Knowledge:Manual of Style/Mathematics

9229: 8053: 2737:. 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. 38: 985:

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.

2838:. 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. 1486:

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

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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

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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

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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

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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

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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,

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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

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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

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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,

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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

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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

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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,

5551:. 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 3885:

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

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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

1925:. 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 7817:) 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 1888:

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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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:

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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

3039:, 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

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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.

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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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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.

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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

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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.

7099: 3848:, 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 2817: 6112: 5982: 7801: 5072:

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

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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

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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 "

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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

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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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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

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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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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

6858: 6976: 3165: 6729: 2910:, 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: 7883: 6500: 6447: 5880: 8199:

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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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(

3773: 7555: 7524: 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". 7741: 7712: 7679: 7647: 7615: 7583: 3288: 2607: 2636: 3883: 7493: 7469: 7445: 7421: 7397: 7373: 7224: 6566: 4588: 8900: 8895: 8128: 6179: 6137: 6056: 6010: 551: 541: 2841:

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

2475: 6344: 2521: 2455: 2694: 2567: 2495: 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. 8042: 6292: 5296: 5240: 7184: 6383: 5815:) 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: 4794: 2667: 7965: 3324: 3003:

before implementation. If there is no positive response, or if planned changes affect more than one article, consider notifying an appropriate Wikiproject, such as

2547: 1858:. Both are acceptable, but an article should be internally consistent. In an already consistent article, editors should refrain from changing one style to another. 8106: 6157: 6032: 2984:

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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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

601: 4602:) and its adjacent characters should be avoided at present, since these characters are not yet universally supported and may have an inconsistent appearance. 3964:

also helps some spell checkers and screen readers treat math markup properly. Note that certain special characters (equal signs, absolute value bars) require

9115: 9042: 8970: 8853: 8281: 8079: 1315: 777: 686: 616: 487: 9087: 9022: 8965: 8920: 6189:, 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. 5592:"–". 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 742: 666: 611: 566: 9012: 8950: 8940: 8130:

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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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.

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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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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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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 (

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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,

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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

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The font size can be slightly larger than that of the surrounding text on some browsers, making text containing inline formulae harder to read.

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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.

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templates (which will set a serif font but not italics), use the wikitext markup of double apostrophes to make variables italic. For example:

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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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lists of facts and formulae, and relying too much on addressing the reader directly and referring to "we". Also avoid contentless clichés as

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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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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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Some notions are defined differently depending on context or author. Articles should contain some references that support the given usage.

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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

9140: 9049: 9037: 8869: 5052:, and is typical when used as a postfix. This character also appears on keyboards, and is thus easier to type and search for. Example: 3898: 693: 681: 511: 373: 329: 70: 8292: 8772: 8704: 8642: 8637: 8617: 8571: 8497: 1106: 1098: 409: 398: 316: 246: 241: 221: 171: 5555:(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 2901: 1268: 9082: 8945: 8725: 8596: 8175: 6192: 6073: 5943: 2999:

from LaTeX to HTML, nor from non-LaTeX to LaTeX without a clear improvement. Proposed changes should generally be discussed on the

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Large-scale formatting changes to an article or group of articles are likely to be controversial. One should not change formatting

2805: 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 738: 586: 341: 196: 4883:

are very likely to be displayed correctly, a significant number of viewers will have problems seeing all the characters listed at

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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. 482: 477: 271: 231: 216: 149: 3118: 8694: 7750: 7272:. Changes from one style to another should be done only to make an article consistent with itself. Formatting changes should 937: 306: 5445:

the formula for a general audience (not just mathematicians), or giving examples of its application, it is prudent to use the

8817: 8812: 8576: 454: 449: 176: 6599: 9155: 9070: 8807: 8802: 8756: 8518: 1748:. In addition to compromising the encyclopedic tone, these abbreviations are a form of jargon that may confuse the reader. 850: 728: 444: 439: 385: 46: 7298:. But this guide is rarely followed in reliable mathematical sources, and it is contradicted by other style guides, like 9195: 9190: 9017: 8581: 8554: 4683: 3556: 837: 832: 661: 181: 154: 7922:); non-metric units can be either type of fraction, but the fraction style should be consistent throughout the article. 3965: 3020:, the community of mathematical editors of English Knowledge currently has no consensus about preferred formatting; see 2845: 1487:

not an equation involving a previously known object. Also identify the nature of the entity being defined. Don't write:

9233: 9130: 8658: 8632: 8525: 7828:, LaTeX blackboard bold currently does not work with numerals. Use bold instead (e.g. {{math|'''1'''}} or <math: --> 4534:

tag for making text bold. Bold notation has been largely replaced by blackboard bold, which may be encoded in LaTeX as

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If an inline formula needs to be typeset in LaTeX, keep the height down by using text-style or horizontal fractions:

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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( 9255: 8797: 8782: 8777: 8699: 8689: 8673: 8142: 3042: 434: 419: 414: 311: 301: 281: 8257:"-" as a valid representation of the minus sign. Except situations where "-" has to represent the minus sign in a 2942: 8838: 8751: 8720: 8668: 6772: 2918:

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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as an operator symbol is also discouraged except in abstract contexts (e.g. to denote an unspecified operator).

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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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at the beginning. Such formatting can be removed if a formula is edited and need not be added to new formulae.

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template to enclose a simple mention of a variable by name. This helps distinguish certain characters such as

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Today, either blackboard bold or ordinary bold letters can be used interchangeably to represent the standard

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Use italic text for variables, but never for numbers or symbols. To ensure an italic serif typeface, use the

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

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contains some details on how to create graphs and other pictures as well as how to include them in articles.

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mathematical printing to denote certain common objects in a style distinct from other uses of bold letters.

6470: 6423: 5846: 1950:. A structure satisfying all the ring axioms except the existence of a multiplicative identity is called a 1267:

Other times, it may be better to separate the statement into its own section, as for long theorems like the

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

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

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Articles should start with a short introductory section, called the "lead". The purpose of the lead is to

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for a point. This allows easy use in LaTeX markup. However, older books tend to use upright letters as in

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The context should clearly state that this is a semidirect product and should state which group is normal.

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In mathematics articles, fractions should always be written either with a horizontal fraction bar (as in

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comma, semicolon, or other punctuation at that place, the formula must have that punctuation at the end.

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article has more information on this and also several examples for how the cited literature should look.

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A picture can really bring home a point, and can often precede the mathematical discussion of a concept.

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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

4952: 6186: 3820: 3734: 3036: 58: 7528: 7497: 4505: 2014: 9260: 8506: 8148: 7717: 7688: 7655: 7623: 7591: 7559: 6920: 3261: 3072: 3056: 3032: 2975: 2583: 1291:. Occasionally, it is appropriate to give a large number of computationally-flavored examples, as in 1035: 900: 118: 50: 17: 2612: 1292: 9125: 9120: 9110: 8483: 8217: 8158: 6251: 5758: 4802:. Formulae formatted without using TeX should use the same syntax to maintain the same appearance. 3889: 3864: 3783:, is adequate for articles that use only simple inline formulae and better for text-only browsers. 3520:

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

6162: 6120: 6039: 5993: 5795:√ can be used when written on its own, but when part of a larger expression, can be problematic. 5068:(&lowast;) for subscripts and when the bottom of the character should roughly align with the 4876: 4691:) for squares. This does not combine well with other powers, as the following comparison shows: 4420: 3243:

is fixed, it will not work in image captions when readers click through to see full-size images.

2460: 1896: 9105: 6404: 6308: 6294:(parentheses may be omitted here, as the argument consists of a single term only; typeset from 5658: 5613: 5466: 2936: 2500: 2440: 1167: 767: 6407:; if there is any risk that a term could become ambiguous for our readership, use parentheses. 5753:. As of December 2010, this character is not interpreted correctly by screen readers such as 2672: 5409: 2552: 2480: 2096: 1308: 8012: 6268: 5924: 2082: 1560: 931: 9185: 9150: 9145: 9054: 7911: 6906: 5754: 5638: 5628: 5395: 5281: 5225: 4887:. One way to guarantee that an uncommon symbol is rendered correctly for all readers is to 3000: 2835: 2187: 2035: 1245: 827: 802: 797: 708: 7157: 6356: 4772: 2645: 1861: 8: 9175: 8532: 8364: 8164: 7886: 7834: 6400: 6256: 5886: 5446: 4857: 4819: 3932:

font to display a formula (whether as SVG or HTML). HTML math expressions should use the

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Note: For potential pitfalls of forms not understood consistently across the board, see

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and reachable in the "Math and logic" drop-down list below the edit box or via template

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is appropriate; do not use the ASCII apostrophe (') or double quote (") in these cases.

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does not line up with that of the running text—the punctuation can be placed after the

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

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to sections. Some of the issues presented by using LaTeX or HTML are discussed below.

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Knowledge:WikiProject Computer science/Manual of style (computer science) § Algorithms

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Include a physical or geometric analogy or diagram if it can help introduce the topic.

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formulae displayed when hovering, they must be written in raw html (without templates

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Commonly used sets of numbers are typeset in boldface, as in the set of real numbers

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tag and then the whole formula (including the punctuation) can be enclosed with the

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

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discouraged in English Knowledge; instead, either the LaTeX rendering (for example

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

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This method should be avoided whenever technically possible to do so. Instead, use

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Not all of the symbols in these lists are displayed correctly on all browsers (see

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the preferred formatting is the LaTeX markup, with a possible exception for simple

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when writing the less-than sign, just like in HTML and XML. For example, to write

4860:(with notable exception of "+", "=", "|", as well as ",", ":", and three sorts of 2042: 979:). In the latter case the LaTeX source is displayed without the tags <math: --> 95: 57:

It is a generally accepted standard that editors should attempt to follow, though

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The download speed of a page is negatively affected if it contains many formulas.

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The lead sentence should informally define or describe the subject. For example:

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Moreover, the TeX engine used on Knowledge may format simple superscripts using

1932: 9214: 8331: 7803:). Font preferences vary from one mathematical author or publisher to another. 6916: 6063:

should be written as prose, to avoid using more vertical space than necessary:

5898: 5799: 5792: 5595: 5456: 5074: 5017: 5010: 4944: 4437: 3811: 2778: 2317: 2241: 2228: 2218: 2200: 2100: 2092: 1947: 1296: 1027: 1001: 872: 130: 8271: 7306:. This makes the more common practice to use an italic face for the constant 5584:

The correct encoding of the minus sign "−" is different from all varieties of

3507:{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {\pi ^{2}}{6}}.} 9249: 8246: 7989: 7970: 7892: 7347: 5809: 5701: 5527: 4971:. (The only exception is when discussing the Unicode characters themselves.) 4201: 4191: 4073: 4055: 3958: 3948: 3935: 3905: 3845: 3839: 2755: 2068: 2064: 2049: 2028: 1951: 971: 8374: 8318: 6525:

includes correct spacing that would not be present with other means such as

4252:

for functions in other cases; for example when we define the function as in

4231: 4046: 2418:

The bar notation is discouraged because it is not supported by all browsers.

1088: 8431: 8254: 7818: 7682: 7586: 7299: 7278: 5494: 3047:

Knowledge allows editors to typeset mathematical formulae in (a subset of)

2385: 2183: 2142: 2121:

need not be bounded. In a bounded lattice, 0 and 1 are allowed to be equal.

2088: 1238: 1234: 961: 925: 7918:

reasons among others. Metric units are given in decimal fractions (e.g.,

7288:. For example, the ISO 80000-2 recommends that the mathematical constant 2408:(with the bar on the side of the non-normal subgroup) with or without the 8396: 8314: 8258: 8250: 8088:

Recent geometry books tend to use an italic serif font in diagrams as in

5750: 5579: 5548: 5169: 5049: 2831: 2741: 1943: 1230: 993: 904: 8412: 8350: 8261:(including wiki code), it should not be seen in a rendered page, though. 8178:—advice on providing references for mathematical and scientific articles 7246:

Some authors prefer to use an upright (Roman) font for operators, as in

7094:{\displaystyle {\frac {dz}{dx}}={\frac {dz}{dy}}\cdot {\frac {dy}{dx}},} 5319:

Knowledge:Manual of Style/Abbreviations § Unicode abbreviation ligatures

1880:, as well as notation, such as the correct symbols to use for a subset. 9215: 7650: 6912: 5255: 4845: 3920: 3901:. Not all templates are recommended for use; in particular, use of the 2914:

Knowledge articles cannot be a substitute for a textbook (that is what

2852:

primes = sieve sieve (p : xs) = p : sieve </syntaxhighlight: -->

2827: 1977: 1963: 1959: 1709:

The reader might not find what you write obvious. Instead, try to hint

132: 8334:(¼, ½, and ¾) work with screen readers, but others, like ⅐, might not. 6185:

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.

8452:

General style manuals often include advice on mathematics, including

8369:(second ed.), SIAM (Society for Industrial and Applied Mathematics), 8204: 5474: 3911:

template to format fractions is discouraged in mathematics articles.

2915: 2823: 2573: 1970: 1955: 1481: 5572:

Metric units often embed the notion of multiplication and division.

5544: 5470: 5418:

Standard algebraic notation is best for formulae, so two variables

5165: 2289: 1740:(if and only if), as well as quantifier symbols ∀ and ∃ instead of 1249: 1198: 1187: 128: 8475: 6911:

For single-letter variables, constants, and operators such as the

5209:

for set substraction. (Either Unicode character can be used where

4276: 8456: 7908: 5576:

endorses the half-high dot (⋅) or a bare space for this purpose.

4861: 4849: 4591: 4218: 3068: 2388:

defining the product. The semidirect product may also be written

2285: 2074:

Separation axioms for topological spaces are as described on the

2038:

is not assumed to be separated. The term "prescheme" is not used.

1988: 1052: 3229:

Having LaTeX-based formulae inline has the following drawbacks:

3071:), depending on user preferences. For more details on this, see 8052: 6219:

If the formula is written in LaTeX, that is, surrounded by the

5904:

method or √ with no overline should be used in image captions.

5585: 3060: 2434: 1775:

when verbalizing quantifiers since it is ambiguous. Instead of

9216: 6107:{\displaystyle \mathbf {F} =\mathbf {b} \times a\mathbf {r} ,} 5977:{\displaystyle \mathbf {F} =\mathbf {b} \times a\mathbf {r} ,} 2811: 2316:) (and with the implied convention that the category is not a 1728:

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: 8233:

Unicode Technical Report #25: Unicode Support for Mathematics

7825: 5564: 5254:(which on some systems is too small and can be confused with 4868:

includes markup for LaTeX and HTML, and Unicode code points.

4853: 4281:

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

3929: 3048: 6923:, Knowledge articles usually use an italic font. One writes 5033:

can be useful to prevent overlap with italicized characters.

3807:. Take care of some necessary substitutions documented for 1723:

By a straightforward, if lengthy, algebraic calculation, ...

911: 6900:

An opinion: Why you should never use \mbox within Knowledge

6346:(parentheses are required to clarify the intended argument) 5589: 5573: 5310:, which on some systems renders as two separate characters. 3174:). Instead, formulas may be placed on their own line using 3064: 3055:); the formulae are, for a default reader, translated into 8137: 7796:{\displaystyle \mathbb {H} ^{i}(X,\Omega _{X}^{\bullet })} 4516:. Again, typically we use wiki markup: three apostrophes ( 4248:, are not in italic font, but we use italic names such as 8282:

Knowledge talk:WikiProject Mathematics/Archive 68#ƒ or f?

4951:(ASCII) letters should be used instead of the equivalent 3052: 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 7585:) and for certain other mathematical objects, including 5532:), which produces a symmetrically spaced centered dot: " 5461:. Do not use the letter "x" to indicate multiplication. 1954:. There is an exception for rings of operators, such as 1347: 7852:

Knowledge:Manual of Style/Dates and numbers § Fractions

6629:{\displaystyle x_{\text{this one}}=y_{\text{that one}}} 4917:" in an elementary article may make it more accessible. 4618:

Knowledge:Manual of Style (superscripts and subscripts)

4426:

For consistency with the LaTeX style, do not italicize

3078:

The LaTeX formulae can be displayed inline (like this:

7907:) is discouraged in mathematics articles. The use of 7863: 4796:

will be an image, and for others it will be HTML like

3797:(optionally excluding the adjacent punctuation), e.g. 3737: 3559: 3266: 2795: 8114: 8094: 8080:

Knowledge:How to create charts for Knowledge articles

8015: 7945: 7862: 7753: 7720: 7691: 7658: 7626: 7594: 7562: 7531: 7500: 7476: 7452: 7428: 7404: 7380: 7356: 7199: 7160: 7021: 6932: 6775: 6682: 6602: 6538: 6473: 6426: 6359: 6311: 6271: 6165: 6145: 6123: 6076: 6042: 6020: 5996: 5946: 5849: 5284: 5228: 4775: 4571: 3867: 3692: 3442: 3304: 3264: 3172:

Knowledge:Manual of Style/Accessibility § Indentation

3121: 3084: 2675: 2648: 2615: 2586: 2555: 2529: 2503: 2483: 2463: 2443: 1344:

Knowledge:Manual of Style/Layout § "See also" section

8355:

A style guide specifically written for mathematics:

8182: 5707:

template to avoid line breaks and use the TeX font.

4769:

depending on user preferences. Thus, for some users

4450:

According to the Unicode Consortium, the characters

3897:Templates supporting HTML formatting are listed in 3623:{\textstyle \sum _{n=1}^{\infty }1/n^{2}=\pi ^{2}/6} 3195:. For instance, the formula above was typeset using 2421:

If the bar notation is used it should be entered as

2199:, or in contexts where there may be confusion with 1689:

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

1283:, while others may deserve their own section, as in 1059:The lead section should include, when appropriate: 8426:Some finer points of typography are discussed in: 8122: 8100: 8036: 7959: 7877: 7795: 7735: 7706: 7673: 7641: 7609: 7577: 7549: 7518: 7487: 7463: 7439: 7415: 7391: 7367: 7218: 7178: 7093: 6970: 6852: 6723: 6628: 6560: 6494: 6441: 6377: 6338: 6286: 6173: 6151: 6131: 6106: 6050: 6026: 6004: 5976: 5874: 5290: 5234: 4888: 4788: 4582: 3877: 3767: 3722: 3622: 3506: 3318: 3282: 3159: 3107: 2688: 2661: 2630: 2601: 2569:symbol should be explicitly explained in the text. 2561: 2541: 2515: 2489: 2469: 2449: 1868:Knowledge:WikiProject Logic/Standards for notation 952:and summarize the article's most important points. 8366:Handbook of Writing for the Mathematical Sciences 4840:may be useful when editing mathematics articles. 4622:Superscripts and subscripts should be wrapped in 3803:, or by replacing the tags with a template, e.g. 1718:It follows directly from this definition that ... 1015:, 'study') is concerned with the properties of a 9247: 5840:tags and \sqrt{}, even if inline. For example: 3108:{\displaystyle \mathbf {x} \in \mathbb {R} ^{2}} 8457:University of Chicago Press Staff, ed. (2010), 7250:, for the differential operator, as opposed to 6897:, but this is now considered undesirable. See 4975:For when to use or not use Roman numerals, see 2744:of vectors should be denoted with a centre-dot 2576:, use superscript non-italic capital letter T: 2227:is used (this does not affect the notation of 8491: 7842:markup should not be used in image captions. 5214:markup cannot be used for technical reasons.) 4885:Mathematical operators and symbols in Unicode 3434:is too large to be used inline, rendering as 3350:Often better formatting can be achieved with 2902:Including citations and literature references 880: 8343:Not all fractions are available precomposed. 7294:should be typeset in an upright Roman font: 6853:{\displaystyle r=x_{predicted}-x_{observed}} 1034:, crumpling and bending, but not tearing or 9116:Categories, lists, and navigation templates 6971:{\displaystyle \int _{0}^{\pi }\sin x\,dx,} 5430:when presented in a formula. That is, when 4977:Knowledge:Manual of Style/Dates and numbers 4879:). Although the symbols that correspond to 3160:{\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 8498: 8484: 8438:, Reading, Massachusetts: Addison-Wesley, 7266:; other authors use Roman boldface, as in 6889:For several years this manual recommended 6724:{\displaystyle \sum _{i=1}^{n}{y_{i}^{2}}} 3919:By default, regular text is rendered in a 3899:Category:Mathematical formatting templates 1430:may be decomposed into cosets, as follows. 1399:can be decomposed into cosets, as follows. 887: 873: 8463:(16th ed.), University of Chicago Press, 8317:before the punctuation instead, but it's 7914:(such as ½) is discouraged entirely, for 7878:{\displaystyle \textstyle {\frac {1}{2}}} 7756: 7723: 7694: 7661: 7629: 7597: 7565: 7534: 7503: 7478: 7454: 7430: 7406: 7382: 7358: 4573: 3095: 2217:; when written multiplicatively, e.g. as 2193:, when written additively, has notation Z 1823:, depending on what you wish to express. 8176:Knowledge:Scientific citation guidelines 8051: 5547:(*) as a multiplication sign outside of 5048:when the character should render like a 4842:Almost all mathematical operator symbols 4498:). This is also required for "micro" by 3844:Images generated from LaTeX markup have 2806:Knowledge:WikiProject Mathematics/Proofs 1969:The ring with one element is called the 6957: 6495:{\displaystyle a\operatorname {tr} (A)} 6442:{\displaystyle 2\operatorname {csch} x} 5875:{\displaystyle {\sqrt {9}},{\sqrt{27}}} 5621:to have the ] treated as literal text. 5168:) in mathematical expressions, because 4889:force the symbol to display as an image 4866:list of mathematical symbols by subject 4834:list of mathematical symbols by subject 3146: 2851:<syntaxhighlight lang="Haskell": --> 2240:The standard notation for the abstract 1299:of an encyclopedia, examples should be 14: 9248: 8395: 8359: 6244:This shows that {{nowrap|<math: --> 4967:, and not precomposed characters like 4953:Unicode characters in the U+21XX range 3832:) added at the end of the formula, or 3632:which fits much better inline. Adding 2980:One may set formulae using LaTeX (the 2622: 1966:, 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 8479: 8430: 5426:being multiplied are best written as 5270:(which on some systems is too large). 5170:tilde has other mathematical meanings 3858:<math alt="Square root of pi": --> 3723:{\displaystyle {\sqrt {x^{2}+y^{2}}}} 3059: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 8399:(1970), "How to Write Mathematics", 8313:It is technically possible to use a 5183:... \smallsetminus ...</math: --> 4606: 2943:Typesetting of mathematical formulae 977:), or in LaTeX (inside <math: --> 32: 9266:Knowledge Manual of Style (science) 8505: 6067:Example 2: The foocity is given by 5937:Example 1: The foocity is given by 5733:There is a special Unicode symbol, 4681:Do not use special characters like 30: 8116: 7776: 7681:, the additive and multiplicative 6550: 6547: 6544: 5911:Explanation of symbols in formulae 3768:{\textstyle {\sqrt {x^{2}+y^{2}}}} 3576: 3459: 2681: 2593: 2145:follows the Serre convention that 1736:(without loss of generality), and 1055:to three given circles in a plane. 31: 9277: 8244:Note that, aside of <math: --> 8171:Knowledge:WikiProject Mathematics 7550:{\displaystyle \mathbb {Z} _{p},} 7519:{\displaystyle \mathbb {F} _{q},} 4109:is a value on the horizontal axis 4097:is a value on the horizontal axis 3115:), 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 9228: 9227: 8143:Help for those writing a formula 7736:{\displaystyle \mathbb {G} _{m}} 7707:{\displaystyle \mathbb {G} _{a}} 7674:{\displaystyle \mathbb {A} _{K}} 7642:{\displaystyle \mathbb {P} ^{n}} 7610:{\displaystyle \mathbb {A} ^{n}} 7578:{\displaystyle \mathbb {Q} _{p}} 6245:\tfrac{1}{2} = 0.5</math: --> 6167: 6159:is the bazness coefficient, and 6125: 6097: 6086: 6078: 6044: 5998: 5967: 5956: 5948: 3283:{\displaystyle {\tfrac {1}{2}}x} 3086: 2602:{\displaystyle X^{\mathrm {T} }} 946:describe and define the subject, 36: 8337: 8324: 5178:... \setminus ...</math: --> 4031:The relationship is defined as 3972:The relationship is defined as 3780: 3779:HTML-generating formatting, as 2631:{\displaystyle X^{\mathsf {T}}} 1421:Instead, write something like: 8307: 8298: 8286: 8275: 8264: 8238: 8226: 8210: 8189: 8154:Knowledge:Mathematical symbols 7790: 7766: 6489: 6483: 6333: 6321: 5743:LATIN SMALL LETTER F WITH HOOK 4838:Knowledge:Mathematical symbols 4419:(It is also possible to enter 3878:{\displaystyle {\sqrt {\pi }}} 2844:Source code should always use 1713:something must hold, such as: 1269:Poincaré–Birkhoff–Witt theorem 1248:(number of elements) of every 1099:discriminant of a number field 13: 1: 9033:References and external links 7488:{\displaystyle \mathbb {H} ,} 7464:{\displaystyle \mathbb {C} ,} 7440:{\displaystyle \mathbb {R} ,} 7416:{\displaystyle \mathbb {Q} ,} 7392:{\displaystyle \mathbb {Z} ,} 7368:{\displaystyle \mathbb {N} ,} 7219:{\displaystyle e^{i\theta }.} 6561:{\displaystyle 2{\rm {sin}}x} 5160:to mean "approximately" (and 4583:{\displaystyle \mathbb {R} .} 3371:tag, which translates to the 3010:For inline formulae, such as 677:References and external links 8319:seldom respected by browsers 8235:, §2.5 Duplicated Characters 8123:{\displaystyle \mathrm {A} } 6893:as a workaround for lack of 6174:{\displaystyle \mathbf {r} } 6132:{\displaystyle \mathbf {b} } 6051:{\displaystyle \mathbf {r} } 6005:{\displaystyle \mathbf {b} } 5276:... \ngtr ...</math: --> 4830:list of mathematical symbols 3663:<math display=inline: --> 3522:<math display=inline: --> 2429:(⋊) for maximum portability. 1354:Writing style in mathematics 7: 8886:Specific naming conventions 8460:The Chicago Manual of Style 8401:Enseignements Mathématiques 6034:is the bazness coefficient, 5220:... \circ ...</math: --> 4612:Superscripts and subscripts 4598:(plain text ℝ or math font 3347:is too tall to fit inline. 3197:<math display=block: --> 3007:for mathematical articles. 2848:. For example this markup: 2787:, never with juxtaposition 2470:{\displaystyle \subsetneq } 2369:is the normal subgroup and 1909:" has two common meanings: 532:Specific naming conventions 10: 9282: 8565:Organizing by subject area 8077: 7849: 7319: 6339:{\displaystyle 2\sin(x+1)} 6196: 6193:Punctuation after formulae 5914: 5772: 5714: 5588:"-‐‑", as well as from en- 5399: 5316: 4974: 4923: 4809: 4615: 4604: 4496:GREEK CAPITAL LETTER OMEGA 4368:would then be typeset by: 3035:of Latin letters, digits, 2973: 2948: 2906:Per the Knowledge policy, 2815: 2516:{\displaystyle A\subset B} 2450:{\displaystyle \subseteq } 1865: 1827: 1752: 1694:It is easily seen that ... 1550: 1479: 1467:It must be emphasized that 1357: 1285:Chain rule § First example 935: 78: 9223: 9204: 9191:Wikimedia sister projects 9098: 9063: 9000: 8979: 8878: 8862: 8831: 8765: 8744: 8713: 8682: 8651: 8605: 8542: 8513: 8201:WP:DICT#Major differences 8149:Help:Displaying a formula 7227: 7187: 7102: 7010: 7004: 6979: 6865: 6732: 6637: 6573: 6503: 6450: 6412: 6390: 6295: 5885:Because of Mediawiki bug 5749:), sometimes used as the 5668: 5501: 5373: 5344: 4748: 4643: 4535: 4523: 4517: 4382:''λ'' + ''y'' 4371: 4308: 4117: 4083: 3973: 3664: 3639: 3633: 3523: 3378: 3351: 3329: 3293: 3250: 3198: 3175: 3073:Help:Displaying a formula 2976:Help:Displaying a formula 2855:generates the following: 2689:{\displaystyle X^{\top }} 2549:). All other uses of the 1921:which may also be called 1913: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 8216:This example, from here 8159:Knowledge:Rendering math 7810:\mathbb{Z}</math: --> 6181:is the quuxance vector. 5765:should be used instead. 5761:. An italicized letter 5759:NonVisual Desktop Access 5697:These templates use the 5453:in HTML or accessed via 3923:font. The TeX markup of 3859:\sqrt{\pi}</math: --> 3037:common punctuation marks 3001:talk page of the article 2857: 2703:, infima are written as 2562:{\displaystyle \subset } 2490:{\displaystyle \subset } 2427:{{unicode|⋊}} 2423:{{unicode|⋉}} 1929:if the context permits. 1862:Mathematical conventions 1045:Euclidean plane geometry 9256:WikiProject Mathematics 8375:10.1137/1.9780898719550 8037:{\displaystyle x^{1/2}} 7277:the same principles as 6287:{\displaystyle 2\sin x} 6139:is the barness vector, 6058:is the quuxance vector. 4877:Help:Special characters 4522:) rather than the HTML 3005:WikiProject Mathematics 2277:odd and greater than 1. 2095:with finite joins, not 1892:Terminology conventions 1459:It should be noted that 8124: 8102: 8075: 8038: 7961: 7879: 7829:\bold{1}</math: --> 7797: 7737: 7708: 7675: 7643: 7611: 7579: 7551: 7520: 7489: 7465: 7441: 7417: 7393: 7369: 7220: 7180: 7095: 7003:—note the thin space ( 6972: 6854: 6731:(correct—typeset from 6725: 6703: 6636:(correct—typeset from 6630: 6562: 6496: 6443: 6405:implied multiplication 6379: 6340: 6288: 6183: 6175: 6153: 6133: 6108: 6061: 6052: 6028: 6012:is the barness vector, 6006: 5978: 5876: 5751:Florin currency symbol 5292: 5291:{\displaystyle \ngtr } 5236: 5235:{\displaystyle \circ } 4790: 4584: 4506:Common sets of numbers 4221:are never italicized: 4217:is the mass of a foo. 3879: 3856:element. For example, 3769: 3724: 3624: 3580: 3508: 3463: 3320: 3284: 3161: 3109: 2937:Knowledge:Cite sources 2690: 2663: 2632: 2603: 2563: 2543: 2517: 2491: 2471: 2451: 2177:Notational conventions 1265: 1237:, states that for any 1216: 1057: 1040: 8823:Writing about fiction 8391:More style guidance: 8125: 8103: 8055: 8039: 8007:x^{1/2}</math: --> 7962: 7929:in abstract algebra: 7925:Only "/" is used for 7912:precomposed fractions 7885:), or with a forward 7880: 7798: 7738: 7709: 7676: 7644: 7612: 7580: 7552: 7521: 7490: 7466: 7442: 7418: 7394: 7370: 7221: 7181: 7179:{\displaystyle x+iy,} 7096: 6973: 6855: 6726: 6683: 6631: 6563: 6497: 6444: 6380: 6378:{\displaystyle 2sinx} 6341: 6289: 6176: 6154: 6134: 6109: 6065: 6053: 6029: 6007: 5979: 5935: 5877: 5543:Do not use the ASCII 5434:a formula, don't use 5293: 5237: 5077:for a canonical list. 4791: 4789:{\displaystyle x^{2}} 4605:Further information: 4590:However, the special 4585: 4484:GREEK SMALL LETTER MU 4430:Greek letters; e.g. 3880: 3821:Deprecated formatting 3799:({{nobr|<math: --> 3770: 3725: 3625: 3560: 3509: 3443: 3321: 3285: 3162: 3110: 2691: 2664: 2662:{\displaystyle X^{T}} 2633: 2604: 2564: 2544: 2518: 2492: 2472: 2452: 2320:unless that is said). 2052:is not assumed to be 1915: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 9166:Talk page guidelines 8854:Stringed instruments 8560:Disambiguation pages 8112: 8092: 8013: 7943: 7860: 7751: 7718: 7689: 7656: 7624: 7592: 7560: 7529: 7498: 7474: 7450: 7426: 7402: 7378: 7354: 7197: 7158: 7019: 6930: 6773: 6680: 6600: 6536: 6471: 6424: 6392:2sin x</math: --> 6357: 6309: 6269: 6163: 6143: 6121: 6074: 6040: 6018: 5994: 5944: 5847: 5282: 5226: 5075:Asterisk#Mathematics 4844:have their specific 4773: 4594:characters, such as 4569: 3865: 3735: 3690: 3557: 3440: 3302: 3262: 3119: 3082: 2836:programming language 2822:An article about an 2673: 2646: 2613: 2584: 2553: 2527: 2501: 2481: 2461: 2441: 2024: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 8971:Trinidad and Tobago 8901:France (and French) 8896:China (and Chinese) 8413:10.5169/seals-43857 8361:Higham, Nicholas J. 8165:General information 8048:Graphs and diagrams 7982:R / A</math: --> 7960:{\displaystyle R/A} 7789: 7189:x+iy,</math: --> 6947: 6907:Roman versus italic 6719: 6401:order of operations 5447:multiplication sign 5396:Multiplication sign 4858:General Punctuation 4565:, which renders as 3861:generates an image 3319:{\displaystyle x/2} 3136: 2846:syntax highlighting 2542:{\displaystyle A=B} 2457:, proper subset by 2273:, and are zero for 1732:(with respect to), 1144:mathematical object 1142:An article about a 617:Trinidad and Tobago 552:France (and French) 542:China (and Chinese) 9171:Template namespace 8270:Latin Extended-B, 8197:ring (mathematics) 8120: 8098: 8076: 8034: 7957: 7875: 7874: 7793: 7775: 7733: 7704: 7671: 7639: 7607: 7575: 7547: 7516: 7485: 7461: 7437: 7413: 7389: 7365: 7216: 7176: 7091: 7001:dx ,</math: --> 6968: 6958: 6933: 6850: 6721: 6705: 6626: 6558: 6492: 6439: 6375: 6336: 6284: 6257:Multi-letter names 6171: 6149: 6129: 6104: 6048: 6024: 6002: 5974: 5925:MOS:EXPLAINSYMBOLS 5872: 5489:An alternative to 5484:−42 = 9 × (−5) + 3 5469:26 by 4, 6 is the 5288: 5232: 4896:with LaTeX markup. 4786: 4580: 4304:would be written: 4238:standard functions 3875: 3852:attribute for the 3765: 3720: 3620: 3504: 3316: 3280: 3275: 3157: 3147: 3122: 3105: 3043:Using LaTeX markup 2686: 2659: 2628: 2599: 2559: 2539: 2513: 2487: 2467: 2447: 2335:should be written 2325:semidirect product 2308:) rather than Mor( 2125:Elliptic functions 2067:for our notion of 2015:Algebraic geometry 1911:{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 9243: 9242: 9181:Understandability 9043:Structure drawing 8992:Latter Day Saints 8793:Lyrics and poetry 8736:Stand-alone lists 8623:Dates and numbers 8101:{\displaystyle A} 7872: 7840:...</math: --> 7086: 7063: 7040: 6623: 6610: 6516:(A)</math: --> 6152:{\displaystyle a} 6027:{\displaystyle a} 5892:...</math: --> 5870: 5855: 5838:...</math: --> 5619:]</nowiki: --> 5212:...</math: --> 5066:ASTERISK OPERATOR 4894:...</math: --> 4607:§ Blackboard bold 3966:special attention 3926:...</math: --> 3873: 3805:({{tmath|1=...}}) 3800:...</math: --> 3794:...</math: --> 3763: 3718: 3499: 3479: 3274: 3051:markup (see also 3022:WP:Rendering math 2986:section headings, 2830:or in some cases 2265:Bernoulli numbers 2254:in geometry and D 2022:algebraic variety 1996:Clifford algebras 1942:is assumed to be 1923: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 9273: 9261:Knowledge how-to 9231: 9230: 9217: 9141:Military history 9050:Computer science 9023:Compound classes 8870:Military history 8500: 8493: 8486: 8477: 8476: 8472: 8447: 8432:Knuth, Donald E. 8415: 8386: 8344: 8341: 8335: 8328: 8322: 8311: 8305: 8302: 8296: 8293:October 2020 RfC 8290: 8284: 8279: 8273: 8268: 8262: 8251:parser functions 8242: 8236: 8230: 8224: 8214: 8208: 8193: 8129: 8127: 8126: 8121: 8119: 8107: 8105: 8104: 8099: 8073: 8069: 8063: 8059: 8043: 8041: 8040: 8035: 8033: 8032: 8028: 8008: 7999: 7995: 7993:1/2</sup: --> 7983: 7974: 7973:|''R'' / ''A''}} 7966: 7964: 7963: 7958: 7953: 7938: 7927:quotient objects 7921: 7906: 7905: 7901: 7896: 7884: 7882: 7881: 7876: 7873: 7865: 7841: 7816: 7815:\Z</math: --> 7811: 7802: 7800: 7799: 7794: 7788: 7783: 7765: 7764: 7759: 7742: 7740: 7739: 7734: 7732: 7731: 7726: 7713: 7711: 7710: 7705: 7703: 7702: 7697: 7680: 7678: 7677: 7672: 7670: 7669: 7664: 7648: 7646: 7645: 7640: 7638: 7637: 7632: 7619:projective space 7616: 7614: 7613: 7608: 7606: 7605: 7600: 7584: 7582: 7581: 7576: 7574: 7573: 7568: 7556: 7554: 7553: 7548: 7543: 7542: 7537: 7525: 7523: 7522: 7517: 7512: 7511: 7506: 7494: 7492: 7491: 7486: 7481: 7470: 7468: 7467: 7462: 7457: 7446: 7444: 7443: 7438: 7433: 7422: 7420: 7419: 7414: 7409: 7398: 7396: 7395: 7390: 7385: 7374: 7372: 7371: 7366: 7361: 7332: 7311: 7297: 7293: 7270: 7265: 7261: 7257: 7253: 7249: 7241: 7239: 7236: 7232: 7225: 7223: 7222: 7217: 7212: 7211: 7190: 7185: 7183: 7182: 7177: 7151: 7149: 7145: 7141: 7138: 7135: 7132: 7128: 7124: 7121: 7117: 7113: 7109: 7106: 7100: 7098: 7097: 7092: 7087: 7085: 7077: 7069: 7064: 7062: 7054: 7046: 7041: 7039: 7031: 7023: 7012: 7008: 7007: 7002: 7000: 6996: 6993: 6990: 6986: 6983: 6977: 6975: 6974: 6969: 6946: 6941: 6896: 6892: 6884: 6882: 6878: 6874: 6870: 6859: 6857: 6856: 6851: 6849: 6848: 6815: 6814: 6761: 6759: 6755: 6751: 6747: 6743: 6739: 6736: 6730: 6728: 6727: 6722: 6720: 6718: 6713: 6702: 6697: 6668: 6666: 6662: 6659: 6656: 6652: 6648: 6645: 6642: 6635: 6633: 6632: 6627: 6625: 6624: 6621: 6612: 6611: 6608: 6587: 6585: 6581: 6578: 6567: 6565: 6564: 6559: 6554: 6553: 6528: 6524: 6517: 6515: 6511: 6508: 6501: 6499: 6498: 6493: 6464: 6462: 6458: 6455: 6448: 6446: 6445: 6440: 6416: 6415: 6393: 6384: 6382: 6381: 6376: 6345: 6343: 6342: 6337: 6302: 6300: 6293: 6291: 6290: 6285: 6247: 6242:template, as in 6241: 6235: 6231: 6226: 6222: 6209: 6180: 6178: 6177: 6172: 6170: 6158: 6156: 6155: 6150: 6138: 6136: 6135: 6130: 6128: 6113: 6111: 6110: 6105: 6100: 6089: 6081: 6057: 6055: 6054: 6049: 6047: 6033: 6031: 6030: 6025: 6011: 6009: 6008: 6003: 6001: 5983: 5981: 5980: 5975: 5970: 5959: 5951: 5927: 5903: 5897: 5893: 5881: 5879: 5878: 5873: 5871: 5869: 5861: 5856: 5851: 5839: 5831: 5830: 5824: 5823: 5814: 5808: 5804: 5798: 5785: 5764: 5748: 5744: 5741: 5738: 5737: 5727: 5706: 5700: 5692: 5682: 5681: 5677: 5674: 5671: 5664:. For instance: 5663: 5657: 5653: 5647: 5643: 5637: 5633: 5627: 5620: 5603: 5599: 5567: 5563: 5560: 5559: 5554: 5531: 5523: 5522: 5519: 5516: 5513: 5510: 5507: 5504: 5499: 5492: 5485: 5480: 5460: 5452: 5449:: "×", coded as 5437: 5412: 5390: 5389: 5385: 5382: 5379: 5376: 5364: 5363: 5359: 5356: 5353: 5350: 5347: 5339: 5332: 5309: 5308:NOT GREATER-THAN 5306: 5303: 5302: 5297: 5295: 5294: 5289: 5277: 5269: 5266: 5263: 5262: 5253: 5250: 5247: 5246: 5241: 5239: 5238: 5233: 5221: 5213: 5208: 5205: 5202: 5201: 5196: 5193: 5190: 5189: 5184: 5179: 5163: 5155: 5152: 5149: 5148: 5143: 5140: 5137: 5136: 5129: 5126: 5123: 5122: 5117: 5114: 5111: 5110: 5103: 5100: 5097: 5096: 5091: 5088: 5085: 5084: 5067: 5064: 5061: 5060: 5055: 5047: 5044: 5041: 5040: 5032: 5026: 5022: 5016: 5008: 5005: 5002: 5001: 4996: 4993: 4990: 4989: 4970: 4966: 4962: 4958: 4936: 4916: 4895: 4836:and the list at 4822: 4801: 4795: 4793: 4792: 4787: 4785: 4784: 4768: 4767: 4764: 4761: 4757: 4754: 4751: 4742: 4737: 4716: 4712: 4690: 4686: 4676: 4675: 4671: 4668: 4664: 4661: 4658: 4655: 4652: 4649: 4646: 4638: 4629: 4625: 4601: 4597: 4589: 4587: 4586: 4581: 4576: 4564: 4563: 4560: 4557: 4554: 4550: 4547: 4544: 4541: 4538: 4533: 4532: 4529: 4526: 4521: 4520: 4515: 4497: 4494: 4491: 4490: 4485: 4482: 4479: 4478: 4473: 4470: 4467: 4466: 4461: 4458: 4455: 4454: 4447: 4445: 4416: 4415: 4411: 4408: 4404: 4401: 4398: 4395: 4392: 4389: 4386: 4383: 4380: 4377: 4374: 4367: 4344: 4342: 4337: 4333: 4329: 4326: 4323: 4320: 4317: 4314: 4311: 4299: 4273: 4271: 4251: 4247: 4243: 4227: 4216: 4206: 4200: 4196: 4190: 4183: 4166: 4165: 4161: 4158: 4155: 4151: 4148: 4145: 4142: 4138: 4135: 4132: 4129: 4126: 4123: 4120: 4108: 4098: 4096: 4092: 4089: 4086: 4078: 4072: 4068: 4064: 4060: 4054: 4041: 4027:will result in: 4022: 4021: 4017: 4014: 4011: 4007: 4004: 4001: 3998: 3994: 3991: 3988: 3985: 3982: 3979: 3976: 3963: 3957: 3953: 3947: 3939: 3927: 3910: 3904: 3884: 3882: 3881: 3876: 3874: 3869: 3860: 3855: 3851: 3835: 3831: 3816: 3810: 3806: 3802: 3795: 3776:, respectively. 3775: 3774: 3772: 3771: 3766: 3764: 3762: 3761: 3749: 3748: 3739: 3729: 3727: 3726: 3721: 3719: 3717: 3716: 3704: 3703: 3694: 3686:which render as 3685: 3683: 3682: 3678: 3674: 3670: 3667: 3660: 3658: 3657: 3653: 3649: 3645: 3642: 3635: 3631: 3629: 3627: 3626: 3621: 3616: 3611: 3610: 3598: 3597: 3588: 3579: 3574: 3551: 3549: 3547: 3544: 3540: 3536: 3533: 3529: 3526: 3519: 3513: 3511: 3510: 3505: 3500: 3495: 3494: 3485: 3480: 3478: 3477: 3465: 3462: 3457: 3433: 3431: 3430: 3426: 3422: 3419: 3416: 3413: 3409: 3405: 3401: 3397: 3394: 3391: 3388: 3384: 3381: 3374: 3370: 3369: 3366: 3363: 3360: 3357: 3354: 3346: 3344: 3343: 3339: 3335: 3332: 3325: 3323: 3322: 3317: 3312: 3297: 3295: 3289: 3287: 3286: 3281: 3276: 3267: 3257: 3255: 3253: 3222: 3220: 3218: 3214: 3211: 3208: 3204: 3201: 3194: 3193: 3190: 3187: 3184: 3181: 3178: 3166: 3164: 3163: 3158: 3135: 3130: 3114: 3112: 3111: 3106: 3104: 3103: 3098: 3089: 3019: 2983: 2968: 2961: 2897: 2894: 2891: 2888: 2885: 2882: 2879: 2876: 2873: 2870: 2867: 2864: 2861: 2768: 2753: 2736: 2726: 2713:or as a product 2712: 2695: 2693: 2692: 2687: 2685: 2684: 2668: 2666: 2665: 2660: 2658: 2657: 2637: 2635: 2634: 2629: 2627: 2626: 2625: 2608: 2606: 2605: 2600: 2598: 2597: 2596: 2568: 2566: 2565: 2560: 2548: 2546: 2545: 2540: 2522: 2520: 2519: 2514: 2496: 2494: 2493: 2488: 2476: 2474: 2473: 2468: 2456: 2454: 2453: 2448: 2428: 2424: 2407: 2397: 2383: 2364: 2349: 2267:are denoted by B 2105:General Topology 2076:separation axiom 1920: 1912: 1840: 1822: 1806: 1790: 1765: 1724: 1719: 1705: 1700: 1695: 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: 403: 368: 367: 134: 115: 114: 105: 98: 91: 40: 39: 33: 27: 9281: 9280: 9276: 9275: 9274: 9272: 9271: 9270: 9246: 9245: 9244: 9239: 9219: 9218: 9213: 9200: 9094: 9059: 8996: 8975: 8874: 8858: 8827: 8773:Anime and manga 8761: 8740: 8709: 8705:Trivia sections 8678: 8664:Image placement 8647: 8643:Titles of works 8638:Text formatting 8601: 8592:Self-references 8572:Gender identity 8538: 8509: 8507:Manual of Style 8504: 8470: 8445: 8416:. Reprinted in 8384: 8353: 8351:Further reading 8348: 8347: 8342: 8338: 8329: 8325: 8312: 8308: 8303: 8299: 8291: 8287: 8280: 8276: 8269: 8265: 8243: 8239: 8231: 8227: 8215: 8211: 8194: 8190: 8185: 8167: 8145: 8140: 8115: 8113: 8110: 8109: 8093: 8090: 8089: 8082: 8071: 8067: 8061: 8057: 8050: 8024: 8020: 8016: 8014: 8011: 8010: 8001: 7997: 7987: 7976: 7968: 7949: 7944: 7941: 7940: 7930: 7919: 7903: 7899: 7898: 7890: 7864: 7861: 7858: 7857: 7854: 7848: 7838: 7826:a rendering bug 7813: 7808: 7784: 7779: 7760: 7755: 7754: 7752: 7749: 7748: 7745:hypercohomology 7727: 7722: 7721: 7719: 7716: 7715: 7698: 7693: 7692: 7690: 7687: 7686: 7665: 7660: 7659: 7657: 7654: 7653: 7633: 7628: 7627: 7625: 7622: 7621: 7601: 7596: 7595: 7593: 7590: 7589: 7569: 7564: 7563: 7561: 7558: 7557: 7538: 7533: 7532: 7530: 7527: 7526: 7507: 7502: 7501: 7499: 7496: 7495: 7477: 7475: 7472: 7471: 7453: 7451: 7448: 7447: 7429: 7427: 7424: 7423: 7405: 7403: 7400: 7399: 7381: 7379: 7376: 7375: 7357: 7355: 7352: 7351: 7340:blackboard bold 7336: 7335: 7328: 7324: 7318: 7316:Blackboard bold 7307: 7295: 7289: 7268: 7263: 7259: 7255: 7251: 7247: 7240:.</math: --> 7237: 7234: 7230: 7204: 7200: 7198: 7195: 7194: 7159: 7156: 7155: 7150:,</math: --> 7147: 7143: 7139: 7136: 7133: 7130: 7126: 7122: 7119: 7115: 7111: 7107: 7104: 7078: 7070: 7068: 7055: 7047: 7045: 7032: 7024: 7022: 7020: 7017: 7016: 7005: 6998: 6994: 6991: 6988: 6984: 6981: 6942: 6937: 6931: 6928: 6927: 6909: 6894: 6890: 6880: 6876: 6872: 6868: 6823: 6819: 6786: 6782: 6774: 6771: 6770: 6757: 6753: 6749: 6745: 6741: 6737: 6734: 6714: 6709: 6704: 6698: 6687: 6681: 6678: 6677: 6664: 6660: 6657: 6654: 6650: 6646: 6643: 6640: 6620: 6616: 6607: 6603: 6601: 6598: 6597: 6586:x</math: --> 6583: 6579: 6576: 6543: 6542: 6537: 6534: 6533: 6526: 6522: 6513: 6509: 6506: 6472: 6469: 6468: 6463:x</math: --> 6460: 6456: 6453: 6425: 6422: 6421: 6413: 6358: 6355: 6354: 6310: 6307: 6306: 6301:x</math: --> 6298: 6270: 6267: 6266: 6259: 6254: 6243: 6239: 6233: 6229: 6224: 6220: 6213: 6212: 6205: 6201: 6195: 6166: 6164: 6161: 6160: 6144: 6141: 6140: 6124: 6122: 6119: 6118: 6096: 6085: 6077: 6075: 6072: 6071: 6043: 6041: 6038: 6037: 6019: 6016: 6015: 5997: 5995: 5992: 5991: 5966: 5955: 5947: 5945: 5942: 5941: 5931: 5930: 5923: 5919: 5913: 5901: 5895: 5890: 5865: 5860: 5850: 5848: 5845: 5844: 5836: 5828: 5826: 5821: 5819: 5812: 5806: 5805:(often seen as 5802: 5796: 5789: 5788: 5781: 5777: 5771: 5762: 5746: 5742: 5739: 5735: 5734: 5731: 5730: 5723: 5719: 5713: 5711:Function symbol 5704: 5698: 5690: 5679: 5675: 5672: 5669: 5661: 5655: 5651: 5645: 5641: 5635: 5631: 5625: 5618:<nowiki: --> 5617: 5610: 5608:Square brackets 5601: 5593: 5582: 5565: 5561: 5557: 5556: 5552: 5525: 5520: 5517: 5514: 5511: 5508: 5505: 5502: 5497: 5490: 5483: 5479:26 = 6 × 4 + 2. 5478: 5454: 5450: 5435: 5416: 5415: 5408: 5404: 5398: 5387: 5383: 5380: 5377: 5374: 5361: 5357: 5354: 5351: 5348: 5345: 5334: 5330: 5326: 5321: 5307: 5304: 5300: 5299: 5283: 5280: 5279: 5274: 5267: 5264: 5260: 5259: 5251: 5248: 5244: 5243: 5227: 5224: 5223: 5218: 5210: 5207:REVERSE SOLIDUS 5206: 5203: 5199: 5198: 5194: 5191: 5187: 5186: 5181: 5176: 5161: 5153: 5150: 5146: 5145: 5141: 5138: 5134: 5133: 5127: 5124: 5120: 5119: 5115: 5112: 5108: 5107: 5101: 5098: 5094: 5093: 5089: 5086: 5082: 5081: 5065: 5062: 5058: 5057: 5053: 5045: 5042: 5038: 5037: 5030: 5024: 5020: 5014: 5006: 5003: 4999: 4998: 4994: 4991: 4987: 4986: 4980: 4968: 4964: 4960: 4956: 4955:. For example, 4940: 4939: 4932: 4928: 4908: 4907:" rather than " 4892: 4826: 4825: 4820:MOS:MATHSPECIAL 4818: 4814: 4808: 4806:Special symbols 4797: 4780: 4776: 4774: 4771: 4770: 4765: 4762: 4759: 4755: 4752: 4749: 4739: 4720: 4714: 4695: 4688: 4682: 4672: 4669: 4666: 4662: 4659: 4656: 4653: 4650: 4647: 4644: 4637: 4631: 4627: 4623: 4620: 4614: 4609: 4599: 4595: 4572: 4570: 4567: 4566: 4561: 4558: 4555: 4552: 4548: 4545: 4542: 4539: 4536: 4530: 4527: 4524: 4518: 4511: 4508: 4500:MOS:UNITSYMBOLS 4495: 4492: 4488: 4487: 4483: 4480: 4476: 4475: 4471: 4468: 4464: 4463: 4459: 4456: 4452: 4451: 4432: 4431: 4412: 4409: 4406: 4402: 4399: 4396: 4393: 4390: 4387: 4384: 4381: 4378: 4375: 4372: 4355: 4352: 4340: 4335: 4331: 4327: 4324: 4321: 4318: 4315: 4312: 4309: 4285: 4279: 4254: 4253: 4249: 4245: 4241: 4234: 4222: 4215: 4209: 4204: 4198: 4194: 4188: 4174: 4163: 4159: 4156: 4153: 4149: 4146: 4143: 4140: 4136: 4133: 4130: 4127: 4124: 4121: 4118: 4106: 4094: 4090: 4087: 4084: 4076: 4070: 4066: 4062: 4058: 4052: 4049: 4032: 4019: 4015: 4012: 4009: 4005: 4002: 3999: 3996: 3992: 3989: 3986: 3983: 3980: 3977: 3974: 3961: 3955: 3951: 3945: 3933: 3924: 3917: 3915:Font formatting 3908: 3902: 3892: 3868: 3866: 3863: 3862: 3857: 3853: 3849: 3842: 3833: 3829: 3823: 3814: 3808: 3804: 3798: 3792: 3791:Directly using 3789: 3781:described below 3757: 3753: 3744: 3740: 3738: 3736: 3733: 3732: 3731: 3712: 3708: 3699: 3695: 3693: 3691: 3688: 3687: 3680: 3676: 3672: 3668: 3665: 3662: 3655: 3651: 3647: 3643: 3640: 3637: 3612: 3606: 3602: 3593: 3589: 3584: 3575: 3564: 3558: 3555: 3554: 3553: 3545: 3542: 3538: 3534: 3531: 3527: 3524: 3521: 3517: 3514: 3490: 3486: 3484: 3473: 3469: 3464: 3458: 3447: 3441: 3438: 3437: 3428: 3424: 3420: 3417: 3414: 3411: 3407: 3403: 3399: 3395: 3392: 3389: 3386: 3382: 3379: 3376: 3372: 3367: 3364: 3361: 3358: 3355: 3352: 3341: 3337: 3333: 3330: 3327: 3308: 3303: 3300: 3299: 3291: 3265: 3263: 3260: 3259: 3251: 3248: 3216: 3212: 3209: 3206: 3202: 3199: 3196: 3191: 3188: 3185: 3182: 3179: 3176: 3131: 3126: 3120: 3117: 3116: 3099: 3094: 3093: 3085: 3083: 3080: 3079: 3045: 3029:on its own line 3011: 2981: 2978: 2972: 2971: 2964: 2957: 2953: 2945: 2904: 2899: 2898: 2895: 2892: 2889: 2886: 2883: 2880: 2877: 2874: 2871: 2868: 2865: 2862: 2859: 2853: 2820: 2814: 2798: 2758: 2745: 2728: 2718: 2704: 2680: 2676: 2674: 2671: 2670: 2653: 2649: 2647: 2644: 2643: 2621: 2620: 2616: 2614: 2611: 2610: 2592: 2591: 2587: 2585: 2582: 2581: 2554: 2551: 2550: 2528: 2525: 2524: 2502: 2499: 2498: 2482: 2479: 2478: 2462: 2459: 2458: 2442: 2439: 2438: 2426: 2422: 2399: 2389: 2370: 2360: 2351: 2345: 2336: 2282:category theory 2272: 2260: 2253: 2236: 2229:isometry groups 2226: 2198: 2179: 2127:are written in 2093:preordered sets 2085: 2045: 2017: 1980:is not assumed 1935: 1927:natural numbers 1919:{1, 2, 3, ...}, 1918: 1910: 1907:natural numbers 1899: 1897:Natural numbers 1894: 1870: 1864: 1844: 1843: 1838:MOS:MATH#PLURAL 1836: 1832: 1808: 1792: 1776: 1769: 1768: 1761: 1757: 1722: 1717: 1703: 1698: 1693: 1655: 1617: 1589:if and only if 1580: 1567: 1566: 1559: 1555: 1543: 1520: 1510: 1491: 1484: 1474: 1470: 1466: 1462: 1458: 1454: 1434: 1425: 1416:is then finite. 1403: 1390: 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: 9279: 9269: 9268: 9263: 9258: 9241: 9240: 9238: 9237: 9224: 9221: 9220: 9211: 9209: 9208: 9206: 9202: 9201: 9199: 9198: 9193: 9188: 9183: 9178: 9173: 9168: 9163: 9158: 9153: 9148: 9143: 9138: 9133: 9128: 9126:Citing sources 9123: 9121:Categorization 9118: 9113: 9111:Article titles 9108: 9102: 9100: 9096: 9095: 9093: 9092: 9091: 9090: 9083:Figure skating 9080: 9079: 9078: 9067: 9065: 9061: 9060: 9058: 9057: 9052: 9047: 9046: 9045: 9040: 9035: 9030: 9025: 9015: 9010: 9004: 9002: 8998: 8997: 8995: 8994: 8989: 8983: 8981: 8977: 8976: 8974: 8973: 8968: 8963: 8958: 8953: 8948: 8943: 8938: 8933: 8928: 8923: 8918: 8913: 8908: 8903: 8898: 8893: 8888: 8882: 8880: 8876: 8875: 8873: 8872: 8866: 8864: 8860: 8859: 8857: 8856: 8851: 8846: 8841: 8835: 8833: 8829: 8828: 8826: 8825: 8820: 8815: 8810: 8805: 8800: 8795: 8790: 8785: 8780: 8775: 8769: 8767: 8763: 8762: 8760: 8759: 8754: 8748: 8746: 8742: 8741: 8739: 8738: 8733: 8731:Road junctions 8728: 8726:Lists of works 8723: 8717: 8715: 8711: 8710: 8708: 8707: 8702: 8697: 8692: 8686: 8684: 8680: 8679: 8677: 8676: 8671: 8666: 8661: 8655: 8653: 8649: 8648: 8646: 8645: 8640: 8635: 8630: 8625: 8620: 8618:Capitalization 8615: 8609: 8607: 8603: 8602: 8600: 8599: 8597:Words to watch 8594: 8589: 8584: 8579: 8574: 8569: 8568: 8567: 8557: 8552: 8546: 8544: 8540: 8539: 8537: 8536: 8529: 8522: 8514: 8511: 8510: 8503: 8502: 8495: 8488: 8480: 8474: 8473: 8468: 8450: 8449: 8443: 8424: 8423: 8389: 8388: 8382: 8352: 8349: 8346: 8345: 8336: 8332:ISO/IEC 8859-1 8330:Characters in 8323: 8306: 8297: 8285: 8274: 8263: 8237: 8225: 8209: 8187: 8186: 8184: 8181: 8180: 8179: 8173: 8166: 8163: 8162: 8161: 8156: 8151: 8144: 8141: 8139: 8136: 8118: 8097: 8066:The length of 8065: 8049: 8046: 8031: 8027: 8023: 8019: 7992:|x<sup: --> 7956: 7952: 7948: 7871: 7868: 7847: 7844: 7792: 7787: 7782: 7778: 7774: 7771: 7768: 7763: 7758: 7730: 7725: 7701: 7696: 7668: 7663: 7636: 7631: 7604: 7599: 7572: 7567: 7546: 7541: 7536: 7515: 7510: 7505: 7484: 7480: 7460: 7456: 7436: 7432: 7412: 7408: 7388: 7384: 7364: 7360: 7348:number systems 7334: 7333: 7325: 7320: 7317: 7314: 7244: 7243: 7226:(typeset from 7215: 7210: 7207: 7203: 7192: 7186:(typeset from 7175: 7172: 7169: 7166: 7163: 7153: 7101:(typeset from 7090: 7084: 7081: 7076: 7073: 7067: 7061: 7058: 7053: 7050: 7044: 7038: 7035: 7030: 7027: 7014: 6978:(typeset from 6967: 6964: 6961: 6956: 6953: 6950: 6945: 6940: 6936: 6921:Euler's number 6917:imaginary unit 6908: 6905: 6887: 6886: 6883:</math: --> 6864:—typeset from 6847: 6844: 6841: 6838: 6835: 6832: 6829: 6826: 6822: 6818: 6813: 6810: 6807: 6804: 6801: 6798: 6795: 6792: 6789: 6785: 6781: 6778: 6764: 6763: 6760:</math: --> 6717: 6712: 6708: 6701: 6696: 6693: 6690: 6686: 6671: 6670: 6667:</math: --> 6619: 6615: 6606: 6590: 6589: 6572:—typeset from 6557: 6552: 6549: 6546: 6541: 6520: 6519: 6502:(typeset from 6491: 6488: 6485: 6482: 6479: 6476: 6466: 6449:(typeset from 6438: 6435: 6432: 6429: 6409: 6408: 6396: 6395: 6389:—typeset from 6374: 6371: 6368: 6365: 6362: 6348: 6347: 6335: 6332: 6329: 6326: 6323: 6320: 6317: 6314: 6304: 6283: 6280: 6277: 6274: 6258: 6255: 6253: 6250: 6230:</math: --> 6225:</math: --> 6211: 6210: 6202: 6197: 6194: 6191: 6169: 6148: 6127: 6115: 6114: 6103: 6099: 6095: 6092: 6088: 6084: 6080: 6060: 6059: 6046: 6035: 6023: 6013: 6000: 5985: 5984: 5973: 5969: 5965: 5962: 5958: 5954: 5950: 5929: 5928: 5920: 5915: 5912: 5909: 5883: 5882: 5868: 5864: 5859: 5854: 5833: 5832: 5793:radical symbol 5787: 5786: 5778: 5773: 5770: 5769:Radical symbol 5767: 5729: 5728: 5720: 5715: 5712: 5709: 5695: 5694: 5684: 5683: 5609: 5606: 5600:) or use the " 5581: 5578: 5500:(also encoded 5487: 5486: 5481: 5441:However, when 5414: 5413: 5405: 5400: 5397: 5394: 5393: 5392: 5367: 5366: 5325: 5324:Less-than sign 5322: 5314: 5312: 5311: 5287: 5271: 5231: 5215: 5173: 5154:TILDE OPERATOR 5130: 5104: 5102:DIVISION SLASH 5078: 5034: 4983: 4982: 4981: 4945:Roman numerals 4938: 4937: 4929: 4924: 4921: 4919: 4918: 4897: 4881:named entities 4871:Keep in mind: 4824: 4823: 4815: 4810: 4807: 4804: 4783: 4779: 4745: 4744: 4741:2</sup: --> 4718: 4679: 4678: 4635: 4613: 4610: 4579: 4575: 4507: 4504: 4351: 4348: 4347: 4346: 4302: 4301: 4278: 4275: 4233: 4230: 4213: 4185: 4184: 4168: 4167: 4111: 4110: 4100: 4099: 4048: 4045: 4044: 4043: 4025: 4024: 3916: 3913: 3891: 3888: 3872: 3841: 3838: 3822: 3819: 3788: 3785: 3760: 3756: 3752: 3747: 3743: 3715: 3711: 3707: 3702: 3698: 3684:</math: --> 3659:</math: --> 3634:display=inline 3619: 3615: 3609: 3605: 3601: 3596: 3592: 3587: 3583: 3578: 3573: 3570: 3567: 3563: 3550:</math: --> 3518:display=inline 3503: 3498: 3493: 3489: 3483: 3476: 3472: 3468: 3461: 3456: 3453: 3450: 3446: 3436: 3432:</math: --> 3345:</math: --> 3315: 3311: 3307: 3296:</math: --> 3279: 3273: 3270: 3256:</math: --> 3245: 3244: 3237: 3234: 3221:</math: --> 3156: 3153: 3150: 3145: 3142: 3139: 3134: 3129: 3125: 3102: 3097: 3092: 3088: 3044: 3041: 3027:For a formula 2970: 2969: 2962: 2954: 2949: 2944: 2941: 2933: 2932: 2929: 2925: 2922: 2919: 2903: 2900: 2858: 2850: 2813: 2810: 2797: 2794: 2793: 2792: 2779:matrix product 2740:The scalar or 2738: 2697: 2683: 2679: 2656: 2652: 2624: 2619: 2595: 2590: 2570: 2558: 2538: 2535: 2532: 2512: 2509: 2506: 2486: 2466: 2446: 2437:is denoted by 2432: 2431: 2430: 2419: 2416: 2356: 2341: 2321: 2318:small category 2278: 2268: 2262: 2255: 2249: 2242:dihedral group 2238: 2232: 2222: 2219:roots of unity 2204:-adic integers 2194: 2178: 2175: 2174: 2173: 2136: 2122: 2115: 2097:partial orders 2084: 2081: 2080: 2079: 2072: 2044: 2041: 2040: 2039: 2032: 2016: 2013: 2012: 2011: 1992: 1974: 1967: 1934: 1931: 1898: 1895: 1893: 1890: 1863: 1860: 1846:The plural of 1842: 1841: 1833: 1828: 1767: 1766: 1758: 1753: 1726: 1725: 1720: 1707: 1706: 1701: 1696: 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: 15: 9: 6: 4: 3: 2: 9278: 9267: 9264: 9262: 9259: 9257: 9254: 9253: 9251: 9236: 9235: 9226: 9225: 9222: 9207: 9203: 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: 9122: 9119: 9117: 9114: 9112: 9109: 9107: 9104: 9103: 9101: 9097: 9089: 9086: 9085: 9084: 9081: 9077: 9074: 9073: 9072: 9069: 9068: 9066: 9062: 9056: 9053: 9051: 9048: 9044: 9041: 9039: 9036: 9034: 9031: 9029: 9026: 9024: 9021: 9020: 9019: 9016: 9014: 9011: 9009: 9006: 9005: 9003: 8999: 8993: 8990: 8988: 8985: 8984: 8982: 8978: 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: 8902: 8899: 8897: 8894: 8892: 8889: 8887: 8884: 8883: 8881: 8877: 8871: 8868: 8867: 8865: 8861: 8855: 8852: 8850: 8849:Record charts 8847: 8845: 8844:Music samples 8842: 8840: 8837: 8836: 8834: 8830: 8824: 8821: 8819: 8816: 8814: 8811: 8809: 8806: 8804: 8801: 8799: 8796: 8794: 8791: 8789: 8786: 8784: 8781: 8779: 8776: 8774: 8771: 8770: 8768: 8764: 8758: 8755: 8753: 8750: 8749: 8747: 8743: 8737: 8734: 8732: 8729: 8727: 8724: 8722: 8719: 8718: 8716: 8712: 8706: 8703: 8701: 8698: 8696: 8693: 8691: 8688: 8687: 8685: 8681: 8675: 8672: 8670: 8667: 8665: 8662: 8660: 8657: 8656: 8654: 8650: 8644: 8641: 8639: 8636: 8634: 8631: 8629: 8628:Pronunciation 8626: 8624: 8621: 8619: 8616: 8614: 8613:Abbreviations 8611: 8610: 8608: 8604: 8598: 8595: 8593: 8590: 8588: 8585: 8583: 8580: 8578: 8575: 8573: 8570: 8566: 8563: 8562: 8561: 8558: 8556: 8553: 8551: 8550:Accessibility 8548: 8547: 8545: 8541: 8535: 8534: 8530: 8528: 8527: 8523: 8521: 8520: 8516: 8515: 8512: 8508: 8501: 8496: 8494: 8489: 8487: 8482: 8481: 8478: 8471: 8469:9780226104201 8466: 8462: 8461: 8455: 8454: 8453: 8446: 8444:0-201-13448-9 8441: 8437: 8433: 8429: 8428: 8427: 8422: 8419: 8414: 8410: 8406: 8402: 8398: 8394: 8393: 8392: 8385: 8383:0-89871-420-6 8380: 8376: 8372: 8368: 8367: 8362: 8358: 8357: 8356: 8340: 8333: 8327: 8320: 8316: 8310: 8301: 8294: 8289: 8283: 8278: 8272: 8267: 8260: 8256: 8252: 8248: 8241: 8234: 8229: 8222: 8218: 8213: 8206: 8202: 8198: 8192: 8188: 8177: 8174: 8172: 8169: 8168: 8160: 8157: 8155: 8152: 8150: 8147: 8146: 8135: 8131: 8095: 8086: 8081: 8054: 8045: 8029: 8025: 8021: 8017: 8005: 7991: 7984: 7980: 7972: 7954: 7950: 7946: 7937: 7933: 7928: 7923: 7917: 7916:accessibility 7913: 7910: 7894: 7888: 7869: 7866: 7853: 7843: 7839:<math: --> 7836: 7831: 7827: 7822: 7820: 7814:<math: --> 7809:<math: --> 7804: 7785: 7780: 7772: 7769: 7761: 7746: 7728: 7699: 7684: 7683:group schemes 7666: 7652: 7634: 7620: 7602: 7588: 7570: 7544: 7539: 7513: 7508: 7482: 7458: 7434: 7410: 7386: 7362: 7349: 7344: 7341: 7331: 7327: 7326: 7323: 7313: 7310: 7305: 7301: 7292: 7287: 7282: 7280: 7275: 7271: 7228:<math: --> 7213: 7208: 7205: 7201: 7193: 7188:<math: --> 7173: 7170: 7167: 7164: 7161: 7154: 7103:<math: --> 7088: 7082: 7079: 7074: 7071: 7065: 7059: 7056: 7051: 7048: 7042: 7036: 7033: 7028: 7025: 7015: 6980:<math: --> 6965: 6962: 6959: 6954: 6951: 6948: 6943: 6938: 6934: 6926: 6925: 6924: 6922: 6918: 6914: 6904: 6903: 6901: 6866:<math: --> 6863: 6845: 6842: 6839: 6836: 6833: 6830: 6827: 6824: 6820: 6816: 6811: 6808: 6805: 6802: 6799: 6796: 6793: 6790: 6787: 6783: 6779: 6776: 6769: 6768: 6767: 6733:<math: --> 6715: 6710: 6706: 6699: 6694: 6691: 6688: 6684: 6676: 6675: 6674: 6638:<math: --> 6617: 6613: 6604: 6596: 6595: 6594: 6574:<math: --> 6571: 6555: 6539: 6532: 6531: 6530: 6523:\operatorname 6507:\operatorname 6504:<math: --> 6486: 6480: 6477: 6474: 6467: 6454:\operatorname 6451:<math: --> 6436: 6433: 6430: 6427: 6420: 6419: 6418: 6414:\operatorname 6406: 6402: 6398: 6397: 6391:<math: --> 6388: 6372: 6369: 6366: 6363: 6360: 6353: 6352: 6351: 6330: 6327: 6324: 6318: 6315: 6312: 6305: 6296:<math: --> 6281: 6278: 6275: 6272: 6265: 6264: 6263: 6249: 6238: 6221:<math: --> 6217: 6208: 6207:MOS:MATH#PUNC 6204: 6203: 6200: 6190: 6188: 6187:Heat equation 6182: 6146: 6101: 6093: 6090: 6082: 6070: 6069: 6068: 6064: 6036: 6021: 6014: 5990: 5989: 5988: 5971: 5963: 5960: 5952: 5940: 5939: 5938: 5934: 5933:A list as in 5926: 5922: 5921: 5918: 5908: 5905: 5900: 5891:<math: --> 5888: 5866: 5862: 5857: 5852: 5843: 5842: 5841: 5837:<math: --> 5818: 5817: 5816: 5811: 5801: 5794: 5784: 5780: 5779: 5776: 5766: 5760: 5756: 5752: 5726: 5722: 5721: 5718: 5708: 5703: 5689: 5688: 5687: 5667: 5666: 5665: 5660: 5659:closed-closed 5650: 5640: 5630: 5622: 5615: 5605: 5597: 5591: 5587: 5577: 5575: 5570: 5568: 5550: 5546: 5541: 5539: 5535: 5529: 5496: 5482: 5476: 5473:and 2 is the 5472: 5468: 5464: 5463: 5462: 5458: 5448: 5444: 5439: 5433: 5429: 5425: 5421: 5411: 5407: 5406: 5403: 5372: 5371: 5370: 5343: 5342: 5341: 5337: 5320: 5315: 5298:) instead of 5285: 5275:<math: --> 5272: 5257: 5252:RING OPERATOR 5242:) instead of 5229: 5219:<math: --> 5216: 5211:<math: --> 5182:<math: --> 5177:<math: --> 5174: 5171: 5167: 5159: 5158:other symbols 5131: 5105: 5079: 5076: 5071: 5051: 5035: 5029: 5019: 5012: 4984: 4978: 4973: 4972: 4954: 4950: 4946: 4942: 4941: 4935: 4931: 4930: 4927: 4922: 4915: 4911: 4906: 4902: 4898: 4893:<math: --> 4890: 4886: 4882: 4878: 4874: 4873: 4872: 4869: 4867: 4863: 4859: 4855: 4852:outside both 4851: 4847: 4843: 4839: 4835: 4831: 4821: 4817: 4816: 4813: 4803: 4800: 4781: 4777: 4736: 4732: 4728: 4724: 4719: 4711: 4707: 4703: 4699: 4694: 4693: 4692: 4685: 4642: 4641: 4640: 4634: 4619: 4608: 4603: 4593: 4577: 4514: 4503: 4501: 4448: 4443: 4439: 4435: 4429: 4424: 4422: 4421:Greek letters 4417: 4369: 4366: 4362: 4358: 4350:Greek letters 4307: 4306: 4305: 4296: 4292: 4288: 4284: 4283: 4282: 4274: 4269: 4265: 4261: 4257: 4239: 4229: 4225: 4220: 4212: 4203: 4193: 4181: 4177: 4173: 4172: 4171: 4116: 4115: 4114: 4105: 4104: 4103: 4102:displays as: 4082: 4081: 4080: 4075: 4057: 4039: 4035: 4030: 4029: 4028: 3971: 3970: 3969: 3967: 3960: 3950: 3943: 3937: 3931: 3925:<math: --> 3922: 3912: 3907: 3900: 3895: 3887: 3870: 3847: 3837: 3834:\displaystyle 3825: 3818: 3813: 3793:<math: --> 3787:Line wrapping 3784: 3782: 3777: 3758: 3754: 3750: 3745: 3741: 3713: 3709: 3705: 3700: 3696: 3638:<math: --> 3617: 3613: 3607: 3603: 3599: 3594: 3590: 3585: 3581: 3571: 3568: 3565: 3561: 3501: 3496: 3491: 3487: 3481: 3474: 3470: 3466: 3454: 3451: 3448: 3444: 3435: 3377:<math: --> 3348: 3328:<math: --> 3313: 3309: 3305: 3292:<math: --> 3277: 3271: 3268: 3249:<math: --> 3242: 3238: 3235: 3232: 3231: 3230: 3227: 3224: 3173: 3167: 3154: 3151: 3148: 3143: 3140: 3137: 3132: 3127: 3123: 3100: 3090: 3076: 3074: 3070: 3066: 3062: 3058: 3054: 3050: 3040: 3038: 3034: 3030: 3025: 3024:for details. 3023: 3018: 3014: 3008: 3006: 3002: 2998: 2993: 2991: 2987: 2982:<math: --> 2977: 2967: 2963: 2960: 2956: 2955: 2952: 2947: 2940: 2938: 2930: 2926: 2923: 2920: 2917: 2913: 2912: 2911: 2909: 2856: 2849: 2847: 2842: 2839: 2837: 2833: 2829: 2825: 2819: 2809: 2807: 2802: 2790: 2786: 2783: 2780: 2776: 2772: 2766: 2762: 2757: 2756:inner product 2752: 2748: 2743: 2739: 2735: 2731: 2725: 2721: 2717:, suprema as 2716: 2711: 2707: 2702: 2698: 2677: 2654: 2650: 2641: 2617: 2588: 2579: 2575: 2572:For a matrix 2571: 2556: 2536: 2533: 2530: 2510: 2507: 2504: 2484: 2477:. The symbol 2464: 2444: 2436: 2433: 2420: 2417: 2414: 2413: 2411: 2406: 2402: 2396: 2392: 2387: 2381: 2377: 2373: 2368: 2363: 2359: 2354: 2348: 2344: 2339: 2334: 2330: 2326: 2322: 2319: 2315: 2311: 2307: 2303: 2299: 2295: 2291: 2287: 2283: 2279: 2276: 2271: 2266: 2263: 2259: 2252: 2247: 2243: 2239: 2235: 2230: 2225: 2220: 2216: 2213: 2209: 2205: 2203: 2197: 2192: 2189: 2185: 2182:The abstract 2181: 2180: 2171: 2167: 2163: 2159: 2156: 2152: 2148: 2144: 2141: 2137: 2134: 2130: 2126: 2123: 2120: 2116: 2113: 2112:0-387-90125-6 2110: 2106: 2102: 2099:as in, e.g., 2098: 2094: 2090: 2089:Directed sets 2087: 2086: 2083:Miscellaneous 2077: 2073: 2070: 2066: 2065:quasi-compact 2062: 2059: 2055: 2051: 2050:compact space 2047: 2046: 2037: 2033: 2030: 2029:algebraic set 2027: 2023: 2019: 2018: 2009: 2005: 2001: 1997: 1993: 1990: 1987: 1983: 1979: 1975: 1972: 1968: 1965: 1961: 1957: 1953: 1949: 1945: 1941: 1937: 1936: 1930: 1928: 1924: 1916: 1908: 1904: 1889: 1885: 1881: 1879: 1875: 1869: 1859: 1857: 1853: 1849: 1839: 1835: 1834: 1831: 1826: 1824: 1820: 1816: 1812: 1804: 1800: 1796: 1788: 1784: 1780: 1774: 1764: 1760: 1759: 1756: 1751: 1749: 1747: 1743: 1739: 1735: 1731: 1721: 1716: 1715: 1714: 1712: 1704:Obviously ... 1702: 1697: 1692: 1691: 1690: 1683: 1679: 1675: 1671: 1667: 1663: 1659: 1658:even function 1654: 1653: 1652: 1645: 1641: 1637: 1633: 1629: 1625: 1621: 1616: 1615: 1614: 1608: 1604: 1600: 1596: 1592: 1588: 1584: 1579: 1578: 1577: 1574: 1572: 1562: 1558: 1557: 1554: 1549: 1540: 1536: 1532: 1528: 1524: 1519: 1518: 1517: 1507: 1503: 1499: 1495: 1490: 1489: 1488: 1483: 1478: 1471:Consider that 1446: 1442: 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: 1351: 1349: 1345: 1339: 1337: 1326: 1323: 1319: 1317: 1312: 1310: 1306: 1305:instructional 1302: 1298: 1294: 1290: 1286: 1282: 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: 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: 929: 927: 923: 919: 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: 794: 791: 789: 786: 784: 781: 779: 776: 774: 771: 769: 766: 765: 759: 758: 744: 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: 625: 618: 615: 613: 610: 608: 605: 603: 600: 598: 595: 593: 590: 588: 585: 583: 580: 578: 575: 573: 570: 568: 565: 563: 560: 558: 555: 553: 550: 548: 545: 543: 540: 538: 535: 533: 530: 529: 526: 521: 520: 513: 510: 509: 506: 501: 500: 489: 486: 484: 483:Record charts 481: 479: 478:Music samples 476: 475: 474: 473: 470: 467: 466: 461: 458: 456: 453: 451: 448: 446: 443: 441: 438: 436: 433: 431: 428: 426: 423: 421: 418: 416: 413: 411: 408: 407: 406: 405: 400: 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: 313: 310: 308: 305: 303: 300: 299: 296: 291: 290: 283: 280: 278: 275: 273: 270: 268: 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: 117: 116: 104: 100: 97: 93: 90: 86: 85: 82: 77: 72: 68: 64: 60: 54: 52: 48: 42: 35: 34: 25: 24:Knowledge:MSM 19: 9232: 9196:WikiProjects 9106:Article size 9007: 8695:Lead section 8531: 8524: 8517: 8459: 8451: 8435: 8425: 8404: 8400: 8397:Halmos, P.R. 8390: 8365: 8354: 8339: 8326: 8309: 8300: 8288: 8277: 8266: 8255:hyphen-minus 8240: 8228: 8212: 8191: 8132: 8087: 8083: 7985: 7935: 7931: 7924: 7855: 7832: 7823: 7819:MOS:STYLERET 7805: 7587:affine space 7345: 7337: 7308: 7303: 7300:Donald Knuth 7290: 7283: 7279:MOS:STYLERET 7273: 7267: 7245: 6913:differential 6910: 6898: 6888: 6861: 6765: 6672: 6591: 6569: 6521: 6410: 6386: 6349: 6260: 6218: 6214: 6184: 6116: 6066: 6062: 5986: 5936: 5932: 5906: 5884: 5834: 5790: 5732: 5696: 5685: 5623: 5611: 5583: 5571: 5553:· 5542: 5537: 5533: 5495:dot operator 5488: 5442: 5440: 5431: 5427: 5423: 5419: 5417: 5368: 5335: 5327: 5313: 5268:WHITE CIRCLE 5011:prime symbol 5007:DOUBLE PRIME 4934:MOS:ROMANNUM 4920: 4913: 4909: 4904: 4900: 4891:, using the 4870: 4827: 4798: 4746: 4740:<sup: --> 4734: 4730: 4726: 4722: 4709: 4705: 4701: 4697: 4680: 4632: 4628:<sub: --> 4624:<sup: --> 4621: 4512: 4509: 4449: 4441: 4433: 4427: 4425: 4418: 4370: 4364: 4360: 4356: 4353: 4303: 4294: 4290: 4286: 4280: 4267: 4263: 4259: 4255: 4235: 4223: 4210: 4186: 4179: 4175: 4170:results in: 4169: 4112: 4101: 4050: 4037: 4033: 4026: 3918: 3896: 3893: 3843: 3826: 3824: 3790: 3778: 3515: 3349: 3246: 3228: 3225: 3168: 3077: 3046: 3028: 3026: 3016: 3012: 3009: 2994: 2990:anchor links 2985: 2979: 2966:MOS:FORMULAE 2946: 2934: 2905: 2854: 2843: 2840: 2826:may include 2821: 2803: 2799: 2788: 2784: 2781: 2774: 2770: 2764: 2760: 2750: 2746: 2733: 2729: 2727:or as a sum 2723: 2719: 2714: 2709: 2705: 2639: 2577: 2409: 2404: 2400: 2394: 2390: 2386:homomorphism 2379: 2375: 2371: 2366: 2361: 2357: 2352: 2346: 2342: 2337: 2332: 2328: 2313: 2309: 2305: 2301: 2297: 2293: 2274: 2269: 2257: 2250: 2245: 2233: 2223: 2214: 2211: 2207: 2201: 2195: 2190: 2184:cyclic group 2169: 2165: 2161: 2157: 2154: 2150: 2146: 2143:modular form 2139: 2128: 2104: 2057: 2025: 2007: 2003: 1999: 1985: 1926: 1922: 1914: 1900: 1886: 1882: 1877: 1873: 1871: 1855: 1851: 1847: 1845: 1825: 1818: 1814: 1810: 1802: 1798: 1794: 1786: 1782: 1778: 1772: 1770: 1763:MOS:MATH#ANY 1750: 1746:there exists 1745: 1741: 1737: 1733: 1729: 1727: 1710: 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: 9088:Terminology 9008:Mathematics 8956:Philippines 8818:Visual arts 8813:Video games 8577:Hidden text 8436:The TeXbook 8407:: 123–152, 8315:word joiner 8259:source code 8253:accept the 8195:Currently, 7833:Due to bug 7651:adele rings 5783:MOS:RADICAL 5673:open-closed 5639:closed-open 5629:open-closed 5602:− 5596:subst:minus 5549:source code 5451:× 5185:instead of 5144:instead of 5118:instead of 5092:instead of 5050:superscript 4949:Basic Latin 4846:code points 4616:Main page: 4423:directly.) 4197:or without 3552:renders as 2959:MOS:FORMULA 2832:source code 2777:), or as a 2742:dot product 2133:half-period 2069:compactness 2063:, who uses 2026:irreducible 1964:C* algebras 1960:B* algebras 1944:associative 1699: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 9250:Categories 9186:User pages 9151:Signatures 9146:Notability 9071:Cue sports 8808:Television 8803:Philosophy 8757:Trademarks 8606:Formatting 8421:0821800558 8205:homographs 8078:See also: 8056:The angle 7967:– markup: 7850:See also: 6252:Font usage 5747:&fnof; 5604:" entity. 5580:Minus sign 5498:⋅ 5477:, because 5443:explaining 5317:See also: 5256:interpunct 5054:C*-algebra 5009:where the 4715:² 4689:² 4460:MICRO SIGN 4240:, such as 4236:Names for 3921:sans serif 3890:Using HTML 3373:\textstyle 3239:Until bug 2974:See also: 2828:pseudocode 2816:See also: 2812:Algorithms 2638:, and not 2327:of groups 2244:of order 2 1982:noetherian 1978:local ring 1956:* algebras 1866:See also: 1850:is either 1813:satisfies 1797:satisfies 1781: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 9028:Chemicals 9018:Chemistry 8966:Singapore 8946:Macedonia 8921:Indonesia 8582:Infoboxes 8555:Biography 8526:Directory 8247:templates 7897:(such as 7846:Fractions 7286:WP:WEIGHT 7009:) before 6871:predicted 6862:incorrect 6570:incorrect 6387:incorrect 5686:produces 5649:open-open 5614:intervals 5475:remainder 5195:SET MINUS 4232:Functions 4069:. Within 4047:Variables 3298:produces 3258:produces 2951:Shortcuts 2916:Wikibooks 2908:WP:VERIFY 2824:algorithm 2574:transpose 2300:, as Hom( 2290:morphisms 2138:A weight 2054:Hausdorff 1971:zero ring 1793: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 9234:Category 9161:Subpages 9156:Overview 9136:Hatnotes 9131:Contents 9055:Taxonomy 9013:Medicine 8980:Religion 8951:Pakistan 8941:Malaysia 8879:Regional 8659:Captions 8633:Spelling 8519:Overview 8434:(1984), 8363:(1998), 8219:, is in 8138:See also 7322:Shortcut 6879:observed 6766:but not 6663:that one 6649:this one 6622:that one 6609:this one 6350:but not 6199:Shortcut 5917:Shortcut 5775:Shortcut 5725:MOS:FNOF 5717:Shortcut 5545:asterisk 5471:quotient 5467:dividing 5402:Shortcut 5358:< 5331:< 5166:negation 5070:baseline 5046:ASTERISK 4926:Shortcut 4903:divides 4862:brackets 4812:Shortcut 4717:) versus 4472:OHM SIGN 4391:π 4262:) = sin( 4219:SI units 3944:. Using 3846:alt text 3840:Alt text 2834:in some 2754:, as an 2286:Hom-sets 2284:, write 2231:called C 2061:Bourbaki 2043:Topology 1856:formulas 1852:formulae 1830:Shortcut 1809:if some 1791:, write 1755: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 9099:Related 9076:Snooker 9001:Science 8926:Ireland 8863:History 8783:Blazons 8587:Linking 8543:Content 8245:, many 8221:Haskell 7909:Unicode 7835:T263572 7824:Due to 7747:(e.g., 7743:), and 7330:MOS:BBB 7304:TeXbook 5887:T263572 5691:(−π, π] 5493:is the 5090:SOLIDUS 4864:). The 4850:Unicode 4592:Unicode 4546:\mathbb 4428:capital 3928:uses a 3516:Adding 3359:display 3241:T263572 3183:display 3069:MathJax 3067:(using 3033:strings 2701:lattice 2425:(⋉) or 2384:is the 2164:), and 2119:lattice 1989:Zariski 1933:Algebra 1874:compact 1848:formula 1777:if any 1742:for all 1178:. Then 1109:of the 1053:tangent 733:Snooker 655:Science 572:Ireland 505:History 420:Blazons 187:Linking 143:Content 9205:Search 9064:Sports 9038:Safety 8961:Poland 8911:Hawaii 8891:Canada 8798:Novels 8778:Comics 8700:Tables 8690:Layout 8683:Layout 8674:Images 8652:Images 7920:5.2 cm 7262:, and 7235:\theta 7191:), and 6919:, and 6237:nowrap 6117:where 5987:where 5736:U+0192 5586:hyphen 5566:BULLET 5558:U+2022 5432:citing 5386:< 3 5340:, use 5338:< 3 5301:U+226F 5261:U+25CB 5245:U+2218 5200:U+005C 5188:U+2216 5156:. Use 5147:U+223C 5135:U+007E 5121:U+2236 5109:U+003A 5095:U+2215 5083:U+002F 5059:U+2217 5056:. Use 5039:U+002A 5028:pprime 5000:U+2033 4988:U+2032 4963:, not 4738:(with 4713:(with 4639:, use 4596:U+211D 4489:U+03A9 4477:U+03BC 4465:U+2126 4453:U+00B5 4266:) cos( 4226:= 5 cm 3535:\infty 3390:\infty 3365:inline 3326:, but 3252:\tfrac 3061:MathML 2997:boldly 2928:topic. 2860:primes 2796:Proofs 2435:Subset 2378:→ Aut( 2365:where 2135:style. 2101:Kelley 2058:contra 2036:scheme 1986:contra 1948:unital 1917:, and 1771: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 8987:Islam 8936:Korea 8931:Japan 8916:India 8906:Egypt 8839:Music 8832:Music 8752:Legal 8745:Legal 8721:Lists 8714:Lists 8669:Icons 8183:Notes 8006:: --> 8000:) or 7981:: --> 7887:slash 7137:\frac 7134:\cdot 7120:\frac 7105:\frac 6895:\text 6891:\mbox 6867:r = x 6658:\text 6644:\text 5899:radic 5800:radic 5678:−π, π 5521:: --> 5515:</ 5512:\cdot 5509:: --> 5465:When 5457:times 5384:''x'' 5355:''x'' 5258:) or 5142:TILDE 5128:RATIO 5116:COLON 5018:prime 4995:PRIME 4854:ASCII 4766:: --> 4760:</ 4756:: --> 4673:: --> 4667:</ 4663:: --> 4654:''c'' 4562:: --> 4556:</ 4543:: --> 4531:: --> 4444:+ 1) 4413:: --> 4407:</ 4403:: --> 4338:: --> 4336:''x'' 4332:''x'' 4319:''A'' 4297:: --> 4160:: --> 4154:</ 4150:: --> 4141:''y'' 4128:''x'' 4016:: --> 4010:</ 4006:: --> 3997:''y'' 3984:''x'' 3930:serif 3812:tmath 3666:\sqrt 3641:\sqrt 3412:\frac 3393:\frac 3368:: --> 3331:\frac 3294:x / 2 3192:: --> 3189:block 3049:LaTeX 2896:sieve 2869:sieve 2866:sieve 2699:In a 2669:, or 2292:from 2288:, or 2188:order 2078:page. 1901:"The 1821:) = 0 1807:, or 1805:) = 0 1789:) = 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:< 9176:Tips 8788:Film 8766:Arts 8533:Tips 8465:ISBN 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