeset from
7110:
7104:
7101:
7096:
7093:
7087:
7081:
7078:
7073:
7070:
7064:
7058:
7055:
7050:
7047:
7034:
6998:(typeset from
6987:
6984:
6981:
6976:
6973:
6970:
6965:
6960:
6956:
6941:Euler's number
6937:imaginary unit
6928:
6925:
6907:
6906:
6903:</math: -->
6884:—typeset from
6867:
6864:
6861:
6858:
6855:
6852:
6849:
6846:
6842:
6838:
6833:
6830:
6827:
6824:
6821:
6818:
6815:
6812:
6809:
6805:
6801:
6798:
6784:
6783:
6780:</math: -->
6737:
6732:
6728:
6721:
6716:
6713:
6710:
6706:
6691:
6690:
6687:</math: -->
6639:
6635:
6626:
6610:
6609:
6592:—typeset from
6577:
6572:
6569:
6566:
6561:
6540:
6539:
6522:(typeset from
6511:
6508:
6505:
6502:
6499:
6496:
6486:
6469:(typeset from
6458:
6455:
6452:
6449:
6429:
6428:
6416:
6415:
6409:—typeset from
6394:
6391:
6388:
6385:
6382:
6368:
6367:
6355:
6352:
6349:
6346:
6343:
6340:
6337:
6334:
6324:
6303:
6300:
6297:
6294:
6278:
6275:
6273:
6270:
6250:</math: -->
6245:</math: -->
6231:
6230:
6222:
6217:
6214:
6211:
6189:
6168:
6147:
6135:
6134:
6123:
6119:
6115:
6112:
6108:
6104:
6100:
6080:
6079:
6066:
6055:
6043:
6033:
6020:
6005:
6004:
5993:
5989:
5985:
5982:
5978:
5974:
5970:
5949:
5948:
5940:
5935:
5932:
5929:
5903:
5902:
5888:
5884:
5879:
5874:
5853:
5852:
5813:radical symbol
5807:
5806:
5798:
5793:
5790:
5789:Radical symbol
5787:
5749:
5748:
5740:
5735:
5732:
5729:
5715:
5714:
5704:
5703:
5629:
5626:
5620:) or use the "
5601:
5598:
5520:(also encoded
5507:
5506:
5501:
5461:However, when
5434:
5433:
5425:
5420:
5417:
5414:
5413:
5412:
5387:
5386:
5345:
5344:Less-than sign
5342:
5334:
5332:
5331:
5307:
5291:
5251:
5235:
5193:
5174:TILDE OPERATOR
5150:
5124:
5122:DIVISION SLASH
5098:
5054:
5003:
5002:
5001:
4965:Roman numerals
4958:
4957:
4949:
4944:
4941:
4939:
4938:
4917:
4901:named entities
4891:Keep in mind:
4844:
4843:
4835:
4830:
4827:
4824:
4803:
4799:
4765:
4764:
4761:2</sup: -->
4738:
4699:
4698:
4655:
4633:
4630:
4599:
4595:
4527:
4524:
4371:
4368:
4367:
4366:
4322:
4321:
4298:
4295:
4253:
4250:
4233:
4205:
4204:
4188:
4187:
4131:
4130:
4120:
4119:
4068:
4065:
4064:
4063:
4045:
4044:
3936:
3933:
3911:
3908:
3892:
3861:
3858:
3842:
3839:
3808:
3805:
3780:
3776:
3772:
3767:
3763:
3735:
3731:
3727:
3722:
3718:
3704:</math: -->
3679:</math: -->
3654:display=inline
3639:
3635:
3629:
3625:
3621:
3616:
3612:
3607:
3603:
3598:
3593:
3590:
3587:
3583:
3570:</math: -->
3538:display=inline
3523:
3518:
3513:
3509:
3503:
3496:
3492:
3488:
3481:
3476:
3473:
3470:
3466:
3456:
3452:</math: -->
3365:</math: -->
3335:
3331:
3327:
3316:</math: -->
3299:
3293:
3290:
3276:</math: -->
3265:
3264:
3257:
3254:
3241:</math: -->
3176:
3173:
3170:
3165:
3162:
3159:
3154:
3149:
3145:
3122:
3117:
3112:
3108:
3064:
3061:
3047:For a formula
2990:
2989:
2982:
2974:
2969:
2964:
2961:
2953:
2952:
2949:
2945:
2942:
2939:
2923:
2920:
2878:
2870:
2833:
2830:
2817:
2814:
2813:
2812:
2799:matrix product
2760:The scalar or
2758:
2717:
2703:
2699:
2676:
2672:
2644:
2639:
2615:
2610:
2590:
2578:
2558:
2555:
2552:
2532:
2529:
2526:
2506:
2486:
2466:
2457:is denoted by
2452:
2451:
2450:
2439:
2436:
2376:
2361:
2341:
2338:small category
2298:
2288:
2282:
2275:
2269:
2262:dihedral group
2258:
2252:
2242:
2239:roots of unity
2224:-adic integers
2214:
2198:
2195:
2194:
2193:
2156:
2142:
2135:
2117:partial orders
2104:
2101:
2100:
2099:
2092:
2064:
2061:
2060:
2059:
2052:
2036:
2033:
2032:
2031:
2012:
1994:
1987:
1954:
1951:
1918:
1915:
1913:
1910:
1883:
1880:
1866:The plural of
1862:
1861:
1853:
1848:
1787:
1786:
1778:
1773:
1746:
1745:
1740:
1727:
1726:
1721:
1716:
1705:
1704:
1696:
1691:
1687:
1686:
1660:is a function
1649:
1648:
1611:
1610:
1565:
1564:
1556:
1551:
1547:
1546:
1541:
1525:by the vector
1514:
1513:
1508:
1450:
1449:
1432:
1419:
1418:
1401:
1379:
1378:
1371:
1363:
1358:
1355:
1352:
1330:
1327:
1311:for details).
1309:WP:NOTTEXTBOOK
1186:if, for every
1090:
1087:
1086:
1085:
1075:
1067:
954:
953:
950:
947:
933:
930:
913:
910:
895:
894:
892:
891:
884:
877:
869:
866:
865:
864:
863:
858:
853:
845:
844:
841:
840:
835:
830:
825:
820:
815:
810:
805:
800:
795:
790:
788:Citing sources
785:
783:Categorization
780:
775:
773:Article titles
770:
764:
761:
760:
757:
756:
751:
750:
747:
746:
739:Figure skating
736:
725:
720:
719:
716:
715:
712:
711:
706:
701:
696:
691:
690:
689:
684:
679:
674:
669:
658:
653:
652:
649:
648:
645:
644:
639:
633:
628:
627:
624:
623:
620:
619:
614:
609:
604:
599:
594:
589:
584:
579:
574:
569:
564:
559:
554:
549:
544:
539:
534:
528:
523:
522:
519:
518:
515:
514:
508:
503:
502:
499:
498:
493:
492:
491:
490:
485:
480:
472:
471:
465:
464:
463:
462:
457:
452:
447:
442:
437:
432:
427:
422:
417:
412:
402:
397:
396:
393:
392:
389:
388:
383:
377:
372:
371:
366:
363:
362:
359:
358:
355:
354:
349:
347:Road junctions
344:
342:Lists of works
339:
333:
328:
327:
324:
323:
320:
319:
314:
309:
304:
298:
293:
292:
289:
288:
285:
284:
279:
274:
269:
263:
258:
257:
254:
253:
250:
249:
244:
239:
234:
229:
224:
222:Capitalization
219:
213:
208:
207:
204:
203:
200:
199:
197:Words to watch
194:
189:
184:
179:
174:
169:
168:
167:
157:
152:
146:
141:
140:
137:
136:
131:
127:
125:
122:
121:
111:
110:
107:
106:
99:
92:
84:
79:
76:
56:
55:
43:
41:
30:
15:
14:
13:
10:
9:
6:
4:
3:
2:
9298:
9287:
9284:
9282:
9279:
9277:
9274:
9273:
9271:
9256:
9255:
9246:
9245:
9242:
9227:
9223:
9217:
9214:
9212:
9209:
9207:
9204:
9202:
9199:
9197:
9194:
9192:
9189:
9187:
9184:
9182:
9179:
9177:
9174:
9172:
9169:
9167:
9164:
9162:
9159:
9157:
9154:
9152:
9149:
9147:
9144:
9142:
9139:
9137:
9134:
9132:
9129:
9127:
9124:
9123:
9121:
9117:
9109:
9106:
9105:
9104:
9101:
9097:
9094:
9093:
9092:
9089:
9088:
9086:
9082:
9076:
9073:
9071:
9068:
9064:
9061:
9059:
9056:
9054:
9051:
9049:
9046:
9044:
9041:
9040:
9039:
9036:
9034:
9031:
9029:
9026:
9025:
9023:
9019:
9013:
9010:
9008:
9005:
9004:
9002:
8998:
8992:
8989:
8987:
8984:
8982:
8979:
8977:
8974:
8972:
8969:
8967:
8964:
8962:
8959:
8957:
8954:
8952:
8949:
8947:
8944:
8942:
8939:
8937:
8934:
8932:
8929:
8927:
8924:
8922:
8919:
8917:
8914:
8912:
8909:
8907:
8904:
8903:
8901:
8897:
8891:
8888:
8887:
8885:
8881:
8875:
8872:
8870:
8869:Record charts
8867:
8865:
8864:Music samples
8862:
8860:
8857:
8856:
8854:
8850:
8844:
8841:
8839:
8836:
8834:
8831:
8829:
8826:
8824:
8821:
8819:
8816:
8814:
8811:
8809:
8806:
8804:
8801:
8799:
8796:
8794:
8791:
8790:
8788:
8784:
8778:
8775:
8773:
8770:
8769:
8767:
8763:
8757:
8754:
8752:
8749:
8747:
8744:
8742:
8739:
8738:
8736:
8732:
8726:
8723:
8721:
8718:
8716:
8713:
8711:
8708:
8707:
8705:
8701:
8695:
8692:
8690:
8687:
8685:
8682:
8680:
8677:
8676:
8674:
8670:
8664:
8661:
8659:
8656:
8654:
8651:
8649:
8648:Pronunciation
8646:
8644:
8641:
8639:
8636:
8634:
8633:Abbreviations
8631:
8630:
8628:
8624:
8618:
8615:
8613:
8610:
8608:
8605:
8603:
8600:
8598:
8595:
8593:
8590:
8586:
8583:
8582:
8581:
8578:
8576:
8573:
8571:
8570:Accessibility
8568:
8567:
8565:
8561:
8555:
8554:
8550:
8548:
8547:
8543:
8541:
8540:
8536:
8535:
8532:
8528:
8521:
8516:
8514:
8509:
8507:
8502:
8501:
8498:
8491:
8489:9780226104201
8486:
8482:
8481:
8475:
8474:
8473:
8466:
8464:0-201-13448-9
8461:
8457:
8453:
8449:
8448:
8447:
8442:
8439:
8434:
8430:
8426:
8422:
8418:
8414:
8413:
8412:
8405:
8403:0-89871-420-6
8400:
8396:
8392:
8388:
8387:
8382:
8378:
8377:
8376:
8370:
8360:
8357:
8353:
8347:
8344:
8340:
8336:
8330:
8327:
8321:
8318:
8314:
8309:
8306:
8303:
8298:
8295:
8292:
8287:
8284:
8280:
8276:
8272:
8268:
8261:
8258:
8254:
8249:
8246:
8242:
8238:
8233:
8230:
8226:
8222:
8218:
8212:
8209:
8202:
8197:
8194:
8192:
8189:
8188:
8184:
8180:
8177:
8175:
8172:
8170:
8167:
8166:
8162:
8157:
8155:
8151:
8115:
8106:
8101:
8074:
8067:
8065:
8049:
8045:
8041:
8037:
8025:
8011:
8004:
8000:
7992:
7974:
7970:
7966:
7957:
7953:
7948:
7943:
7937:
7936:accessibility
7933:
7930:
7914:
7908:
7889:
7886:
7873:
7865:
7863:
7859:<math: -->
7856:
7851:
7847:
7842:
7840:
7834:<math: -->
7829:<math: -->
7824:
7805:
7800:
7792:
7789:
7781:
7766:
7748:
7719:
7704:
7703:group schemes
7686:
7672:
7654:
7640:
7622:
7608:
7590:
7564:
7559:
7533:
7528:
7502:
7478:
7454:
7430:
7406:
7382:
7369:
7364:
7361:
7351:
7347:
7346:
7343:
7335:
7333:
7330:
7325:
7321:
7312:
7307:
7302:
7300:
7295:
7291:
7248:<math: -->
7233:
7228:
7225:
7221:
7213:
7208:<math: -->
7193:
7190:
7187:
7184:
7181:
7174:
7123:<math: -->
7108:
7102:
7099:
7094:
7091:
7085:
7079:
7076:
7071:
7068:
7062:
7056:
7053:
7048:
7045:
7035:
7000:<math: -->
6985:
6982:
6979:
6974:
6971:
6968:
6963:
6958:
6954:
6946:
6945:
6944:
6942:
6938:
6934:
6926:
6924:
6923:
6921:
6886:<math: -->
6883:
6865:
6862:
6859:
6856:
6853:
6850:
6847:
6844:
6840:
6836:
6831:
6828:
6825:
6822:
6819:
6816:
6813:
6810:
6807:
6803:
6799:
6796:
6789:
6788:
6787:
6753:<math: -->
6735:
6730:
6726:
6719:
6714:
6711:
6708:
6704:
6696:
6695:
6694:
6658:<math: -->
6637:
6633:
6624:
6616:
6615:
6614:
6594:<math: -->
6591:
6575:
6559:
6552:
6551:
6550:
6543:\operatorname
6527:\operatorname
6524:<math: -->
6506:
6500:
6497:
6494:
6487:
6474:\operatorname
6471:<math: -->
6456:
6453:
6450:
6447:
6440:
6439:
6438:
6434:\operatorname
6426:
6422:
6418:
6417:
6411:<math: -->
6408:
6392:
6389:
6386:
6383:
6380:
6373:
6372:
6371:
6350:
6347:
6344:
6338:
6335:
6332:
6325:
6316:<math: -->
6301:
6298:
6295:
6292:
6285:
6284:
6283:
6276:
6271:
6269:
6258:
6241:<math: -->
6237:
6228:
6227:MOS:MATH#PUNC
6224:
6223:
6220:
6212:
6210:
6208:
6207:Heat equation
6202:
6166:
6121:
6113:
6110:
6102:
6090:
6089:
6088:
6084:
6056:
6041:
6034:
6010:
6009:
6008:
5991:
5983:
5980:
5972:
5960:
5959:
5958:
5954:
5953:A list as in
5946:
5942:
5941:
5938:
5930:
5928:
5925:
5920:
5911:<math: -->
5908:
5886:
5882:
5877:
5872:
5863:
5862:
5861:
5857:<math: -->
5838:
5837:
5836:
5831:
5821:
5814:
5804:
5800:
5799:
5796:
5788:
5786:
5780:
5776:
5772:
5746:
5742:
5741:
5738:
5730:
5728:
5723:
5709:
5708:
5707:
5687:
5686:
5685:
5680:
5679:closed-closed
5670:
5660:
5650:
5642:
5635:
5627:
5625:
5617:
5611:
5607:
5599:
5597:
5595:
5590:
5587:
5570:
5566:
5561:
5559:
5555:
5549:
5516:
5502:
5496:
5493:and 2 is the
5492:
5488:
5484:
5483:
5482:
5478:
5468:
5464:
5459:
5453:
5449:
5445:
5441:
5431:
5427:
5426:
5423:
5415:
5392:
5391:
5390:
5363:
5362:
5361:
5357:
5343:
5340:
5335:
5318:) instead of
5305:
5295:<math: -->
5292:
5277:
5272:RING OPERATOR
5262:) instead of
5249:
5239:<math: -->
5236:
5231:<math: -->
5202:<math: -->
5197:<math: -->
5194:
5191:
5187:
5179:
5178:other symbols
5151:
5125:
5099:
5096:
5091:
5071:
5055:
5049:
5039:
5032:
5004:
4998:
4993:
4992:
4974:
4970:
4966:
4962:
4961:
4955:
4951:
4950:
4947:
4942:
4935:
4931:
4926:
4922:
4918:
4913:<math: -->
4910:
4906:
4902:
4898:
4894:
4893:
4892:
4889:
4887:
4883:
4879:
4875:
4872:outside both
4871:
4867:
4863:
4859:
4855:
4851:
4841:
4837:
4836:
4833:
4825:
4823:
4820:
4801:
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4441:Greek letters
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4370:Greek letters
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4122:displays as:
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3991:
3990:
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3945:<math: -->
3942:
3934:
3932:
3927:
3920:
3915:
3909:
3907:
3890:
3867:
3859:
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3854:\displaystyle
3845:
3840:
3838:
3833:
3813:<math: -->
3807:Line wrapping
3806:
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3368:
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3297:
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3269:<math: -->
3262:
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3120:
3110:
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3090:
3086:
3082:
3078:
3074:
3070:
3062:
3060:
3058:
3054:
3050:
3045:
3044:for details.
3043:
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3026:
3022:
3018:
3013:
3011:
3007:
3002:<math: -->
2997:
2987:
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2822:
2815:
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2806:
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2800:
2796:
2792:
2786:
2782:
2777:
2776:inner product
2772:
2768:
2763:
2759:
2755:
2751:
2745:
2741:
2737:, suprema as
2736:
2731:
2727:
2722:
2718:
2697:
2674:
2670:
2661:
2637:
2608:
2599:
2595:
2592:For a matrix
2591:
2576:
2556:
2553:
2550:
2530:
2527:
2524:
2504:
2497:. The symbol
2484:
2464:
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2440:
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2426:
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2416:
2412:
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2250:
2245:
2240:
2236:
2233:
2229:
2225:
2223:
2217:
2212:
2209:
2205:
2202:The abstract
2201:
2200:
2196:
2191:
2187:
2183:
2179:
2176:
2172:
2168:
2164:
2161:
2157:
2154:
2150:
2146:
2143:
2140:
2136:
2133:
2132:0-387-90125-6
2130:
2126:
2122:
2119:as in, e.g.,
2118:
2114:
2110:
2109:Directed sets
2107:
2106:
2103:Miscellaneous
2102:
2097:
2093:
2090:
2086:
2085:quasi-compact
2082:
2079:
2075:
2071:
2070:compact space
2067:
2066:
2062:
2057:
2053:
2050:
2049:algebraic set
2047:
2043:
2039:
2038:
2034:
2029:
2025:
2021:
2017:
2013:
2010:
2007:
2003:
1999:
1995:
1992:
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1732:
1724:Obviously ...
1722:
1717:
1712:
1711:
1710:
1702:
1698:
1697:
1694:
1689:
1683:
1679:
1675:
1671:
1667:
1663:
1659:
1658:even function
1654:
1653:
1652:
1645:
1641:
1637:
1633:
1629:
1625:
1621:
1616:
1615:
1614:
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1519:
1518:
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1507:
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1499:
1495:
1490:
1489:
1488:
1483:
1478:
1471:Consider that
1446:
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1438:
1433:
1429:
1424:
1423:
1422:
1415:
1411:
1407:
1402:
1398:
1394:
1391:Suppose that
1389:
1388:
1387:
1384:
1376:
1375:MOS:MATH#NOWE
1372:
1369:
1368:MOS:MATH#TONE
1365:
1364:
1361:
1353:
1351:
1349:
1345:
1339:
1337:
1328:
1326:
1323:
1319:
1317:
1312:
1310:
1306:
1305:instructional
1302:
1298:
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1290:
1286:
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1276:
1274:
1270:
1264:
1262:
1258:
1254:
1251:
1247:
1243:
1240:
1236:
1232:
1228:
1223:
1220:
1215:
1213:
1209:
1204:
1200:
1196:
1192:
1189:
1185:
1181:
1177:
1173:
1169:
1165:
1161:
1157:
1153:
1147:
1145:
1140:
1138:
1134:
1130:
1126:
1122:
1117:
1115:
1112:
1108:
1104:
1100:
1096:
1088:
1083:
1079:
1076:
1072:
1068:
1065:
1062:
1061:
1060:
1056:
1054:
1050:
1046:
1039:
1037:
1033:
1029:
1025:
1022:
1018:
1003:
999:
995:
989:
986:
982:
973:
963:
951:
948:
945:
944:
943:
939:
931:
929:
927:
923:
919:
911:
909:
906:
902:
890:
885:
883:
878:
876:
871:
870:
868:
867:
862:
859:
857:
854:
852:
849:
848:
847:
846:
839:
836:
834:
831:
829:
826:
824:
821:
819:
816:
814:
811:
809:
806:
804:
801:
799:
796:
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791:
789:
786:
784:
781:
779:
776:
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771:
769:
766:
765:
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758:
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740:
737:
734:
730:
727:
726:
723:
718:
717:
710:
707:
705:
702:
700:
697:
695:
692:
688:
685:
683:
680:
678:
675:
673:
670:
668:
665:
664:
663:
660:
659:
656:
651:
650:
643:
640:
638:
635:
634:
631:
626:
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618:
615:
613:
610:
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583:
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560:
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510:
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506:
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500:
489:
486:
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483:Record charts
481:
479:
478:Music samples
476:
475:
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466:
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458:
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406:
405:
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395:
394:
387:
384:
382:
379:
378:
375:
370:
369:
364:By topic area
361:
360:
353:
350:
348:
345:
343:
340:
338:
335:
334:
331:
326:
325:
318:
315:
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265:
264:
261:
256:
255:
248:
245:
243:
240:
238:
235:
233:
232:Pronunciation
230:
228:
225:
223:
220:
218:
217:Abbreviations
215:
214:
211:
206:
205:
198:
195:
193:
190:
188:
185:
183:
180:
178:
175:
173:
170:
166:
163:
162:
161:
158:
156:
153:
151:
150:Accessibility
148:
147:
144:
139:
138:
124:
123:
120:
116:
104:
100:
97:
93:
90:
86:
85:
82:
77:
72:
68:
64:
60:
54:
52:
48:
42:
35:
34:
25:
19:
9252:
9216:WikiProjects
9126:Article size
9027:
8715:Lead section
8551:
8544:
8537:
8479:
8471:
8455:
8445:
8424:
8420:
8417:Halmos, P.R.
8410:
8385:
8374:
8359:
8346:
8329:
8320:
8308:
8297:
8286:
8275:hyphen-minus
8260:
8248:
8232:
8211:
8152:
8107:
8103:
8005:
7955:
7951:
7944:
7875:
7852:
7843:
7839:MOS:STYLERET
7825:
7607:affine space
7365:
7357:
7328:
7323:
7320:Donald Knuth
7310:
7303:
7299:MOS:STYLERET
7293:
7287:
7265:
6933:differential
6930:
6918:
6908:
6881:
6785:
6692:
6611:
6589:
6541:
6430:
6406:
6369:
6280:
6238:
6234:
6204:
6136:
6086:
6082:
6006:
5956:
5952:
5926:
5904:
5854:
5810:
5752:
5716:
5705:
5643:
5631:
5603:
5591:
5573:·
5562:
5557:
5553:
5515:dot operator
5508:
5462:
5460:
5451:
5447:
5443:
5439:
5437:
5388:
5355:
5347:
5333:
5288:WHITE CIRCLE
5031:prime symbol
5027:DOUBLE PRIME
4954:MOS:ROMANNUM
4940:
4933:
4929:
4924:
4920:
4911:, using the
4890:
4847:
4818:
4766:
4760:<sup: -->
4754:
4750:
4746:
4742:
4729:
4725:
4721:
4717:
4700:
4652:
4648:<sub: -->
4644:<sup: -->
4641:
4532:
4529:
4469:
4461:
4453:
4447:
4445:
4438:
4390:
4384:
4380:
4376:
4373:
4323:
4314:
4310:
4306:
4300:
4287:
4283:
4279:
4275:
4255:
4243:
4230:
4206:
4199:
4195:
4190:results in:
4189:
4132:
4121:
4070:
4057:
4053:
4046:
3938:
3916:
3913:
3863:
3846:
3844:
3810:
3798:
3535:
3369:
3266:
3248:
3245:
3188:
3097:
3066:
3048:
3046:
3036:
3032:
3029:
3014:
3010:anchor links
3005:
2999:
2986:MOS:FORMULAE
2966:
2954:
2925:
2874:
2863:
2860:
2846:may include
2841:
2823:
2819:
2808:
2804:
2801:
2794:
2790:
2784:
2780:
2770:
2766:
2753:
2749:
2747:or as a sum
2743:
2739:
2734:
2729:
2725:
2659:
2597:
2429:
2424:
2420:
2414:
2410:
2406:homomorphism
2399:
2395:
2391:
2386:
2381:
2377:
2372:
2366:
2362:
2357:
2352:
2348:
2333:
2329:
2325:
2321:
2317:
2313:
2294:
2289:
2277:
2270:
2265:
2253:
2243:
2234:
2231:
2227:
2221:
2215:
2210:
2204:cyclic group
2189:
2185:
2181:
2177:
2174:
2170:
2166:
2163:modular form
2159:
2148:
2124:
2077:
2045:
2027:
2023:
2019:
2005:
1946:
1942:
1934:
1920:
1906:
1902:
1897:
1893:
1891:
1875:
1871:
1867:
1865:
1845:
1838:
1834:
1830:
1822:
1818:
1814:
1806:
1802:
1798:
1792:
1790:
1783:MOS:MATH#ANY
1770:
1766:there exists
1765:
1761:
1757:
1753:
1749:
1747:
1730:
1728:
1708:
1688:
1681:
1677:
1673:
1669:
1665:
1661:
1657:
1650:
1643:
1639:
1635:
1631:
1627:
1623:
1619:
1612:
1606:
1602:
1598:
1594:
1590:
1586:
1582:
1575:
1570:
1568:
1548:
1538:
1534:
1530:
1526:
1522:
1521:Multiplying
1515:
1505:
1501:
1497:
1493:
1492:Multiplying
1485:
1451:
1444:
1440:
1436:
1427:
1420:
1413:
1409:
1405:
1396:
1395:is a group.
1392:
1385:
1382:
1340:
1332:
1324:
1320:
1313:
1304:
1303:rather than
1300:
1277:
1266:
1260:
1256:
1252:
1241:
1239:finite group
1235:group theory
1226:
1225:
1221:
1217:
1211:
1207:
1202:
1194:
1190:
1183:
1179:
1175:
1171:
1163:
1155:
1151:
1149:
1141:
1136:
1132:
1128:
1124:
1120:
1118:
1113:
1107:discriminant
1102:
1097:) means the
1094:
1092:
1089:Article body
1082:applications
1081:
1077:
1070:
1063:
1058:
1048:
1042:
1024:deformations
997:
991:
987:
983:
955:
941:
926:group theory
915:
898:
838:WikiProjects
768:Article size
698:
307:Lead section
62:
44:
9108:Terminology
9028:Mathematics
8976:Philippines
8838:Visual arts
8833:Video games
8597:Hidden text
8456:The TeXbook
8427:: 123–152,
8335:word joiner
8279:source code
8273:accept the
8215:Currently,
7853:Due to bug
7671:adele rings
5803:MOS:RADICAL
5693:open-closed
5659:closed-open
5649:open-closed
5622:−
5616:subst:minus
5569:source code
5471:×
5205:instead of
5164:instead of
5138:instead of
5112:instead of
5070:superscript
4969:Basic Latin
4866:code points
4636:Main page:
4443:directly.)
4217:or without
3572:renders as
2979:MOS:FORMULA
2852:source code
2797:), or as a
2762:dot product
2153:half-period
2089:compactness
2083:, who uses
2046:irreducible
1984:C* algebras
1980:B* algebras
1964:associative
1719:Clearly ...
1618:A function
1581:A function
1529:defined by
1475:We see that
1301:informative
1231:mathematics
994:mathematics
936:Main page:
905:mathematics
743:Terminology
699:Mathematics
602:Philippines
455:Visual arts
450:Video games
177:Hidden text
63:substantive
9270:Categories
9206:User pages
9171:Signatures
9166:Notability
9091:Cue sports
8828:Television
8823:Philosophy
8777:Trademarks
8626:Formatting
8441:0821800558
8225:homographs
8098:See also:
8076:The angle
7987:– markup:
7870:See also:
6272:Font usage
5767:ƒ
5624:" entity.
5600:Minus sign
5518:⋅
5497:, because
5463:explaining
5337:See also:
5276:interpunct
5074:C*-algebra
5029:where the
4735:²
4709:²
4480:MICRO SIGN
4260:, such as
4256:Names for
3941:sans serif
3910:Using HTML
3393:\textstyle
3259:Until bug
2994:See also:
2848:pseudocode
2836:See also:
2832:Algorithms
2658:, and not
2347:of groups
2264:of order 2
2002:noetherian
1998:local ring
1976:* algebras
1886:See also:
1870:is either
1833:satisfies
1817:satisfies
1801:satisfies
1680:) for all
1664:such that
1642:) for all
1605:) for all
1480:See also:
1447:is finite.
1184:continuous
1182:is called
1162:, and let
1078:Motivation
1028:stretching
1026:, such as
1021:continuous
1000:(from the
828:User pages
803:Signatures
798:Notability
729:Cue sports
445:Television
440:Philosophy
386:Trademarks
210:Formatting
9048:Chemicals
9038:Chemistry
8986:Singapore
8966:Macedonia
8941:Indonesia
8602:Infoboxes
8575:Biography
8546:Directory
8267:templates
7917:(such as
7866:Fractions
7306:WP:WEIGHT
7029:) before
6891:predicted
6882:incorrect
6590:incorrect
6407:incorrect
5706:produces
5669:open-open
5634:intervals
5495:remainder
5215:SET MINUS
4252:Functions
4089:. Within
4067:Variables
3318:produces
3278:produces
2971:Shortcuts
2936:Wikibooks
2928:WP:VERIFY
2844:algorithm
2594:transpose
2320:, as Hom(
2310:morphisms
2158:A weight
2074:Hausdorff
1991:zero ring
1813:if every
1482:MOS:NOTED
1455:Note that
1360:Shortcuts
1229:, in the
1105:) is the
912:Structure
672:Chemicals
662:Chemistry
612:Singapore
587:Macedonia
567:Indonesia
182:Infoboxes
155:Biography
103:MOS:MATHS
81:Shortcuts
71:talk page
67:consensus
47:guideline
9254:Category
9181:Subpages
9176:Overview
9156:Hatnotes
9151:Contents
9075:Taxonomy
9033:Medicine
9000:Religion
8971:Pakistan
8961:Malaysia
8899:Regional
8679:Captions
8653:Spelling
8539:Overview
8454:(1984),
8383:(1998),
8239:, is in
8158:See also
7342:Shortcut
6899:observed
6786:but not
6683:that one
6669:this one
6642:that one
6629:this one
6370:but not
6219:Shortcut
5937:Shortcut
5795:Shortcut
5745:MOS:FNOF
5737:Shortcut
5565:asterisk
5491:quotient
5487:dividing
5422:Shortcut
5378:<
5351:<
5186:negation
5090:baseline
5066:ASTERISK
4946:Shortcut
4923:divides
4882:brackets
4832:Shortcut
4737:) versus
4492:OHM SIGN
4411:π
4282:) = sin(
4239:SI units
3964:. Using
3866:alt text
3860:Alt text
2854:in some
2774:, as an
2306:Hom-sets
2304:, write
2251:called C
2081:Bourbaki
2063:Topology
1876:formulas
1872:formulae
1850:Shortcut
1829:if some
1811:, write
1775:Shortcut
1693:Shortcut
1553:Shortcut
1443:. Then
1426:A group
1250:subgroup
1199:preimage
1188:open set
1168:function
1032:twisting
998:topology
856:Contents
851:Overview
808:Subpages
793:Hatnotes
709:Taxonomy
704:Medicine
630:Religion
597:Pakistan
592:Malaysia
525:Regional
267:Captions
237:Spelling
96:MOS:MATH
9119:Related
9096:Snooker
9021:Science
8946:Ireland
8883:History
8803:Blazons
8607:Linking
8563:Content
8265:, many
8241:Haskell
7929:Unicode
7855:T263572
7844:Due to
7767:(e.g.,
7763:), and
7350:MOS:BBB
7324:TeXbook
5907:T263572
5711:(−π, π]
5513:is the
5110:SOLIDUS
4884:). The
4870:Unicode
4612:Unicode
4566:\mathbb
4448:capital
3948:uses a
3536:Adding
3379:display
3261:T263572
3203:display
3089:MathJax
3087:(using
3053:strings
2721:lattice
2445:(⋉) or
2404:is the
2184:), and
2139:lattice
2009:Zariski
1953:Algebra
1894:compact
1868:formula
1797:if any
1762:for all
1178:. Then
1109:of the
1053:tangent
733:Snooker
655:Science
572:Ireland
505:History
420:Blazons
187:Linking
143:Content
9225:Search
9084:Sports
9058:Safety
8981:Poland
8931:Hawaii
8911:Canada
8818:Novels
8798:Comics
8720:Tables
8710:Layout
8703:Layout
8694:Images
8672:Images
7940:5.2 cm
7282:, and
7255:\theta
7211:), and
6939:, and
6257:nowrap
6137:where
6007:where
5756:U+0192
5606:hyphen
5586:BULLET
5578:U+2022
5452:citing
5406:< 3
5360:, use
5358:< 3
5321:U+226F
5281:U+25CB
5265:U+2218
5220:U+005C
5208:U+2216
5176:. Use
5167:U+223C
5155:U+007E
5141:U+2236
5129:U+003A
5115:U+2215
5103:U+002F
5079:U+2217
5076:. Use
5059:U+002A
5048:pprime
5020:U+2033
5008:U+2032
4983:, not
4758:(with
4733:(with
4659:, use
4616:U+211D
4509:U+03A9
4497:U+03BC
4485:U+2126
4473:U+00B5
4286:) cos(
4246:= 5 cm
3555:\infty
3410:\infty
3385:inline
3346:, but
3272:\tfrac
3081:MathML
3017:boldly
2948:topic.
2880:primes
2816:Proofs
2455:Subset
2398:→ Aut(
2385:where
2155:style.
2121:Kelley
2078:contra
2056:scheme
2006:contra
1968:unital
1937:, and
1791:Avoid
1613:write
1473:, and
1336:fields
1244:, the
1197:, the
1036:gluing
722:Sports
682:Safety
607:Poland
557:Hawaii
537:Canada
435:Novels
415:Comics
312:Tables
302:Layout
295:Layout
282:Images
260:Images
89:WP:MSM
9007:Islam
8956:Korea
8951:Japan
8936:India
8926:Egypt
8859:Music
8852:Music
8772:Legal
8765:Legal
8741:Lists
8734:Lists
8689:Icons
8203:Notes
8026:: -->
8020:) or
8001:: -->
7907:slash
7157:\frac
7154:\cdot
7140:\frac
7125:\frac
6915:\text
6911:\mbox
6887:r = x
6678:\text
6664:\text
5919:radic
5820:radic
5698:−π, π
5541:: -->
5535:</
5532:\cdot
5529:: -->
5485:When
5477:times
5404:''x''
5375:''x''
5278:) or
5162:TILDE
5148:RATIO
5136:COLON
5038:prime
5015:PRIME
4874:ASCII
4786:: -->
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3661:\sqrt
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3351:\frac
3314:x / 2
3212:: -->
3209:block
3069:LaTeX
2916:sieve
2889:sieve
2886:sieve
2719:In a
2689:, or
2312:from
2308:, or
2208:order
2098:page.
1921:"The
1841:) = 0
1827:, or
1825:) = 0
1809:) = 0
1544:, ...
1511:, ...
1307:(see
1246:order
1170:from
1166:be a
1111:field
1012:λόγος
1006:τόπος
1002:Greek
918:field
637:Islam
582:Korea
577:Japan
562:India
547:Egypt
469:Music
381:Legal
374:Legal
337:Lists
330:Lists
277:Icons
45:This
16:<
9196:Tips
8808:Film
8786:Arts
8553:Tips
8485:ISBN
8460:ISBN
8438:ISBN
8399:ISBN
8269:and
8024:math
8022:<
8010:math
7999:math
7997:<
7991:math
7913:frac
7734:and
7358:The
7301:.
7015:\sin
7002:\int
6755:\sum
6693:and
6479:csch
6451:csch
6423:and
6319:\sin
6243:and
5830:sqrt
5811:The
5777:and
5775:JAWS
5722:math
5610:dash
5594:NIST
5548:sdot
5538:math
5526:math
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5430:WP:⋅
5398:math
5389:not
5369:math
5293:Use
5237:Use
5195:Use
5184:for
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5126:Use
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5005:Use
4979:and
4963:For
4876:and
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4417:<
4396:math
4333:math
4297:Sets
4264:and
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4212:mvar
4202:+ 2)
4198:= −(
4182:+ 2)
4164:<
4142:math
4133:and
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4094:math
4085:and
4076:mvar
4060:+ 2)
4056:= −(
4038:+ 2)
4020:<
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3969:math
3962:skin
3956:math
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3750:and
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3233:\sin
3220:\int
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2955:The
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2351:and
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2173:) =
2169:(−1/
2129:ISBN
2111:are
2018:use
2014:For
1966:and
1960:ring
1898:ring
1896:and
1764:and
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1672:) =
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1435:Let
1404:Let
1297:tone
1154:and
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972:math
861:Tips
425:Film
399:Arts
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8080:is
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8064:).
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7832:or
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7294:not
7012:\pi
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6895:- x
6760:i=1
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6602:sin
6600:\rm
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6296:sin
6266:.}}
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5217:or
5200:or
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4773:sup
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4680:sub
4656:3+5
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4266:cos
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3443:2
3441:^
3435:{
3428:}
3426:2
3424:^
3422:n
3418:1
3416:{
3382:=
3362:}
3360:2
3356:x
3354:{
3334:2
3330:/
3326:x
3298:x
3292:2
3289:1
3235:x
3227:^
3225:0
3223:_
3206:=
3175:.
3172:x
3169:d
3164:x
3148:0
3121:2
3116:R
3107:x
3037:b
3033:a
2913::
2910:p
2907:=
2904:)
2898::
2895:p
2892:(
2883:=
2811:.
2805:b
2802:a
2795:b
2793:,
2791:a
2787:⟩
2785:b
2783:,
2781:a
2779:⟨
2771:b
2767:a
2754:b
2750:a
2744:b
2740:a
2730:b
2726:a
2716:.
2698:X
2675:T
2671:X
2660:X
2643:T
2638:X
2614:T
2609:X
2598:X
2557:B
2554:=
2551:A
2531:B
2525:A
2430:φ
2425:K
2421:Q
2415:Q
2411:K
2402:)
2400:K
2396:Q
2392:φ
2387:K
2382:K
2378:φ
2375:×
2373:Q
2367:Q
2363:φ
2360:×
2358:K
2353:Q
2349:K
2334:B
2332:,
2330:A
2326:B
2324:,
2322:A
2318:B
2314:A
2295:n
2290:n
2278:n
2276:2
2271:n
2266:n
2254:n
2244:n
2235:Z
2232:n
2230:/
2228:Z
2222:p
2216:n
2211:n
2192:.
2190:e
2186:q
2182:τ
2180:(
2178:f
2175:τ
2171:τ
2167:f
2160:k
2149:ω
2123:(
2076:(
2051:.
2028:v
2026:(
2024:Q
2020:v
2004:(
1993:.
1839:x
1837:(
1835:F
1831:x
1823:x
1821:(
1819:F
1815:x
1807:x
1805:(
1803:F
1799:x
1684:.
1682:x
1678:x
1676:(
1674:f
1670:x
1666:f
1662:f
1646:.
1644:x
1640:x
1638:(
1636:f
1632:x
1628:f
1620:f
1607:x
1603:x
1601:(
1599:f
1595:x
1591:f
1583:f
1571::
1542:0
1539:v
1535:v
1531:u
1527:u
1523:M
1509:0
1506:v
1502:v
1498:u
1494:M
1445:H
1441:G
1437:H
1428:G
1414:H
1410:G
1406:H
1397:G
1393:G
1261:G
1257:G
1253:H
1242:G
1212:S
1208:O
1206:(
1203:f
1195:T
1191:O
1180:f
1176:T
1172:S
1164:f
1156:T
1152:S
1137:x
1133:n
1129:x
1125:n
1123:^
1121:x
1114:K
1103:K
1095:K
1038:.
888:e
881:t
874:v
745:)
741:(
735:)
731:(
73:.
53:.
26:)
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