2738:. 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.
9247:
986:
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.
8054:
2839:. Knowledge (XXG) does not have a standard programming language or languages, and not all readers will understand any particular language even if the language is well-known and easy to read, so consider whether the algorithm could be expressed in some other way. If source code is used always choose a programming language that expresses the algorithm as clearly as possible.
38:
1487:
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,
7277:
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
7807:
A particular concern for the use of blackboard bold on
Knowledge (XXG) 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
6228:
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
1453:
Mathematics articles are often written in a conversational style similar to a whiteboard lecture. However, a narrative pedagogical style runs counter to
Knowledge (XXG)'s recommended encyclopedic tone. While opinions vary on the most edifying style, authors should generally strike a balance between
3797:
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
1888:
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 (XXG)'s readers come to articles with widely different conventions in mind. These readers will often
6216:
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,
985:
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
1322:
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
957:
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
2801:
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,
1884:
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
1074:
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.
7343:
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
4208:
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,
5552:. 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
1889:
not be familiar with our conventions, which may differ greatly from the conventions they see outside
Knowledge (XXG). 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.
3886:
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.
3828:
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
6900:
5329:
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
1926:. 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
7818:) 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
6593:
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:
907:
and for the use of mathematical notation in
Knowledge (XXG) 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 (XXG).
6262:
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:
1342:
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
3040:, 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.
1478:. 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.
1279:
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
8582:
2818:
164:
8134:
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.
1334:
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
2928:
Today many research papers or even books are freely available online and thus virtually just one click away from
Knowledge (XXG). Newcomers would greatly profit from having an immediate connection to further discussions of a
3513:
1219:
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.
8085:
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.
7100:
9050:
676:
3849:, 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
916:
Probably the hardest part of writing a
Knowledge (XXG) article on a mathematical topic, and generally any Knowledge (XXG) article, is addressing a reader's level of knowledge. For example, when writing about a
6113:
5983:
8918:
8913:
7802:
551:
541:
5073:
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
3170:
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
4900:
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 "
6635:
1873:
A number of conventions have been developed to make
Knowledge (XXG)'s mathematics articles more consistent with each other. These conventions cover choices of terminology, such as the definitions of
5625:
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
3941:
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
3629:
4188:
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
2805:
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
3114:
8488:
8080:
1316:
6859:
4618:
6977:
3166:
8973:
6730:
2911:, 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:
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9133:
9060:
8988:
8871:
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6448:
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686:
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and related articles attempt to cover both unital rings and non-unital rings: they do not consistently implement this interpretation. This attempt to cover multiple meanings violates
9105:
9040:
8983:
8938:
3729:
742:
666:
611:
566:
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8968:
8958:
1094:
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(
703:
596:
591:
3774:
7556:
7525:
1140:) should define the notations. If an article requires extensive notation, consider introducing the notation as a bulleted list or separating it into a section titled "Notation".
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8609:
7742:
7713:
7680:
7648:
7616:
7584:
3289:
2608:
1868:
571:
191:
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606:
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9004:
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8129:
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6138:
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6011:
822:
636:
581:
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Articles should not include multiple implementations of the same algorithm in different programming languages unless there is encyclopedic interest in each implementation.
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6345:
2522:
2456:
8903:
8840:
2695:
531:
459:
209:
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1067:, including names and dates, especially if the article does not have a "History" section. The origin of the subject's name should be explained if it is not self-evident.
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159:
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4881:
9045:
8748:
7185:
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5816:) 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:
4795:
2668:
671:
629:
524:
346:
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Generally, one way to determine which usage is appropriate on
Knowledge (XXG) is to look at prevalence in reliable sources in addition to relevant style guides, per
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3325:
3004:
before implementation. If there is no positive response, or if planned changes affect more than one article, consider notifying an appropriate Wikiproject, such as
2548:
1859:. Both are acceptable, but an article should be internally consistent. In an already consistent article, editors should refrain from changing one style to another.
9283:
654:
504:
142:
8107:
6158:
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2985:
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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8753:
8640:
7852:
4977:
721:
641:
294:
259:
226:
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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
9158:
9067:
9055:
8887:
8131:
and many diagrams in Knowledge (XXG) use sans-serif upright A instead. Graphs in books tend to use LaTeX conventions, but yet again there are wide variations.
693:
681:
511:
373:
329:
70:
4603:) and its adjacent characters should be avoided at present, since these characters are not yet universally supported and may have an inconsistent appearance.
3965:
also helps some spell checkers and screen readers treat math markup properly. Note that certain special characters (equal signs, absolute value bars) require
8790:
8722:
8660:
8655:
8635:
8589:
409:
398:
316:
246:
241:
221:
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6190:, 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.
5593:"–". 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
9100:
8963:
8743:
8614:
8176:
2806:
738:
586:
341:
196:
4475:
are intended for compatibility with legacy character sets, and Unicode-capable environments (like Knowledge (XXG)) should use the Greek letters instead (
4355:
Italicize lower-case Greek letters when they are variables or constants (in line with the general advice to italicize variables): the example expression
3899:
1269:
1120:
Use standard notation when possible. If an article requires non-standard or uncommon notation, they should be defined. For example, an article that uses
8866:
8861:
8645:
8630:
8567:
5319:
3172:
2932:
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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477:
231:
216:
149:
3227:
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.
1223:
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:
8515:
1107:
1099:
8712:
2802:
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.
938:
306:
8835:
8830:
8594:
5613:
Square brackets have two problems; they can occasionally cause problems with wiki markup, and editors sometimes 'fix' the brackets in asymmetrical
3440:
454:
449:
176:
4866:
4834:
2498:
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,
1454:
bare lists of facts and formulae, and relying too much on addressing the reader directly and referring to "we". Also avoid contentless clichés as
929:? A general approach to writing an article is to start simple and then move towards more abstract and technical subjects later on in the article.
9173:
9088:
8825:
8820:
8774:
8536:
4631:
tags, respectively, with no other formatting info. Font sizes and such should be entrusted to be handled with stylesheets. For example, to write
850:
728:
444:
439:
385:
3234:
The font size can be slightly larger than that of the surrounding text on some browsers, making text containing inline formulae harder to read.
2262:
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.
9213:
9208:
9035:
8599:
8572:
8305:
This style, adopted by Knowledge (XXG), is shared by Higham (1998), Halmos (1970), the Chicago Manual of Style, and many mathematics journals.
4080:
templates (which will set a serif font but not italics), use the wikitext markup of double apostrophes to make variables italic. For example:
1885:
conventions common in that area. Thus the act of changing an article from one set of conventions to another should not be undertaken lightly.
837:
832:
661:
181:
154:
7019:
1326:
If not included in the introduction, a history section can provide additional context and details on the topic's motivation and connections.
9251:
9148:
8676:
8650:
8543:
855:
266:
236:
3637:
renders exponents lower, especially under square roots, often resulting in a smaller square root which fits better in inline text: compare
9093:
8604:
8171:
3005:
2922:
Some notions are defined differently depending on context or author. Articles should contain some references that support the given usage.
732:
186:
46:
7831:), which is more common anyway. If absolutely necessary (e.g. when discussing the notation itself), use the Unicode character (e.g. 𝟙).
4684:
2989:
which should use HTML only, as LaTeX markup might cause uneven spacing in the table of contents, as well as the appearance of illegible
8815:
8800:
8795:
8717:
8707:
8691:
5053:, and is typical when used as a postfix. This character also appears on keyboards, and is thus easier to type and search for. Example:
1344:
434:
419:
414:
311:
301:
281:
8856:
8769:
8738:
8686:
468:
380:
336:
276:
8468:
8443:
8382:
5556:(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
2112:
9183:
8805:
8154:
6074:
5944:
4838:
3000:
from LaTeX to HTML, nor from non-LaTeX to LaTeX without a clear improvement. Proposed changes should generally be discussed on the
2996:
Large-scale formatting changes to an article or group of articles are likely to be controversial. One should not change formatting
1347:. Lastly, a well-written and complete article should have a "References" section. This topic is discussed in detail in the section
1296:. It may also be edifying to list non-examples, which almost-but-not-quite satisfy the definition. In keeping with the purpose and
812:
424:
4884:
are very likely to be displayed correctly, a significant number of viewers will have problems seeing all the characters listed at
9273:
5895:
markup is incompatible with the Media Viewer (used for full-screen image viewing on mobile devices), so until that is fixed, the
1147:
should provide an exact definition of the object, perhaps in a "Definition" section after section(s) of motivation. For example:
1085:, which can illuminate the use of the topic and its connections to other areas of mathematics or other non-mathematical subjects.
3119:
8293:
7751:
7273:. Changes from one style to another should be done only to make an article consistent with itself. Formatting changes should
886:
9188:
5446:
the formula for a general audience (not just mathematicians), or giving examples of its application, it is prudent to use the
3021:, the community of mathematical editors of English Knowledge (XXG) currently has no consensus about preferred formatting; see
817:
8421:
8221:
4238:
8810:
6600:
429:
351:
1749:. In addition to compromising the encyclopedic tone, these abbreviations are a form of jargon that may confuse the reader.
8508:
7299:. But this guide is rarely followed in reliable mathematical sources, and it is contradicted by other style guides, like
8681:
3557:
271:
58:
7923:); non-metric units can be either type of fraction, but the fraction style should be consistent throughout the article.
4830:
2846:
1488:
not an equation involving a previously known object. Also identify the nature of the entity being defined. Don't write:
9278:
8524:
7829:, LaTeX blackboard bold currently does not work with numerals. Use bold instead (e.g. {{math|'''1'''}} or <math: -->
4535:
tag for making text bold. Bold notation has been largely replaced by blackboard bold, which may be encoded in LaTeX as
900:
118:
50:
17:
4949:
9143:
9138:
9128:
8159:
3248:
If an inline formula needs to be typeset in LaTeX, keep the height down by using text-style or horizontal fractions:
3082:
3022:
787:
782:
772:
2925:
Important theorems should cite historical papers as an additional information (not necessarily for looking them up).
1102:, but others will never have encountered the notation. The latter group will be helped by an aside like "...where Δ(
3037:
8258:"-" as a valid representation of the minus sign. Except situations where "-" has to represent the minus sign in a
8149:
6921:
6773:
3073:
3057:
3033:
2976:
2919:
is for). Also, often one might want to find out more details (like the proof of a theorem stated in the article).
1036:
9230:
9228:
9123:
6930:
5570:
as an operator symbol is also discouraged except in abstract contexts (e.g. to denote an unspecified operator).
2937:
767:
126:
8501:
8483:
7890:
and with the baseline of the numbers aligned with the baseline of the surrounding text (as in 1/2). The use of
6680:
5759:
3837:
at the beginning. Such formatting can be removed if a formula is edited and need not be added to new formulae.
7860:
4062:
template to enclose a simple mention of a variable by name. This helps distinguish certain characters such as
1309:
7347:
Today, either blackboard bold or ordinary bold letters can be used interchangeably to represent the standard
4052:
Use italic text for variables, but never for numbers or symbols. To ensure an italic serif typeface, use the
1652:
If it is reasonable to do so, rephrase the sentence to avoid the use of the word "if" entirely. For example,
1319:
contains some details on how to create graphs and other pictures as well as how to include them in articles.
7344:
mathematical printing to denote certain common objects in a style distinct from other uses of bold letters.
6471:
6424:
5847:
4877:
1951:. A structure satisfying all the ring axioms except the existence of a multiplicative identity is called a
1281:
1268:
Other times, it may be better to separate the statement into its own section, as for long theorems like the
9203:
9168:
9163:
5908:
The use of √ with no overline is acceptable for simple expressions, as long as the operand is unambiguous.
3895:
The following sections cover the way of presenting simple inline formulae in HTML, instead of using LaTeX.
3001:
943:
Articles should start with a short introductory section, called the "lead". The purpose of the lead is to
827:
802:
797:
8109:
for a point. This allows easy use in LaTeX markup. However, older books tend to use upright letters as in
6405:
5659:
5614:
5467:
3690:
2416:
The context should clearly state that this is a semidirect product and should state which group is normal.
1168:
9193:
8550:
7857:
In mathematics articles, fractions should always be written either with a horizontal fraction bar (as in
6217:
comma, semicolon, or other punctuation at that place, the formula must have that punctuation at the end.
2940:
article has more information on this and also several examples for how the cited literature should look.
1315:
A picture can really bring home a point, and can often precede the mathematical discussion of a concept.
903:
contains guidelines for writing and editing clear, encyclopedic, attractive, and interesting articles on
860:
66:
7987:
For simple fractional subscripts or superscripts, the horizontal style is visually the least confusing:
5617:
to make them symmetrical. The nowiki tag can be used as a general solution to problems like this, as in
2097:
9178:
7322:
6199:
5917:
5775:
5717:
5402:
4926:
4812:
3735:
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807:
80:
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7624:
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5755:
5639:
5629:
3262:
2836:
2584:
2188:
2036:
1292:. Occasionally, it is appropriate to give a large number of computationally-flavored examples, as in
1246:
708:
9153:
2997:
2613:
792:
7887:
6401:
5447:
4953:
4858:
4803:. Formulae formatted without using TeX should use the same syntax to maintain the same appearance.
3865:
3784:, is adequate for articles that use only simple inline formulae and better for text-only browsers.
3521:
generates a smaller summation symbol and moves the limits to its right side. The rewritten formula
1336:
1144:
1111:
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1021:
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879:
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might be given as the hypothesis of a theorem whose conclusion is obviously true in the case that
1384:
There are several issues of writing style that are particularly relevant in mathematical writing.
8197:
8112:
7255:
for a variable. Upright fonts are sometimes used for standard, nearly universal constants, as in
6163:
6121:
6040:
5994:
5796:√ can be used when written on its own, but when part of a larger expression, can be problematic.
5649:
5069:(∗) for subscripts and when the bottom of the character should roughly align with the
2325:
2133:
1940:
1293:
1289:
1045:
1024:
9233:
4692:) for squares. This does not combine well with other powers, as the following comparison shows:
3942:
3244:
is fixed, it will not work in image captions when readers click through to see full-size images.
2461:
132:
6309:
6295:(parentheses may be omitted here, as the argument consists of a single term only; typeset from
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2441:
1273:
8465:
8440:
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8379:
7916:
6408:; if there is any risk that a term could become ambiguous for our readership, use parentheses.
5754:. As of December 2010, this character is not interpreted correctly by screen readers such as
2673:
2125:
2109:
2022:
1903:
1160:
8201:
2553:
2481:
1297:
8409:
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2819:
Knowledge (XXG):WikiProject Computer science/Manual of style (computer science) § Algorithms
2265:
2076:
2061:
1996:
922:
128:
5282:
5226:
4888:. One way to guarantee that an uncommon symbol is rendered correctly for all readers is to
3846:
8361:
7927:
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6357:
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5028:
4773:
4500:
2701:
2646:
2282:
2119:
2054:
1982:
1907:
8365:
7835:
7808:
discouraged in English Knowledge (XXG); instead, either the LaTeX rendering (for example
5887:
3933:
font to display a formula (whether as SVG or HTML). HTML math expressions should use the
3241:
7943:
6400:
Note: For potential pitfalls of forms not understood consistently across the board, see
5525:
and reachable in the "Math and logic" drop-down list below the edit box or via template
5014:
is appropriate; do not use the ASCII apostrophe (') or double quote (") in these cases.
3302:
2527:
8332:
6917:
6229:
does not line up with that of the running text—the punctuation can be placed after the
5899:
5800:
5793:
5596:
5457:
5018:
5011:
4945:
4438:
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3812:
2779:
2318:
2242:
2229:
2219:
2201:
2101:
2093:
1948:
1577:
When defining a term, do not use the phrase "if and only if". For example, instead of
1028:
1002:
872:
8092:
8004:
7979:
6143:
6018:
4748:
Moreover, the TeX engine used on Knowledge (XXG) may format simple superscripts using
2993:
to sections. Some of the issues presented by using LaTeX or HTML are discussed below.
1075:
Include a physical or geometric analogy or diagram if it can help introduce the topic.
958:
formulae displayed when hovering, they must be written in raw html (without templates
9267:
9232:
8478:
8247:
8224:, not a well-known language so generally not a good choice when showing an algorithm.
7990:
7971:
7893:
7348:
6187:
5810:
5702:
5528:
5158:
4511:
Commonly used sets of numbers are typeset in boldface, as in the set of real numbers
4202:
4192:
4074:
4056:
3966:
3959:
3949:
3936:
3906:
2756:
2069:
2065:
2050:
2029:
1952:
972:
130:
6233:
tag and then the whole formula (including the punctuation) can be enclosed with the
1387:
In the interest of clarity, sentences should not begin with a symbol. Do not write:
8432:
8255:
8233:
7819:
7683:
7587:
7300:
7279:
6412:
When operator (function) names do not have a pre-defined abbreviation, we may use
5836:
This method should be avoided whenever technically possible to do so. Instead, use
5495:
4969:
4965:
4876:
Not all of the symbols in these lists are displayed correctly on all browsers (see
3032:
the preferred formatting is the LaTeX markup, with a possible exception for simple
2386:
2184:
2143:
2089:
1777:
1704:
1699:
1694:
1581:
1492:
1475:
1471:
1467:
1463:
1459:
1455:
1404:
1391:
1239:
1235:
962:
926:
5334:
when writing the less-than sign, just like in HTML and XML. For example, to write
4861:(with notable exception of "+", "=", "|", as well as ",", ":", and three sorts of
980:). In the latter case the LaTeX source is displayed without the tags <math: -->
57:
It is a generally accepted standard that editors should attempt to follow, though
5054:
4961:
4957:
3237:
The download speed of a page is negatively affected if it contains many formulas.
3048:
Knowledge (XXG) allows editors to typeset mathematical formulae in (a subset of)
1809:
1793:
1723:
1718:
1656:
1618:
1521:
1435:
1426:
989:
The lead sentence should informally define or describe the subject. For example:
8459:
8397:
8315:
8259:
8251:
5751:
5549:
5050:
2832:
2742:
1944:
1231:
994:
904:
7804:). Font preferences vary from one mathematical author or publisher to another.
6064:
should be written as prose, to avoid using more vertical space than necessary:
8272:
7651:
7307:. This makes the more common practice to use an italic face for the constant
6913:
5585:
The correct encoding of the minus sign "−" is different from all varieties of
5320:
Knowledge (XXG):Manual of Style/Abbreviations § Unicode abbreviation ligatures
5256:
4846:
3921:
3508:{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {\pi ^{2}}{6}}.}
2828:
1978:
1964:
1960:
1285:
4972:. (The only exception is when discussing the Unicode characters themselves.)
2915:
Knowledge (XXG) articles cannot be a substitute for a textbook (that is what
8375:
8319:
8205:
6526:
includes correct spacing that would not be present with other means such as
5475:
4253:
for functions in other cases; for example when we define the function as in
2916:
2824:
2574:
2419:
The bar notation is discouraged because it is not supported by all browsers.
1971:
1956:
1482:
2122:
need not be bounded. In a bounded lattice, 0 and 1 are allowed to be equal.
23:
8053:
7919:
reasons among others. Metric units are given in decimal fractions (e.g.,
7289:. For example, the ISO 80000-2 recommends that the mathematical constant
2409:(with the bar on the side of the non-normal subgroup) with or without the
8089:
Recent geometry books tend to use an italic serif font in diagrams as in
5545:
5471:
5166:
5075:
2290:
1250:
1199:
1188:
8413:
8262:(including wiki code), it should not be seen in a rendered page, though.
8179:—advice on providing references for mathematical and scientific articles
7247:
Some authors prefer to use an upright (Roman) font for operators, as in
7095:{\displaystyle {\frac {dz}{dx}}={\frac {dz}{dy}}\cdot {\frac {dy}{dx}},}
1881:, as well as notation, such as the correct symbols to use for a subset.
7909:
4862:
4850:
4592:
4219:
3902:. Not all templates are recommended for use; in particular, use of the
3069:
2853:
primes = sieve sieve (p : xs) = p : sieve </syntaxhighlight: -->
2286:
1989:
1710:
The reader might not find what you write obvious. Instead, try to hint
1053:
8335:(¼, ½, and ¾) work with screen readers, but others, like ⅐, might not.
6186:
An exception would be if some of the definitions are very long (as in
1323:
should be highlighted with words such as "is defined by" in the text.
8453:
General style manuals often include advice on mathematics, including
8370:(second ed.), SIAM (Society for Industrial and Applied Mathematics),
5586:
3912:
template to format fractions is discouraged in mathematics articles.
3061:
2435:
5573:
Metric units often embed the notion of multiplication and division.
5565:
5419:
Standard algebraic notation is best for formulae, so two variables
1741:(if and only if), as well as quantifier symbols ∀ and ∃ instead of
8493:
8052:
6924:, Knowledge (XXG) articles usually use an italic font. One writes
6912:
For single-letter variables, constants, and operators such as the
5210:
for set substraction. (Either Unicode character can be used where
5170:
4854:
3930:
3049:
8081:
Knowledge (XXG):How to create charts for Knowledge (XXG) articles
6901:
An opinion: Why you should never use \mbox within Knowledge (XXG)
5577:
endorses the half-high dot (⋅) or a bare space for this purpose.
2389:
defining the product. The semidirect product may also be written
2075:
Separation axioms for topological spaces are as described on the
2039:
is not assumed to be separated. The term "prescheme" is not used.
5590:
5574:
3230:
Having LaTeX-based formulae inline has the following drawbacks:
3072:), depending on user preferences. For more details on this, see
3065:
8497:
8283:
Knowledge (XXG) talk:WikiProject Mathematics/Archive 68#ƒ or f?
6220:
If the formula is written in LaTeX, that is, surrounded by the
5905:
method or √ with no overline should be used in image captions.
1776:
when verbalizing quantifiers since it is ambiguous. Instead of
9234:
6108:{\displaystyle \mathbf {F} =\mathbf {b} \times a\mathbf {r} ,}
5978:{\displaystyle \mathbf {F} =\mathbf {b} \times a\mathbf {r} ,}
3053:
2317:) (and with the implied convention that the category is not a
1729:
Articles should avoid common blackboard abbreviations such as
1288:. Multiple related examples may also be given together, as in
925:, is it best to assume that a reader is already familiar with
133:
32:
8234:
Unicode Technical Report #25: Unicode Support for Mathematics
7853:
Knowledge (XXG):Manual of Style/Dates and numbers § Fractions
7826:
5255:(which on some systems is too small and can be confused with
4869:
includes markup for LaTeX and HTML, and Unicode code points.
4619:
Knowledge (XXG):Manual of Style (superscripts and subscripts)
4282:
Sets are usually written in upper case italics; for example:
5034:
can be useful to prevent overlap with italicized characters.
3808:. Take care of some necessary substitutions documented for
1724:
By a straightforward, if lengthy, algebraic calculation, ...
6347:(parentheses are required to clarify the intended argument)
5311:, which on some systems renders as two separate characters.
3175:). Instead, formulas may be placed on their own line using
3173:
Knowledge (XXG):Manual of Style/Accessibility § Indentation
3056:); the formulae are, for a default reader, translated into
1345:
Knowledge (XXG):Manual of Style/Layout § "See also" section
7797:{\displaystyle \mathbb {H} ^{i}(X,\Omega _{X}^{\bullet })}
4517:. Again, typically we use wiki markup: three apostrophes (
4249:, are not in italic font, but we use italic names such as
4952:(ASCII) letters should be used instead of the equivalent
1570:
In definitions, the symbol "=" is preferred over "≡" or "
1282:
Algebraic number theory § Failure of unique factorization
1272:, or to present multiple equivalent formulations, as for
7586:) and for certain other mathematical objects, including
5533:), which produces a symmetrically spaced centered dot: "
5462:. Do not use the letter "x" to indicate multiplication.
1955:. There is an exception for rings of operators, such as
1869:
Knowledge (XXG):WikiProject Logic/Standards for notation
1348:
8218:
7330:
6630:{\displaystyle x_{\text{this one}}=y_{\text{that one}}}
6207:
5925:
5783:
5725:
5410:
4934:
4918:" in an elementary article may make it more accessible.
4820:
4427:
For consistency with the LaTeX style, do not italicize
3079:
The LaTeX formulae can be displayed inline (like this:
2966:
2959:
1838:
1763:
1561:
1375:
1368:
102:
95:
88:
7908:) is discouraged in mathematics articles. The use of
7864:
4797:
will be an image, and for others it will be HTML like
3798:(optionally excluding the adjacent punctuation), e.g.
3738:
3560:
3267:
8115:
8095:
8016:
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7863:
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6146:
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6077:
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4776:
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3085:
2676:
2649:
2616:
2587:
2556:
2530:
2504:
2484:
2464:
2444:
8356:
A style guide specifically written for mathematics:
5708:
template to avoid line breaks and use the TeX font.
4770:
depending on user preferences. Thus, for some users
4451:
According to the Unicode Consortium, the characters
3898:Templates supporting HTML formatting are listed in
3624:{\textstyle \sum _{n=1}^{\infty }1/n^{2}=\pi ^{2}/6}
3196:. For instance, the formula above was typeset using
2422:
If the bar notation is used it should be entered as
2200:, or in contexts where there may be confusion with
1690:
Avoid, as far as possible, useless phrases such as:
1284:, while others may deserve their own section, as in
9222:
9116:
9081:
9018:
8997:
8896:
8880:
8849:
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3665:
3640:
3634:
3524:
3379:
3352:
3330:
3294:
3251:
3199:
3176:
1060:The lead section should include, when appropriate:
8427:Some finer points of typography are discussed in:
8123:
8101:
8037:
7960:
7878:
7796:
7736:
7707:
7674:
7642:
7610:
7578:
7550:
7519:
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7392:
7368:
7219:
7179:
7094:
6971:
6853:
6724:
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3723:
3623:
3507:
3319:
3283:
3160:
3108:
2689:
2662:
2631:
2602:
2570:symbol should be explicitly explained in the text.
2562:
2542:
2516:
2490:
2470:
2450:
953:and summarize the article's most important points.
8367:Handbook of Writing for the Mathematical Sciences
4978:Knowledge (XXG):Manual of Style/Dates and numbers
4841:may be useful when editing mathematics articles.
4623:Superscripts and subscripts should be wrapped in
3804:, or by replacing the tags with a template, e.g.
1719:It follows directly from this definition that ...
1317:How to create graphs for Knowledge (XXG) articles
1016:, 'study') is concerned with the properties of a
5841:tags and \sqrt{}, even if inline. For example:
3109:{\displaystyle \mathbf {x} \in \mathbb {R} ^{2}}
8458:University of Chicago Press Staff, ed. (2010),
7251:, for the differential operator, as opposed to
6898:, but this is now considered undesirable. See
4976:For when to use or not use Roman numerals, see
2745:of vectors should be denoted with a centre-dot
2577:, use superscript non-italic capital letter T:
8177:Knowledge (XXG):Scientific citation guidelines
2807:Knowledge (XXG):WikiProject Mathematics/Proofs
2228:is used (this does not affect the notation of
8509:
7843:markup should not be used in image captions.
5215:markup cannot be used for technical reasons.)
4886:Mathematical operators and symbols in Unicode
3435:is too large to be used inline, rendering as
3351:Often better formatting can be achieved with
2903:Including citations and literature references
880:
8:
8344:Not all fractions are available precomposed.
7295:should be typeset in an upright Roman font:
6854:{\displaystyle r=x_{predicted}-x_{observed}}
1035:, crumpling and bending, but not tearing or
939:Knowledge (XXG):Manual of Style/Lead section
9134:Categories, lists, and navigation templates
6972:{\displaystyle \int _{0}^{\pi }\sin x\,dx,}
5431:when presented in a formula. That is, when
4880:). Although the symbols that correspond to
3161:{\displaystyle \int _{0}^{\pi }\sin x\,dx.}
1290:Adjunction formula § Applications to curves
1011:
1005:
778:Categories, lists, and navigation templates
49:is a part of the English Knowledge (XXG)'s
8516:
8502:
8494:
8439:, Reading, Massachusetts: Addison-Wesley,
7267:; other authors use Roman boldface, as in
6890:For several years this manual recommended
6725:{\displaystyle \sum _{i=1}^{n}{y_{i}^{2}}}
3920:By default, regular text is rendered in a
3900:Category:Mathematical formatting templates
1431:may be decomposed into cosets, as follows.
1400:can be decomposed into cosets, as follows.
887:
873:
403:
367:
114:
9284:Knowledge (XXG) Manual of Style (science)
8464:(16th ed.), University of Chicago Press,
8318:before the punctuation instead, but it's
8116:
8114:
8094:
8025:
8021:
8015:
7950:
7945:
7915:(such as ½) is discouraged entirely, for
7879:{\displaystyle \textstyle {\frac {1}{2}}}
7865:
7862:
7785:
7780:
7761:
7757:
7756:
7753:
7728:
7724:
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7720:
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7695:
7694:
7691:
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7658:
7634:
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7602:
7598:
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7594:
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7565:
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7531:
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7455:
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7431:
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7406:
7404:
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7380:
7359:
7358:
7356:
7205:
7199:
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7069:
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6824:
6787:
6775:
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6688:
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6608:
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6544:
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6359:
6311:
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6097:
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2593:
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2586:
2555:
2529:
2503:
2483:
2463:
2443:
2218:; when written multiplicatively, e.g. as
2194:, when written additively, has notation Z
1824:, depending on what you wish to express.
5548:(*) as a multiplication sign outside of
5049:when the character should render like a
4843:Almost all mathematical operator symbols
4499:). This is also required for "micro" by
3845:Images generated from LaTeX markup have
1970:The ring with one element is called the
8487:) is being considered for merging. See
8189:
8172:Knowledge (XXG):WikiProject Mathematics
6958:
6496:{\displaystyle a\operatorname {tr} (A)}
6443:{\displaystyle 2\operatorname {csch} x}
5876:{\displaystyle {\sqrt {9}},{\sqrt{27}}}
5622:to have the ] treated as literal text.
5169:) in mathematical expressions, because
4890:force the symbol to display as an image
4867:list of mathematical symbols by subject
4835:list of mathematical symbols by subject
3147:
2852:<syntaxhighlight lang="Haskell": -->
2241:The standard notation for the abstract
1300:of an encyclopedia, examples should be
467:
117:
6245:This shows that {{nowrap|<math: -->
4968:, and not precomposed characters like
4954:Unicode characters in the U+21XX range
3833:) added at the end of the formula, or
3633:which fits much better inline. Adding
2981:One may set formulae using LaTeX (the
2623:
1967:, which we do not assume to be unital.
950:provide context regarding the subject,
69:. When in doubt, discuss first on the
5427:being multiplied are best written as
5271:(which on some systems is too large).
5171:tilde has other mathematical meanings
3859:<math alt="Square root of pi": -->
3724:{\displaystyle {\sqrt {x^{2}+y^{2}}}}
3060:images. They may also be rendered as
1349:§ Including literature and references
1136:to denote exponentiation (instead of
7:
8400:(1970), "How to Write Mathematics",
8314:It is technically possible to use a
8155:Knowledge (XXG):Mathematical symbols
5184:... \smallsetminus ...</math: -->
4839:Knowledge (XXG):Mathematical symbols
4607:
2944:Typesetting of mathematical formulae
978:), or in LaTeX (inside <math: -->
8002:
7977:
7839:
6068:Example 2: The foocity is given by
5938:Example 1: The foocity is given by
5891:
5837:
5734:There is a special Unicode symbol,
5211:
4893:
4682:Do not use special characters like
3925:
2982:
8117:
7777:
7682:, the additive and multiplicative
6551:
6548:
6545:
5912:Explanation of symbols in formulae
3769:{\textstyle {\sqrt {x^{2}+y^{2}}}}
3577:
3460:
2682:
2594:
2146:follows the Serre convention that
1737:(without loss of generality), and
1056:to three given circles in a plane.
31:
8245:Note that, aside of <math: -->
7551:{\displaystyle \mathbb {Z} _{p},}
7520:{\displaystyle \mathbb {F} _{q},}
4110:is a value on the horizontal axis
4098:is a value on the horizontal axis
3116:), as well as on their own line:
1440:be the corresponding subgroup of
1409:be the corresponding subgroup of
1294:Lambert W function § Applications
1052:is to construct circles that are
65:edit to this page should reflect
9246:
9245:
8144:Help for those writing a formula
7737:{\displaystyle \mathbb {G} _{m}}
7708:{\displaystyle \mathbb {G} _{a}}
7675:{\displaystyle \mathbb {A} _{K}}
7643:{\displaystyle \mathbb {P} ^{n}}
7611:{\displaystyle \mathbb {A} ^{n}}
7579:{\displaystyle \mathbb {Q} _{p}}
6246:\tfrac{1}{2} = 0.5</math: -->
6168:
6160:is the bazness coefficient, and
6126:
6098:
6087:
6079:
6045:
5999:
5968:
5957:
5949:
3284:{\displaystyle {\tfrac {1}{2}}x}
3087:
2907:Per the Knowledge (XXG) policy,
2603:{\displaystyle X^{\mathrm {T} }}
947:describe and define the subject,
36:
5179:... \setminus ...</math: -->
4032:The relationship is defined as
3973:The relationship is defined as
3781:
3780:HTML-generating formatting, as
2632:{\displaystyle X^{\mathsf {T}}}
1422:Instead, write something like:
18:Knowledge (XXG):Manual of Style
8160:Knowledge (XXG):Rendering math
7791:
7767:
6490:
6484:
6334:
6322:
5744:LATIN SMALL LETTER F WITH HOOK
4420:(It is also possible to enter
3879:{\displaystyle {\sqrt {\pi }}}
2845:Source code should always use
1714:something must hold, such as:
1270:Poincaré–Birkhoff–Witt theorem
1249:(number of elements) of every
1100:discriminant of a number field
1:
9051:References and external links
7489:{\displaystyle \mathbb {H} ,}
7465:{\displaystyle \mathbb {C} ,}
7441:{\displaystyle \mathbb {R} ,}
7417:{\displaystyle \mathbb {Q} ,}
7393:{\displaystyle \mathbb {Z} ,}
7369:{\displaystyle \mathbb {N} ,}
7220:{\displaystyle e^{i\theta }.}
6562:{\displaystyle 2{\rm {sin}}x}
5161:to mean "approximately" (and
4584:{\displaystyle \mathbb {R} .}
3372:tag, which translates to the
3011:For inline formulae, such as
677:References and external links
8491:to help reach a consensus. ›
8320:seldom respected by browsers
8236:, §2.5 Duplicated Characters
8124:{\displaystyle \mathrm {A} }
6894:as a workaround for lack of
6175:{\displaystyle \mathbf {r} }
6133:{\displaystyle \mathbf {b} }
6052:{\displaystyle \mathbf {r} }
6006:{\displaystyle \mathbf {b} }
5277:... \ngtr ...</math: -->
4831:list of mathematical symbols
3664:<math display=inline: -->
3523:<math display=inline: -->
2938:Knowledge (XXG):Cite sources
2430:(⋊) for maximum portability.
1355:Writing style in mathematics
8904:Specific naming conventions
8461:The Chicago Manual of Style
8402:Enseignements Mathématiques
6035:is the bazness coefficient,
5221:... \circ ...</math: -->
4613:Superscripts and subscripts
4599:(plain text ℝ or math font
3348:is too tall to fit inline.
3198:<math display=block: -->
3008:for mathematical articles.
2849:. For example this markup:
2788:, never with juxtaposition
2471:{\displaystyle \subsetneq }
2370:is the normal subgroup and
1910:" has two common meanings:
532:Specific naming conventions
9300:
8583:Organizing by subject area
8078:
7850:
7320:
6340:{\displaystyle 2\sin(x+1)}
6197:
6194:Punctuation after formulae
5915:
5773:
5715:
5589:"-‐‑", as well as from en-
5400:
5317:
4975:
4924:
4810:
4616:
4605:
4497:GREEK CAPITAL LETTER OMEGA
4369:would then be typeset by:
3036:of Latin letters, digits,
2974:
2949:
2816:
2517:{\displaystyle A\subset B}
2451:{\displaystyle \subseteq }
1866:
1828:
1753:
1695:It is easily seen that ...
1551:
1480:
1468:It must be emphasized that
1358:
1286:Chain rule § First example
936:
78:
9241:
9209:Wikimedia sister projects
8531:
8202:WP:DICT#Major differences
8150:Help:Displaying a formula
5886:Because of Mediawiki bug
5750:), sometimes used as the
4383:''λ'' + ''y''
3074:Help:Displaying a formula
2977:Help:Displaying a formula
2856:generates the following:
2690:{\displaystyle X^{\top }}
2550:). All other uses of the
1922:which may also be called
1914:which may also be called
1464:It must be mentioned that
1020:that are preserved under
1012:
1006:
833:Wikimedia sister projects
8489:templates for discussion
8217:This example, from here
7811:\mathbb{Z}</math: -->
6182:is the quuxance vector.
5766:should be used instead.
5762:. An italicized letter
5760:NonVisual Desktop Access
5698:These templates use the
5454:in HTML or accessed via
3924:font. The TeX markup of
3860:\sqrt{\pi}</math: -->
3038:common punctuation marks
3002:talk page of the article
2858:
2704:, infima are written as
2563:{\displaystyle \subset }
2491:{\displaystyle \subset }
2428:{{unicode|⋊}}
2424:{{unicode|⋉}}
1930:if the context permits.
1863:Mathematical conventions
1046:Euclidean plane geometry
9274:WikiProject Mathematics
8376:10.1137/1.9780898719550
8038:{\displaystyle x^{1/2}}
7278:the same principles as
6288:{\displaystyle 2\sin x}
6140:is the barness vector,
6059:is the quuxance vector.
4878:Help:Special characters
4523:) rather than the HTML
3006:WikiProject Mathematics
2278:odd and greater than 1.
2096:with finite joins, not
1893:Terminology conventions
1460:It should be noted that
9279:Knowledge (XXG) how-to
8125:
8103:
8076:
8039:
7962:
7880:
7830:\bold{1}</math: -->
7798:
7738:
7709:
7676:
7644:
7612:
7580:
7552:
7521:
7490:
7466:
7442:
7418:
7394:
7370:
7221:
7181:
7096:
7004:—note the thin space (
6973:
6855:
6732:(correct—typeset from
6726:
6704:
6637:(correct—typeset from
6631:
6563:
6497:
6444:
6406:implied multiplication
6380:
6341:
6289:
6184:
6176:
6154:
6134:
6109:
6062:
6053:
6029:
6013:is the barness vector,
6007:
5979:
5877:
5752:Florin currency symbol
5293:
5292:{\displaystyle \ngtr }
5237:
5236:{\displaystyle \circ }
4791:
4585:
4507:Common sets of numbers
4222:are never italicized:
4218:is the mass of a foo.
3880:
3857:element. For example,
3770:
3725:
3625:
3581:
3509:
3464:
3321:
3285:
3162:
3110:
2691:
2664:
2633:
2604:
2564:
2544:
2518:
2492:
2472:
2452:
2178:Notational conventions
1266:
1238:, states that for any
1217:
1058:
1041:
8841:Writing about fiction
8392:More style guidance:
8126:
8104:
8056:
8040:
8008:x^{1/2}</math: -->
7963:
7930:in abstract algebra:
7926:Only "/" is used for
7913:precomposed fractions
7886:), or with a forward
7881:
7799:
7739:
7710:
7677:
7645:
7613:
7581:
7553:
7522:
7491:
7467:
7443:
7419:
7395:
7371:
7222:
7182:
7180:{\displaystyle x+iy,}
7097:
6974:
6856:
6727:
6684:
6632:
6564:
6498:
6445:
6381:
6379:{\displaystyle 2sinx}
6342:
6290:
6177:
6155:
6135:
6110:
6066:
6054:
6030:
6008:
5980:
5936:
5878:
5544:Do not use the ASCII
5435:a formula, don't use
5294:
5238:
5078:for a canonical list.
4792:
4790:{\displaystyle x^{2}}
4606:Further information:
4591:However, the special
4586:
4485:GREEK SMALL LETTER MU
4431:Greek letters; e.g.
3881:
3822:Deprecated formatting
3800:({{nobr|<math: -->
3771:
3726:
3626:
3561:
3510:
3444:
3322:
3286:
3163:
3111:
2692:
2665:
2663:{\displaystyle X^{T}}
2634:
2605:
2565:
2545:
2519:
2493:
2473:
2453:
2321:unless that is said).
2053:is not assumed to be
1916:non-negative integers
1260:divides the order of
1225:
1149:
1072:informal introduction
1065:Historical motivation
1042:
991:
460:Writing about fiction
165:Organizing by subject
119:Manual of Style (MoS)
59:occasional exceptions
9184:Talk page guidelines
8872:Stringed instruments
8578:Disambiguation pages
8113:
8093:
8014:
7944:
7861:
7752:
7719:
7690:
7657:
7625:
7593:
7561:
7530:
7499:
7475:
7451:
7427:
7403:
7379:
7355:
7198:
7159:
7020:
6931:
6774:
6681:
6601:
6537:
6472:
6425:
6393:2sin x</math: -->
6358:
6310:
6270:
6164:
6144:
6122:
6075:
6041:
6019:
5995:
5945:
5848:
5283:
5227:
5076:Asterisk#Mathematics
4845:have their specific
4774:
4595:characters, such as
4570:
3866:
3736:
3691:
3558:
3441:
3303:
3263:
3120:
3083:
2837:programming language
2823:An article about an
2674:
2647:
2614:
2585:
2554:
2528:
2502:
2482:
2462:
2442:
2025:is assumed to be an
1211:) is an open set in
1050:Apollonius's problem
933:Article introduction
899:This subpage of the
813:Talk page guidelines
488:Stringed instruments
160:Disambiguation pages
8989:Trinidad and Tobago
8919:France (and French)
8914:China (and Chinese)
8414:10.5169/seals-43857
8362:Higham, Nicholas J.
8166:General information
8049:Graphs and diagrams
7983:R / A</math: -->
7961:{\displaystyle R/A}
7790:
7190:x+iy,</math: -->
6948:
6908:Roman versus italic
6720:
6402:order of operations
5448:multiplication sign
5397:Multiplication sign
4859:General Punctuation
4566:, which renders as
3862:generates an image
3320:{\displaystyle x/2}
3137:
2847:syntax highlighting
2543:{\displaystyle A=B}
2458:, proper subset by
2274:, and are zero for
1733:(with respect to),
1145:mathematical object
1143:An article about a
617:Trinidad and Tobago
552:France (and French)
542:China (and Chinese)
9189:Template namespace
8271:Latin Extended-B,
8198:ring (mathematics)
8121:
8099:
8077:
8035:
7958:
7876:
7875:
7794:
7776:
7734:
7705:
7672:
7640:
7608:
7576:
7548:
7517:
7486:
7462:
7438:
7414:
7390:
7366:
7217:
7177:
7092:
7002:dx ,</math: -->
6969:
6959:
6934:
6851:
6722:
6706:
6627:
6559:
6493:
6440:
6376:
6337:
6285:
6258:Multi-letter names
6172:
6150:
6130:
6105:
6049:
6025:
6003:
5975:
5926:MOS:EXPLAINSYMBOLS
5873:
5490:An alternative to
5485:−42 = 9 × (−5) + 3
5470:26 by 4, 6 is the
5289:
5233:
4897:with LaTeX markup.
4787:
4581:
4305:would be written:
4239:standard functions
3876:
3853:attribute for the
3766:
3721:
3621:
3505:
3317:
3281:
3276:
3158:
3148:
3123:
3106:
3044:Using LaTeX markup
2687:
2660:
2629:
2600:
2560:
2540:
2514:
2488:
2468:
2448:
2336:should be written
2326:semidirect product
2309:) rather than Mor(
2126:Elliptic functions
2068:for our notion of
2016:Algebraic geometry
1912:{0, 1, 2, 3, ...},
1562:MOS:MATH#DEFSYMBOL
1330:Concluding matters
1228:Lagrange's theorem
1161:topological spaces
981:and </math: -->
921:in the context of
818:Template namespace
762:Related guidelines
9261:
9260:
9199:Understandability
9061:Structure drawing
9010:Latter Day Saints
8811:Lyrics and poetry
8754:Stand-alone lists
8641:Dates and numbers
8102:{\displaystyle A}
7873:
7841:...</math: -->
7087:
7064:
7041:
6624:
6611:
6517:(A)</math: -->
6153:{\displaystyle a}
6028:{\displaystyle a}
5893:...</math: -->
5871:
5856:
5839:...</math: -->
5620:]</nowiki: -->
5213:...</math: -->
5067:ASTERISK OPERATOR
4895:...</math: -->
4608:§ Blackboard bold
3967:special attention
3927:...</math: -->
3874:
3806:({{tmath|1=...}})
3801:...</math: -->
3795:...</math: -->
3764:
3719:
3500:
3480:
3275:
3052:markup (see also
3023:WP:Rendering math
2987:section headings,
2831:or in some cases
2266:Bernoulli numbers
2255:in geometry and D
2023:algebraic variety
1997:Clifford algebras
1943:is assumed to be
1924:positive integers
979:...</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
9291:
9249:
9248:
9235:
9159:Military history
9068:Computer science
9041:Compound classes
8888:Military history
8518:
8511:
8504:
8495:
8473:
8448:
8433:Knuth, Donald E.
8416:
8387:
8345:
8342:
8336:
8329:
8323:
8312:
8306:
8303:
8297:
8294:October 2020 RfC
8291:
8285:
8280:
8274:
8269:
8263:
8252:parser functions
8243:
8237:
8231:
8225:
8215:
8209:
8194:
8130:
8128:
8127:
8122:
8120:
8108:
8106:
8105:
8100:
8074:
8070:
8064:
8060:
8044:
8042:
8041:
8036:
8034:
8033:
8029:
8009:
8000:
7996:
7994:1/2</sup: -->
7984:
7975:
7974:|''R'' / ''A''}}
7967:
7965:
7964:
7959:
7954:
7939:
7928:quotient objects
7922:
7907:
7906:
7902:
7897:
7885:
7883:
7882:
7877:
7874:
7866:
7842:
7817:
7816:\Z</math: -->
7812:
7803:
7801:
7800:
7795:
7789:
7784:
7766:
7765:
7760:
7743:
7741:
7740:
7735:
7733:
7732:
7727:
7714:
7712:
7711:
7706:
7704:
7703:
7698:
7681:
7679:
7678:
7673:
7671:
7670:
7665:
7649:
7647:
7646:
7641:
7639:
7638:
7633:
7620:projective space
7617:
7615:
7614:
7609:
7607:
7606:
7601:
7585:
7583:
7582:
7577:
7575:
7574:
7569:
7557:
7555:
7554:
7549:
7544:
7543:
7538:
7526:
7524:
7523:
7518:
7513:
7512:
7507:
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7493:
7492:
7487:
7482:
7471:
7469:
7468:
7463:
7458:
7447:
7445:
7444:
7439:
7434:
7423:
7421:
7420:
7415:
7410:
7399:
7397:
7396:
7391:
7386:
7375:
7373:
7372:
7367:
7362:
7333:
7312:
7298:
7294:
7271:
7266:
7262:
7258:
7254:
7250:
7242:
7240:
7237:
7233:
7226:
7224:
7223:
7218:
7213:
7212:
7191:
7186:
7184:
7183:
7178:
7152:
7150:
7146:
7142:
7139:
7136:
7133:
7129:
7125:
7122:
7118:
7114:
7110:
7107:
7101:
7099:
7098:
7093:
7088:
7086:
7078:
7070:
7065:
7063:
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7047:
7042:
7040:
7032:
7024:
7013:
7009:
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6994:
6991:
6987:
6984:
6978:
6976:
6975:
6970:
6947:
6942:
6897:
6893:
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6883:
6879:
6875:
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6729:
6728:
6723:
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6669:
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6636:
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6582:
6579:
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6566:
6565:
6560:
6555:
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6518:
6516:
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6502:
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6499:
6494:
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6456:
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6292:
6291:
6286:
6248:
6243:template, as in
6242:
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6232:
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6223:
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6179:
6178:
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5683:
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5675:
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5665:. For instance:
5664:
5658:
5654:
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5638:
5634:
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5621:
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5600:
5568:
5564:
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5438:
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5360:
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5310:
5309:NOT GREATER-THAN
5307:
5304:
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5296:
5295:
5290:
5278:
5270:
5267:
5264:
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5251:
5248:
5247:
5242:
5240:
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5234:
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5214:
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5206:
5203:
5202:
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4997:
4994:
4991:
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4971:
4967:
4963:
4959:
4937:
4917:
4896:
4837:and the list at
4823:
4802:
4796:
4794:
4793:
4788:
4786:
4785:
4769:
4768:
4765:
4762:
4758:
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4752:
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4630:
4626:
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4598:
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4399:
4396:
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4330:
4327:
4324:
4321:
4318:
4315:
4312:
4300:
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4272:
4252:
4248:
4244:
4228:
4217:
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4167:
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4097:
4093:
4090:
4087:
4079:
4073:
4069:
4065:
4061:
4055:
4042:
4028:will result in:
4023:
4022:
4018:
4015:
4012:
4008:
4005:
4002:
3999:
3995:
3992:
3989:
3986:
3983:
3980:
3977:
3964:
3958:
3954:
3948:
3940:
3928:
3911:
3905:
3885:
3883:
3882:
3877:
3875:
3870:
3861:
3856:
3852:
3836:
3832:
3817:
3811:
3807:
3803:
3796:
3777:, respectively.
3776:
3775:
3773:
3772:
3767:
3765:
3763:
3762:
3750:
3749:
3740:
3730:
3728:
3727:
3722:
3720:
3718:
3717:
3705:
3704:
3695:
3687:which render as
3686:
3684:
3683:
3679:
3675:
3671:
3668:
3661:
3659:
3658:
3654:
3650:
3646:
3643:
3636:
3632:
3630:
3628:
3627:
3622:
3617:
3612:
3611:
3599:
3598:
3589:
3580:
3575:
3552:
3550:
3548:
3545:
3541:
3537:
3534:
3530:
3527:
3520:
3514:
3512:
3511:
3506:
3501:
3496:
3495:
3486:
3481:
3479:
3478:
3466:
3463:
3458:
3434:
3432:
3431:
3427:
3423:
3420:
3417:
3414:
3410:
3406:
3402:
3398:
3395:
3392:
3389:
3385:
3382:
3375:
3371:
3370:
3367:
3364:
3361:
3358:
3355:
3347:
3345:
3344:
3340:
3336:
3333:
3326:
3324:
3323:
3318:
3313:
3298:
3296:
3290:
3288:
3287:
3282:
3277:
3268:
3258:
3256:
3254:
3223:
3221:
3219:
3215:
3212:
3209:
3205:
3202:
3195:
3194:
3191:
3188:
3185:
3182:
3179:
3167:
3165:
3164:
3159:
3136:
3131:
3115:
3113:
3112:
3107:
3105:
3104:
3099:
3090:
3020:
2984:
2969:
2962:
2898:
2895:
2892:
2889:
2886:
2883:
2880:
2877:
2874:
2871:
2868:
2865:
2862:
2769:
2754:
2737:
2727:
2714:or as a product
2713:
2696:
2694:
2693:
2688:
2686:
2685:
2669:
2667:
2666:
2661:
2659:
2658:
2638:
2636:
2635:
2630:
2628:
2627:
2626:
2609:
2607:
2606:
2601:
2599:
2598:
2597:
2569:
2567:
2566:
2561:
2549:
2547:
2546:
2541:
2523:
2521:
2520:
2515:
2497:
2495:
2494:
2489:
2477:
2475:
2474:
2469:
2457:
2455:
2454:
2449:
2429:
2425:
2408:
2398:
2384:
2365:
2350:
2268:are denoted by B
2106:General Topology
2077:separation axiom
1921:
1913:
1841:
1823:
1807:
1791:
1766:
1725:
1720:
1706:
1701:
1696:
1686:
1648:
1610:
1564:
1546:
1517:Instead, write:
1513:
1477:
1473:
1469:
1465:
1461:
1457:
1449:
1432:
1418:
1401:
1378:
1371:
1274:Nakayama's lemma
1206:
1018:geometric object
1015:
1014:
1009:
1008:
977:
971:
967:
961:
923:abstract algebra
889:
882:
875:
694:Computer science
667:Compound classes
512:Military history
404:
368:
134:
115:
105:
98:
91:
40:
39:
33:
27:
9299:
9298:
9294:
9293:
9292:
9290:
9289:
9288:
9264:
9263:
9262:
9257:
9237:
9236:
9231:
9218:
9112:
9077:
9014:
8993:
8892:
8876:
8845:
8791:Anime and manga
8779:
8758:
8727:
8723:Trivia sections
8696:
8682:Image placement
8665:
8661:Titles of works
8656:Text formatting
8619:
8610:Self-references
8590:Gender identity
8556:
8527:
8525:Manual of Style
8522:
8492:
8484:Manual of Style
8471:
8457:
8446:
8431:
8417:. Reprinted in
8396:
8385:
8360:
8354:
8352:Further reading
8349:
8348:
8343:
8339:
8330:
8326:
8313:
8309:
8304:
8300:
8292:
8288:
8281:
8277:
8270:
8266:
8244:
8240:
8232:
8228:
8216:
8212:
8195:
8191:
8186:
8168:
8146:
8141:
8111:
8110:
8091:
8090:
8083:
8072:
8068:
8062:
8058:
8051:
8017:
8012:
8011:
7998:
7988:
7969:
7942:
7941:
7931:
7920:
7904:
7900:
7899:
7891:
7859:
7858:
7855:
7849:
7827:a rendering bug
7814:
7809:
7755:
7750:
7749:
7746:hypercohomology
7722:
7717:
7716:
7693:
7688:
7687:
7660:
7655:
7654:
7628:
7623:
7622:
7596:
7591:
7590:
7564:
7559:
7558:
7533:
7528:
7527:
7502:
7497:
7496:
7473:
7472:
7449:
7448:
7425:
7424:
7401:
7400:
7377:
7376:
7353:
7352:
7341:blackboard bold
7337:
7336:
7329:
7325:
7319:
7317:Blackboard bold
7308:
7296:
7290:
7269:
7264:
7260:
7256:
7252:
7248:
7241:.</math: -->
7238:
7235:
7231:
7201:
7196:
7195:
7157:
7156:
7151:,</math: -->
7148:
7144:
7140:
7137:
7134:
7131:
7127:
7123:
7120:
7116:
7112:
7108:
7105:
7079:
7071:
7056:
7048:
7033:
7025:
7018:
7017:
7006:
6999:
6995:
6992:
6989:
6985:
6982:
6929:
6928:
6910:
6895:
6891:
6881:
6877:
6873:
6869:
6820:
6783:
6772:
6771:
6758:
6754:
6750:
6746:
6742:
6738:
6735:
6679:
6678:
6665:
6661:
6658:
6655:
6651:
6647:
6644:
6641:
6617:
6604:
6599:
6598:
6587:x</math: -->
6584:
6580:
6577:
6535:
6534:
6527:
6523:
6514:
6510:
6507:
6470:
6469:
6464:x</math: -->
6461:
6457:
6454:
6423:
6422:
6414:
6356:
6355:
6308:
6307:
6302:x</math: -->
6299:
6268:
6267:
6260:
6255:
6244:
6240:
6234:
6230:
6225:
6221:
6214:
6213:
6206:
6202:
6196:
6162:
6161:
6142:
6141:
6120:
6119:
6073:
6072:
6039:
6038:
6017:
6016:
5993:
5992:
5943:
5942:
5932:
5931:
5924:
5920:
5914:
5902:
5896:
5846:
5845:
5829:
5827:
5822:
5820:
5813:
5807:
5806:(often seen as
5803:
5797:
5790:
5789:
5782:
5778:
5772:
5763:
5747:
5743:
5740:
5736:
5735:
5732:
5731:
5724:
5720:
5714:
5712:Function symbol
5705:
5699:
5691:
5680:
5676:
5673:
5670:
5662:
5656:
5652:
5646:
5642:
5636:
5632:
5626:
5619:<nowiki: -->
5618:
5611:
5609:Square brackets
5602:
5594:
5583:
5566:
5562:
5558:
5557:
5553:
5526:
5521:
5518:
5515:
5512:
5509:
5506:
5503:
5498:
5491:
5484:
5480:26 = 6 × 4 + 2.
5479:
5455:
5451:
5436:
5417:
5416:
5409:
5405:
5399:
5388:
5384:
5381:
5378:
5375:
5362:
5358:
5355:
5352:
5349:
5346:
5335:
5331:
5327:
5322:
5308:
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5301:
5300:
5281:
5280:
5275:
5268:
5265:
5261:
5260:
5252:
5249:
5245:
5244:
5225:
5224:
5219:
5208:REVERSE SOLIDUS
5207:
5204:
5200:
5199:
5195:
5192:
5188:
5187:
5182:
5177:
5162:
5154:
5151:
5147:
5146:
5142:
5139:
5135:
5134:
5128:
5125:
5121:
5120:
5116:
5113:
5109:
5108:
5102:
5099:
5095:
5094:
5090:
5087:
5083:
5082:
5066:
5063:
5059:
5058:
5046:
5043:
5039:
5038:
5031:
5025:
5021:
5015:
5007:
5004:
5000:
4999:
4995:
4992:
4988:
4987:
4981:
4956:. For example,
4941:
4940:
4933:
4929:
4909:
4908:" rather than "
4827:
4826:
4821:MOS:MATHSPECIAL
4819:
4815:
4809:
4807:Special symbols
4798:
4777:
4772:
4771:
4766:
4763:
4760:
4756:
4753:
4750:
4740:
4721:
4715:
4696:
4689:
4683:
4673:
4670:
4667:
4663:
4660:
4657:
4654:
4651:
4648:
4645:
4638:
4632:
4628:
4624:
4621:
4615:
4610:
4600:
4596:
4568:
4567:
4562:
4559:
4556:
4553:
4549:
4546:
4543:
4540:
4537:
4531:
4528:
4525:
4519:
4512:
4509:
4501:MOS:UNITSYMBOLS
4496:
4493:
4489:
4488:
4484:
4481:
4477:
4476:
4472:
4469:
4465:
4464:
4460:
4457:
4453:
4452:
4433:
4432:
4413:
4410:
4407:
4403:
4400:
4397:
4394:
4391:
4388:
4385:
4382:
4379:
4376:
4373:
4356:
4353:
4341:
4336:
4332:
4328:
4325:
4322:
4319:
4316:
4313:
4310:
4286:
4280:
4255:
4254:
4250:
4246:
4242:
4235:
4223:
4216:
4210:
4205:
4199:
4195:
4189:
4175:
4164:
4160:
4157:
4154:
4150:
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4144:
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4137:
4134:
4131:
4128:
4125:
4122:
4119:
4107:
4095:
4091:
4088:
4085:
4077:
4071:
4067:
4063:
4059:
4053:
4050:
4033:
4020:
4016:
4013:
4010:
4006:
4003:
4000:
3997:
3993:
3990:
3987:
3984:
3981:
3978:
3975:
3962:
3956:
3952:
3946:
3934:
3918:
3916:Font formatting
3909:
3903:
3893:
3864:
3863:
3858:
3854:
3850:
3843:
3834:
3830:
3824:
3815:
3809:
3805:
3799:
3793:
3792:Directly using
3790:
3782:described below
3754:
3741:
3734:
3733:
3732:
3709:
3696:
3689:
3688:
3681:
3677:
3673:
3669:
3666:
3663:
3656:
3652:
3648:
3644:
3641:
3638:
3603:
3590:
3556:
3555:
3554:
3546:
3543:
3539:
3535:
3532:
3528:
3525:
3522:
3518:
3515:
3487:
3470:
3439:
3438:
3429:
3425:
3421:
3418:
3415:
3412:
3408:
3404:
3400:
3396:
3393:
3390:
3387:
3383:
3380:
3377:
3373:
3368:
3365:
3362:
3359:
3356:
3353:
3342:
3338:
3334:
3331:
3328:
3301:
3300:
3292:
3261:
3260:
3252:
3249:
3217:
3213:
3210:
3207:
3203:
3200:
3197:
3192:
3189:
3186:
3183:
3180:
3177:
3118:
3117:
3094:
3081:
3080:
3046:
3030:on its own line
3012:
2979:
2973:
2972:
2965:
2958:
2954:
2946:
2905:
2900:
2899:
2896:
2893:
2890:
2887:
2884:
2881:
2878:
2875:
2872:
2869:
2866:
2863:
2860:
2854:
2821:
2815:
2799:
2759:
2746:
2729:
2719:
2705:
2677:
2672:
2671:
2650:
2645:
2644:
2617:
2612:
2611:
2588:
2583:
2582:
2552:
2551:
2526:
2525:
2500:
2499:
2480:
2479:
2460:
2459:
2440:
2439:
2427:
2423:
2400:
2390:
2371:
2361:
2352:
2346:
2337:
2283:category theory
2273:
2261:
2254:
2237:
2230:isometry groups
2227:
2199:
2180:
2128:are written in
2094:preordered sets
2086:
2046:
2018:
1981:is not assumed
1936:
1928:natural numbers
1920:{1, 2, 3, ...},
1919:
1911:
1908:natural numbers
1900:
1898:Natural numbers
1895:
1871:
1865:
1845:
1844:
1839:MOS:MATH#PLURAL
1837:
1833:
1770:
1769:
1762:
1758:
1590:if and only if
1568:
1567:
1560:
1556:
1544:
1511:
1485:
1417:is then finite.
1382:
1381:
1374:
1367:
1363:
1357:
1332:
1202:
1092:
1010:, 'place', and
975:
969:
965:
959:
941:
935:
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:
9297:
9295:
9287:
9286:
9281:
9276:
9266:
9265:
9259:
9258:
9256:
9255:
9242:
9239:
9238:
9229:
9227:
9226:
9224:
9220:
9219:
9217:
9216:
9211:
9206:
9201:
9196:
9191:
9186:
9181:
9176:
9171:
9166:
9161:
9156:
9151:
9146:
9144:Citing sources
9141:
9139:Categorization
9136:
9131:
9129:Article titles
9126:
9120:
9118:
9114:
9113:
9111:
9110:
9109:
9108:
9101:Figure skating
9098:
9097:
9096:
9085:
9083:
9079:
9078:
9076:
9075:
9070:
9065:
9064:
9063:
9058:
9053:
9048:
9043:
9033:
9028:
9022:
9020:
9016:
9015:
9013:
9012:
9007:
9001:
8999:
8995:
8994:
8992:
8991:
8986:
8981:
8976:
8971:
8966:
8961:
8956:
8951:
8946:
8941:
8936:
8931:
8926:
8921:
8916:
8911:
8906:
8900:
8898:
8894:
8893:
8891:
8890:
8884:
8882:
8878:
8877:
8875:
8874:
8869:
8864:
8859:
8853:
8851:
8847:
8846:
8844:
8843:
8838:
8833:
8828:
8823:
8818:
8813:
8808:
8803:
8798:
8793:
8787:
8785:
8781:
8780:
8778:
8777:
8772:
8766:
8764:
8760:
8759:
8757:
8756:
8751:
8749:Road junctions
8746:
8744:Lists of works
8741:
8735:
8733:
8729:
8728:
8726:
8725:
8720:
8715:
8710:
8704:
8702:
8698:
8697:
8695:
8694:
8689:
8684:
8679:
8673:
8671:
8667:
8666:
8664:
8663:
8658:
8653:
8648:
8643:
8638:
8636:Capitalization
8633:
8627:
8625:
8621:
8620:
8618:
8617:
8615:Words to watch
8612:
8607:
8602:
8597:
8592:
8587:
8586:
8585:
8575:
8570:
8564:
8562:
8558:
8557:
8555:
8554:
8547:
8540:
8532:
8529:
8528:
8523:
8521:
8520:
8513:
8506:
8498:
8476:
8475:
8474:
8469:
8451:
8450:
8444:
8425:
8424:
8390:
8389:
8383:
8353:
8350:
8347:
8346:
8337:
8333:ISO/IEC 8859-1
8331:Characters in
8324:
8307:
8298:
8286:
8275:
8264:
8238:
8226:
8210:
8188:
8187:
8185:
8182:
8181:
8180:
8174:
8167:
8164:
8163:
8162:
8157:
8152:
8145:
8142:
8140:
8137:
8119:
8098:
8067:The length of
8066:
8050:
8047:
8032:
8028:
8024:
8020:
7993:|x<sup: -->
7957:
7953:
7949:
7872:
7869:
7848:
7845:
7793:
7788:
7783:
7779:
7775:
7772:
7769:
7764:
7759:
7731:
7726:
7702:
7697:
7669:
7664:
7637:
7632:
7605:
7600:
7573:
7568:
7547:
7542:
7537:
7516:
7511:
7506:
7485:
7481:
7461:
7457:
7437:
7433:
7413:
7409:
7389:
7385:
7365:
7361:
7349:number systems
7335:
7334:
7326:
7321:
7318:
7315:
7245:
7244:
7227:(typeset from
7216:
7211:
7208:
7204:
7193:
7187:(typeset from
7176:
7173:
7170:
7167:
7164:
7154:
7102:(typeset from
7091:
7085:
7082:
7077:
7074:
7068:
7062:
7059:
7054:
7051:
7045:
7039:
7036:
7031:
7028:
7015:
6979:(typeset from
6968:
6965:
6962:
6957:
6954:
6951:
6946:
6941:
6937:
6922:Euler's number
6918:imaginary unit
6909:
6906:
6888:
6887:
6884:</math: -->
6865:—typeset from
6848:
6845:
6842:
6839:
6836:
6833:
6830:
6827:
6823:
6819:
6814:
6811:
6808:
6805:
6802:
6799:
6796:
6793:
6790:
6786:
6782:
6779:
6765:
6764:
6761:</math: -->
6718:
6713:
6709:
6702:
6697:
6694:
6691:
6687:
6672:
6671:
6668:</math: -->
6620:
6616:
6607:
6591:
6590:
6573:—typeset from
6558:
6553:
6550:
6547:
6542:
6521:
6520:
6503:(typeset from
6492:
6489:
6486:
6483:
6480:
6477:
6467:
6450:(typeset from
6439:
6436:
6433:
6430:
6410:
6409:
6397:
6396:
6390:—typeset from
6375:
6372:
6369:
6366:
6363:
6349:
6348:
6336:
6333:
6330:
6327:
6324:
6321:
6318:
6315:
6305:
6284:
6281:
6278:
6275:
6259:
6256:
6254:
6251:
6231:</math: -->
6226:</math: -->
6212:
6211:
6203:
6198:
6195:
6192:
6170:
6149:
6128:
6116:
6115:
6104:
6100:
6096:
6093:
6089:
6085:
6081:
6061:
6060:
6047:
6036:
6024:
6014:
6001:
5986:
5985:
5974:
5970:
5966:
5963:
5959:
5955:
5951:
5930:
5929:
5921:
5916:
5913:
5910:
5884:
5883:
5869:
5865:
5860:
5855:
5834:
5833:
5794:radical symbol
5788:
5787:
5779:
5774:
5771:
5770:Radical symbol
5768:
5730:
5729:
5721:
5716:
5713:
5710:
5696:
5695:
5685:
5684:
5610:
5607:
5601:) or use the "
5582:
5579:
5501:(also encoded
5488:
5487:
5482:
5442:However, when
5415:
5414:
5406:
5401:
5398:
5395:
5394:
5393:
5368:
5367:
5326:
5325:Less-than sign
5323:
5315:
5313:
5312:
5288:
5272:
5232:
5216:
5174:
5155:TILDE OPERATOR
5131:
5105:
5103:DIVISION SLASH
5079:
5035:
4984:
4983:
4982:
4946:Roman numerals
4939:
4938:
4930:
4925:
4922:
4920:
4919:
4898:
4882:named entities
4872:Keep in mind:
4825:
4824:
4816:
4811:
4808:
4805:
4784:
4780:
4746:
4745:
4742:2</sup: -->
4719:
4680:
4679:
4636:
4614:
4611:
4580:
4576:
4508:
4505:
4352:
4349:
4348:
4347:
4303:
4302:
4279:
4276:
4234:
4231:
4214:
4186:
4185:
4169:
4168:
4112:
4111:
4101:
4100:
4049:
4046:
4045:
4044:
4026:
4025:
3917:
3914:
3892:
3889:
3873:
3842:
3839:
3823:
3820:
3789:
3786:
3761:
3757:
3753:
3748:
3744:
3716:
3712:
3708:
3703:
3699:
3685:</math: -->
3660:</math: -->
3635:display=inline
3620:
3616:
3610:
3606:
3602:
3597:
3593:
3588:
3584:
3579:
3574:
3571:
3568:
3564:
3551:</math: -->
3519:display=inline
3504:
3499:
3494:
3490:
3484:
3477:
3473:
3469:
3462:
3457:
3454:
3451:
3447:
3437:
3433:</math: -->
3346:</math: -->
3316:
3312:
3308:
3297:</math: -->
3280:
3274:
3271:
3257:</math: -->
3246:
3245:
3238:
3235:
3222:</math: -->
3157:
3154:
3151:
3146:
3143:
3140:
3135:
3130:
3126:
3103:
3098:
3093:
3089:
3045:
3042:
3028:For a formula
2971:
2970:
2963:
2955:
2950:
2945:
2942:
2934:
2933:
2930:
2926:
2923:
2920:
2904:
2901:
2859:
2851:
2814:
2811:
2798:
2795:
2794:
2793:
2780:matrix product
2741:The scalar or
2739:
2698:
2684:
2680:
2657:
2653:
2625:
2620:
2596:
2591:
2571:
2559:
2539:
2536:
2533:
2513:
2510:
2507:
2487:
2467:
2447:
2438:is denoted by
2433:
2432:
2431:
2420:
2417:
2357:
2342:
2322:
2319:small category
2279:
2269:
2263:
2256:
2250:
2243:dihedral group
2239:
2233:
2223:
2220:roots of unity
2205:-adic integers
2195:
2179:
2176:
2175:
2174:
2137:
2123:
2116:
2098:partial orders
2085:
2082:
2081:
2080:
2073:
2045:
2042:
2041:
2040:
2033:
2017:
2014:
2013:
2012:
1993:
1975:
1968:
1935:
1932:
1899:
1896:
1894:
1891:
1864:
1861:
1847:The plural of
1843:
1842:
1834:
1829:
1768:
1767:
1759:
1754:
1727:
1726:
1721:
1708:
1707:
1702:
1697:
1688:
1687:
1661:is a function
1650:
1649:
1612:
1611:
1566:
1565:
1557:
1552:
1548:
1547:
1542:
1526:by the vector
1515:
1514:
1509:
1451:
1450:
1433:
1420:
1419:
1402:
1380:
1379:
1372:
1364:
1359:
1356:
1353:
1331:
1328:
1312:for details).
1310:WP:NOTTEXTBOOK
1187:if, for every
1091:
1088:
1087:
1086:
1076:
1068:
955:
954:
951:
948:
934:
931:
913:
910:
895:
894:
892:
891:
884:
877:
869:
866:
865:
864:
863:
858:
853:
845:
844:
841:
840:
835:
830:
825:
820:
815:
810:
805:
800:
795:
790:
788:Citing sources
785:
783:Categorization
780:
775:
773:Article titles
770:
764:
761:
760:
757:
756:
751:
750:
747:
746:
739:Figure skating
736:
725:
720:
719:
716:
715:
712:
711:
706:
701:
696:
691:
690:
689:
684:
679:
674:
669:
658:
653:
652:
649:
648:
645:
644:
639:
633:
628:
627:
624:
623:
620:
619:
614:
609:
604:
599:
594:
589:
584:
579:
574:
569:
564:
559:
554:
549:
544:
539:
534:
528:
523:
522:
519:
518:
515:
514:
508:
503:
502:
499:
498:
493:
492:
491:
490:
485:
480:
472:
471:
465:
464:
463:
462:
457:
452:
447:
442:
437:
432:
427:
422:
417:
412:
402:
397:
396:
393:
392:
389:
388:
383:
377:
372:
371:
366:
363:
362:
359:
358:
355:
354:
349:
347:Road junctions
344:
342:Lists of works
339:
333:
328:
327:
324:
323:
320:
319:
314:
309:
304:
298:
293:
292:
289:
288:
285:
284:
279:
274:
269:
263:
258:
257:
254:
253:
250:
249:
244:
239:
234:
229:
224:
222:Capitalization
219:
213:
208:
207:
204:
203:
200:
199:
197:Words to watch
194:
189:
184:
179:
174:
169:
168:
167:
157:
152:
146:
141:
140:
137:
136:
131:
127:
125:
122:
121:
111:
110:
107:
106:
99:
92:
84:
79:
76:
56:
55:
43:
41:
30:
15:
14:
13:
10:
9:
6:
4:
3:
2:
9296:
9285:
9282:
9280:
9277:
9275:
9272:
9271:
9269:
9254:
9253:
9244:
9243:
9240:
9225:
9221:
9215:
9212:
9210:
9207:
9205:
9202:
9200:
9197:
9195:
9192:
9190:
9187:
9185:
9182:
9180:
9177:
9175:
9172:
9170:
9167:
9165:
9162:
9160:
9157:
9155:
9152:
9150:
9147:
9145:
9142:
9140:
9137:
9135:
9132:
9130:
9127:
9125:
9122:
9121:
9119:
9115:
9107:
9104:
9103:
9102:
9099:
9095:
9092:
9091:
9090:
9087:
9086:
9084:
9080:
9074:
9071:
9069:
9066:
9062:
9059:
9057:
9054:
9052:
9049:
9047:
9044:
9042:
9039:
9038:
9037:
9034:
9032:
9029:
9027:
9024:
9023:
9021:
9017:
9011:
9008:
9006:
9003:
9002:
9000:
8996:
8990:
8987:
8985:
8982:
8980:
8977:
8975:
8972:
8970:
8967:
8965:
8962:
8960:
8957:
8955:
8952:
8950:
8947:
8945:
8942:
8940:
8937:
8935:
8932:
8930:
8927:
8925:
8922:
8920:
8917:
8915:
8912:
8910:
8907:
8905:
8902:
8901:
8899:
8895:
8889:
8886:
8885:
8883:
8879:
8873:
8870:
8868:
8867:Record charts
8865:
8863:
8862:Music samples
8860:
8858:
8855:
8854:
8852:
8848:
8842:
8839:
8837:
8834:
8832:
8829:
8827:
8824:
8822:
8819:
8817:
8814:
8812:
8809:
8807:
8804:
8802:
8799:
8797:
8794:
8792:
8789:
8788:
8786:
8782:
8776:
8773:
8771:
8768:
8767:
8765:
8761:
8755:
8752:
8750:
8747:
8745:
8742:
8740:
8737:
8736:
8734:
8730:
8724:
8721:
8719:
8716:
8714:
8711:
8709:
8706:
8705:
8703:
8699:
8693:
8690:
8688:
8685:
8683:
8680:
8678:
8675:
8674:
8672:
8668:
8662:
8659:
8657:
8654:
8652:
8649:
8647:
8646:Pronunciation
8644:
8642:
8639:
8637:
8634:
8632:
8631:Abbreviations
8629:
8628:
8626:
8622:
8616:
8613:
8611:
8608:
8606:
8603:
8601:
8598:
8596:
8593:
8591:
8588:
8584:
8581:
8580:
8579:
8576:
8574:
8571:
8569:
8568:Accessibility
8566:
8565:
8563:
8559:
8553:
8552:
8548:
8546:
8545:
8541:
8539:
8538:
8534:
8533:
8530:
8526:
8519:
8514:
8512:
8507:
8505:
8500:
8499:
8496:
8490:
8486:
8485:
8480:
8472:
8470:9780226104201
8467:
8463:
8462:
8456:
8455:
8454:
8447:
8445:0-201-13448-9
8442:
8438:
8434:
8430:
8429:
8428:
8423:
8420:
8415:
8411:
8407:
8403:
8399:
8395:
8394:
8393:
8386:
8384:0-89871-420-6
8381:
8377:
8373:
8369:
8368:
8363:
8359:
8358:
8357:
8351:
8341:
8338:
8334:
8328:
8325:
8321:
8317:
8311:
8308:
8302:
8299:
8295:
8290:
8287:
8284:
8279:
8276:
8273:
8268:
8265:
8261:
8257:
8253:
8249:
8242:
8239:
8235:
8230:
8227:
8223:
8219:
8214:
8211:
8207:
8203:
8199:
8193:
8190:
8183:
8178:
8175:
8173:
8170:
8169:
8165:
8161:
8158:
8156:
8153:
8151:
8148:
8147:
8143:
8138:
8136:
8132:
8096:
8087:
8082:
8055:
8048:
8046:
8030:
8026:
8022:
8018:
8006:
7992:
7985:
7981:
7973:
7955:
7951:
7947:
7938:
7934:
7929:
7924:
7918:
7917:accessibility
7914:
7911:
7895:
7889:
7870:
7867:
7854:
7846:
7844:
7840:<math: -->
7837:
7832:
7828:
7823:
7821:
7815:<math: -->
7810:<math: -->
7805:
7786:
7781:
7773:
7770:
7762:
7747:
7729:
7700:
7685:
7684:group schemes
7667:
7653:
7635:
7621:
7603:
7589:
7571:
7545:
7540:
7514:
7509:
7483:
7459:
7435:
7411:
7387:
7363:
7350:
7345:
7342:
7332:
7328:
7327:
7324:
7316:
7314:
7311:
7306:
7302:
7293:
7288:
7283:
7281:
7276:
7272:
7229:<math: -->
7214:
7209:
7206:
7202:
7194:
7189:<math: -->
7174:
7171:
7168:
7165:
7162:
7155:
7104:<math: -->
7089:
7083:
7080:
7075:
7072:
7066:
7060:
7057:
7052:
7049:
7043:
7037:
7034:
7029:
7026:
7016:
6981:<math: -->
6966:
6963:
6960:
6955:
6952:
6949:
6944:
6939:
6935:
6927:
6926:
6925:
6923:
6919:
6915:
6907:
6905:
6904:
6902:
6867:<math: -->
6864:
6846:
6843:
6840:
6837:
6834:
6831:
6828:
6825:
6821:
6817:
6812:
6809:
6806:
6803:
6800:
6797:
6794:
6791:
6788:
6784:
6780:
6777:
6770:
6769:
6768:
6734:<math: -->
6716:
6711:
6707:
6700:
6695:
6692:
6689:
6685:
6677:
6676:
6675:
6639:<math: -->
6618:
6614:
6605:
6597:
6596:
6595:
6575:<math: -->
6572:
6556:
6540:
6533:
6532:
6531:
6524:\operatorname
6508:\operatorname
6505:<math: -->
6487:
6481:
6478:
6475:
6468:
6455:\operatorname
6452:<math: -->
6437:
6434:
6431:
6428:
6421:
6420:
6419:
6415:\operatorname
6407:
6403:
6399:
6398:
6392:<math: -->
6389:
6373:
6370:
6367:
6364:
6361:
6354:
6353:
6352:
6331:
6328:
6325:
6319:
6316:
6313:
6306:
6297:<math: -->
6282:
6279:
6276:
6273:
6266:
6265:
6264:
6257:
6252:
6250:
6239:
6222:<math: -->
6218:
6209:
6208:MOS:MATH#PUNC
6205:
6204:
6201:
6193:
6191:
6189:
6188:Heat equation
6183:
6147:
6102:
6094:
6091:
6083:
6071:
6070:
6069:
6065:
6037:
6022:
6015:
5991:
5990:
5989:
5972:
5964:
5961:
5953:
5941:
5940:
5939:
5935:
5934:A list as in
5927:
5923:
5922:
5919:
5911:
5909:
5906:
5901:
5892:<math: -->
5889:
5867:
5863:
5858:
5853:
5844:
5843:
5842:
5838:<math: -->
5819:
5818:
5817:
5812:
5802:
5795:
5785:
5781:
5780:
5777:
5769:
5767:
5761:
5757:
5753:
5727:
5723:
5722:
5719:
5711:
5709:
5704:
5690:
5689:
5688:
5668:
5667:
5666:
5661:
5660:closed-closed
5651:
5641:
5631:
5623:
5616:
5608:
5606:
5598:
5592:
5588:
5580:
5578:
5576:
5571:
5569:
5551:
5547:
5542:
5540:
5536:
5530:
5497:
5483:
5477:
5474:and 2 is the
5473:
5469:
5465:
5464:
5463:
5459:
5449:
5445:
5440:
5434:
5430:
5426:
5422:
5412:
5408:
5407:
5404:
5396:
5373:
5372:
5371:
5344:
5343:
5342:
5338:
5324:
5321:
5316:
5299:) instead of
5286:
5276:<math: -->
5273:
5258:
5253:RING OPERATOR
5243:) instead of
5230:
5220:<math: -->
5217:
5212:<math: -->
5183:<math: -->
5178:<math: -->
5175:
5172:
5168:
5160:
5159:other symbols
5132:
5106:
5080:
5077:
5072:
5052:
5036:
5030:
5020:
5013:
4985:
4979:
4974:
4973:
4955:
4951:
4947:
4943:
4942:
4936:
4932:
4931:
4928:
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4853:outside both
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4422:Greek letters
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4351:Greek letters
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4103:displays as:
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3923:
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3835:\displaystyle
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3794:<math: -->
3788:Line wrapping
3787:
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3067:
3063:
3059:
3055:
3051:
3043:
3041:
3039:
3035:
3031:
3026:
3025:for details.
3024:
3019:
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3009:
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3003:
2999:
2994:
2992:
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2983:<math: -->
2978:
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2758:
2757:inner product
2753:
2749:
2744:
2740:
2736:
2732:
2726:
2722:
2718:, suprema as
2717:
2712:
2708:
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2699:
2678:
2655:
2651:
2642:
2618:
2589:
2580:
2576:
2573:For a matrix
2572:
2557:
2537:
2534:
2531:
2511:
2508:
2505:
2485:
2478:. The symbol
2465:
2445:
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2407:
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2397:
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2240:
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2210:
2206:
2204:
2198:
2193:
2190:
2186:
2183:The abstract
2182:
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2177:
2172:
2168:
2164:
2160:
2157:
2153:
2149:
2145:
2142:
2138:
2135:
2131:
2127:
2124:
2121:
2117:
2114:
2113:0-387-90125-6
2111:
2107:
2103:
2100:as in, e.g.,
2099:
2095:
2091:
2090:Directed sets
2088:
2087:
2084:Miscellaneous
2083:
2078:
2074:
2071:
2067:
2066:quasi-compact
2063:
2060:
2056:
2052:
2051:compact space
2048:
2047:
2043:
2038:
2034:
2031:
2030:algebraic set
2028:
2024:
2020:
2019:
2015:
2010:
2006:
2002:
1998:
1994:
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1988:
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1715:
1713:
1705:Obviously ...
1703:
1698:
1693:
1692:
1691:
1684:
1680:
1676:
1672:
1668:
1664:
1660:
1659:even function
1655:
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1653:
1646:
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1638:
1634:
1630:
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1617:
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1520:
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1518:
1508:
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1500:
1496:
1491:
1490:
1489:
1484:
1479:
1472:Consider that
1447:
1443:
1439:
1434:
1430:
1425:
1424:
1423:
1416:
1412:
1408:
1403:
1399:
1395:
1392:Suppose that
1390:
1389:
1388:
1385:
1377:
1376:MOS:MATH#NOWE
1373:
1370:
1369:MOS:MATH#TONE
1366:
1365:
1362:
1354:
1352:
1350:
1346:
1340:
1338:
1329:
1327:
1324:
1320:
1318:
1313:
1311:
1307:
1306:instructional
1303:
1299:
1295:
1291:
1287:
1283:
1277:
1275:
1271:
1265:
1263:
1259:
1255:
1252:
1248:
1244:
1241:
1237:
1233:
1229:
1224:
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1210:
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1197:
1193:
1190:
1186:
1182:
1178:
1174:
1170:
1166:
1162:
1158:
1154:
1148:
1146:
1141:
1139:
1135:
1131:
1127:
1123:
1118:
1116:
1113:
1109:
1105:
1101:
1097:
1089:
1084:
1080:
1077:
1073:
1069:
1066:
1063:
1062:
1061:
1057:
1055:
1051:
1047:
1040:
1038:
1034:
1030:
1026:
1023:
1019:
1004:
1000:
996:
990:
987:
983:
974:
964:
952:
949:
946:
945:
944:
940:
932:
930:
928:
924:
920:
911:
909:
906:
902:
890:
885:
883:
878:
876:
871:
870:
868:
867:
862:
859:
857:
854:
852:
849:
848:
847:
846:
839:
836:
834:
831:
829:
826:
824:
821:
819:
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811:
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806:
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801:
799:
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789:
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784:
781:
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771:
769:
766:
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758:
744:
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737:
734:
730:
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723:
718:
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710:
707:
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697:
695:
692:
688:
685:
683:
680:
678:
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673:
670:
668:
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664:
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660:
659:
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634:
631:
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583:
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510:
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500:
489:
486:
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483:Record charts
481:
479:
478:Music samples
476:
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408:
407:
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405:
400:
395:
394:
387:
384:
382:
379:
378:
375:
370:
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364:By topic area
361:
360:
353:
350:
348:
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343:
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338:
335:
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331:
326:
325:
318:
315:
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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:
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166:
163:
162:
161:
158:
156:
153:
151:
150:Accessibility
148:
147:
144:
139:
138:
124:
123:
120:
116:
104:
100:
97:
93:
90:
86:
85:
82:
77:
72:
68:
64:
60:
54:
52:
48:
42:
35:
34:
25:
19:
9250:
9214:WikiProjects
9124:Article size
9025:
8713:Lead section
8549:
8542:
8535:
8482:
8460:
8452:
8436:
8426:
8405:
8401:
8398:Halmos, P.R.
8391:
8366:
8355:
8340:
8327:
8310:
8301:
8289:
8278:
8267:
8256:hyphen-minus
8241:
8229:
8213:
8192:
8133:
8088:
8084:
7986:
7936:
7932:
7925:
7856:
7833:
7824:
7820:MOS:STYLERET
7806:
7588:affine space
7346:
7338:
7309:
7304:
7301:Donald Knuth
7291:
7284:
7280:MOS:STYLERET
7274:
7268:
7246:
6914:differential
6911:
6899:
6889:
6862:
6766:
6673:
6592:
6570:
6522:
6411:
6387:
6350:
6261:
6219:
6215:
6185:
6117:
6067:
6063:
5987:
5937:
5933:
5907:
5885:
5835:
5791:
5733:
5697:
5686:
5624:
5612:
5584:
5572:
5554:·
5543:
5538:
5534:
5496:dot operator
5489:
5443:
5441:
5432:
5428:
5424:
5420:
5418:
5369:
5336:
5328:
5314:
5269:WHITE CIRCLE
5012:prime symbol
5008:DOUBLE PRIME
4935:MOS:ROMANNUM
4921:
4914:
4910:
4905:
4901:
4892:, using the
4871:
4828:
4799:
4747:
4741:<sup: -->
4735:
4731:
4727:
4723:
4710:
4706:
4702:
4698:
4681:
4633:
4629:<sub: -->
4625:<sup: -->
4622:
4513:
4510:
4450:
4442:
4434:
4428:
4426:
4419:
4371:
4365:
4361:
4357:
4354:
4304:
4295:
4291:
4287:
4281:
4268:
4264:
4260:
4256:
4236:
4224:
4211:
4187:
4180:
4176:
4171:results in:
4170:
4113:
4102:
4051:
4038:
4034:
4027:
3919:
3897:
3894:
3844:
3827:
3825:
3791:
3779:
3516:
3350:
3247:
3229:
3226:
3169:
3078:
3047:
3029:
3027:
3017:
3013:
3010:
2995:
2991:anchor links
2986:
2980:
2967:MOS:FORMULAE
2947:
2935:
2906:
2855:
2844:
2841:
2827:may include
2822:
2804:
2800:
2789:
2785:
2782:
2775:
2771:
2765:
2761:
2751:
2747:
2734:
2730:
2728:or as a sum
2724:
2720:
2715:
2710:
2706:
2640:
2578:
2410:
2405:
2401:
2395:
2391:
2387:homomorphism
2380:
2376:
2372:
2367:
2362:
2358:
2353:
2347:
2343:
2338:
2333:
2329:
2314:
2310:
2306:
2302:
2298:
2294:
2275:
2270:
2258:
2251:
2246:
2234:
2224:
2215:
2212:
2208:
2202:
2196:
2191:
2185:cyclic group
2170:
2166:
2162:
2158:
2155:
2151:
2147:
2144:modular form
2140:
2129:
2105:
2058:
2026:
2008:
2004:
2000:
1986:
1927:
1923:
1915:
1901:
1887:
1883:
1878:
1874:
1872:
1856:
1852:
1848:
1846:
1826:
1819:
1815:
1811:
1803:
1799:
1795:
1787:
1783:
1779:
1773:
1771:
1764:MOS:MATH#ANY
1751:
1747:there exists
1746:
1742:
1738:
1734:
1730:
1728:
1711:
1709:
1689:
1682:
1678:
1674:
1670:
1666:
1662:
1658:
1651:
1644:
1640:
1636:
1632:
1628:
1624:
1620:
1613:
1607:
1603:
1599:
1595:
1591:
1587:
1583:
1576:
1571:
1569:
1549:
1539:
1535:
1531:
1527:
1523:
1522:Multiplying
1516:
1506:
1502:
1498:
1494:
1493:Multiplying
1486:
1452:
1445:
1441:
1437:
1428:
1421:
1414:
1410:
1406:
1397:
1396:is a group.
1393:
1386:
1383:
1341:
1333:
1325:
1321:
1314:
1305:
1304:rather than
1301:
1278:
1267:
1261:
1257:
1253:
1242:
1240:finite group
1236:group theory
1227:
1226:
1222:
1218:
1212:
1208:
1203:
1195:
1191:
1184:
1180:
1176:
1172:
1164:
1156:
1152:
1150:
1142:
1137:
1133:
1129:
1125:
1121:
1119:
1114:
1108:discriminant
1103:
1098:) means the
1095:
1093:
1090:Article body
1083:applications
1082:
1078:
1071:
1064:
1059:
1049:
1043:
1025:deformations
998:
992:
988:
984:
956:
942:
927:group theory
915:
898:
838:WikiProjects
768:Article size
698:
307:Lead section
62:
44:
9106:Terminology
9026:Mathematics
8974:Philippines
8836:Visual arts
8831:Video games
8595:Hidden text
8437:The TeXbook
8408:: 123–152,
8316:word joiner
8260:source code
8254:accept the
8196:Currently,
7834:Due to bug
7652:adele rings
5784:MOS:RADICAL
5674:open-closed
5640:closed-open
5630:open-closed
5603:−
5597:subst:minus
5550:source code
5452:×
5186:instead of
5145:instead of
5119:instead of
5093:instead of
5051:superscript
4950:Basic Latin
4847:code points
4617:Main page:
4424:directly.)
4198:or without
3553:renders as
2960:MOS:FORMULA
2833:source code
2778:), or as a
2743:dot product
2134:half-period
2070:compactness
2064:, who uses
2027:irreducible
1965:C* algebras
1961:B* algebras
1945:associative
1700:Clearly ...
1619:A function
1582:A function
1530:defined by
1476:We see that
1302:informative
1232:mathematics
995:mathematics
937:Main page:
905:mathematics
743:Terminology
699:Mathematics
602:Philippines
455:Visual arts
450:Video games
177:Hidden text
63:substantive
24:MOS:RADICAL
9268:Categories
9204:User pages
9169:Signatures
9164:Notability
9089:Cue sports
8826:Television
8821:Philosophy
8775:Trademarks
8624:Formatting
8422:0821800558
8206:homographs
8079:See also:
8057:The angle
7968:– markup:
7851:See also:
6253:Font usage
5748:ƒ
5605:" entity.
5581:Minus sign
5499:⋅
5478:, because
5444:explaining
5318:See also:
5257:interpunct
5055:C*-algebra
5010:where the
4716:²
4690:²
4461:MICRO SIGN
4241:, such as
4237:Names for
3922:sans serif
3891:Using HTML
3374:\textstyle
3240:Until bug
2975:See also:
2829:pseudocode
2817:See also:
2813:Algorithms
2639:, and not
2328:of groups
2245:of order 2
1983:noetherian
1979:local ring
1957:* algebras
1867:See also:
1851:is either
1814:satisfies
1798:satisfies
1782:satisfies
1681:) for all
1665:such that
1643:) for all
1606:) for all
1481:See also:
1448:is finite.
1185:continuous
1183:is called
1163:, and let
1079:Motivation
1029:stretching
1027:, such as
1022:continuous
1001:(from the
828:User pages
803:Signatures
798:Notability
729:Cue sports
445:Television
440:Philosophy
386:Trademarks
210:Formatting
9046:Chemicals
9036:Chemistry
8984:Singapore
8964:Macedonia
8939:Indonesia
8600:Infoboxes
8573:Biography
8544:Directory
8248:templates
7898:(such as
7847:Fractions
7287:WP:WEIGHT
7010:) before
6872:predicted
6863:incorrect
6571:incorrect
6388:incorrect
5687:produces
5650:open-open
5615:intervals
5476:remainder
5196:SET MINUS
4233:Functions
4070:. Within
4048:Variables
3299:produces
3259:produces
2952:Shortcuts
2917:Wikibooks
2909:WP:VERIFY
2825:algorithm
2575:transpose
2301:, as Hom(
2291:morphisms
2139:A weight
2055:Hausdorff
1972:zero ring
1794:if every
1483:MOS:NOTED
1456:Note that
1361:Shortcuts
1230:, in the
1106:) 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
9252:Category
9179:Subpages
9174:Overview
9154:Hatnotes
9149:Contents
9073:Taxonomy
9031:Medicine
8998:Religion
8969:Pakistan
8959:Malaysia
8897:Regional
8677:Captions
8651:Spelling
8537:Overview
8479:template
8435:(1984),
8364:(1998),
8220:, is in
8139:See also
7323:Shortcut
6880:observed
6767:but not
6664:that one
6650:this one
6623:that one
6610:this one
6351:but not
6200:Shortcut
5918:Shortcut
5776:Shortcut
5726:MOS:FNOF
5718:Shortcut
5546:asterisk
5472:quotient
5468:dividing
5403:Shortcut
5359:<
5332:<
5167:negation
5071:baseline
5047:ASTERISK
4927:Shortcut
4904:divides
4863:brackets
4813:Shortcut
4718:) versus
4473:OHM SIGN
4392:π
4263:) = sin(
4220:SI units
3945:. Using
3847:alt text
3841:Alt text
2835:in some
2755:, as an
2287:Hom-sets
2285:, write
2232:called C
2062:Bourbaki
2044:Topology
1857:formulas
1853:formulae
1831:Shortcut
1810:if some
1792:, write
1756:Shortcut
1554:Shortcut
1444:. Then
1427:A group
1251:subgroup
1200:preimage
1189:open set
1169:function
1033:twisting
999: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
9117:Related
9094:Snooker
9019:Science
8944:Ireland
8881:History
8801:Blazons
8605:Linking
8561:Content
8481:below (
8246:, many
8222:Haskell
7910:Unicode
7836:T263572
7825:Due to
7748:(e.g.,
7744:), and
7331:MOS:BBB
7305:TeXbook
5888:T263572
5692:(−π, π]
5494:is the
5091:SOLIDUS
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4851:Unicode
4593:Unicode
4547:\mathbb
4429:capital
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3517:Adding
3360:display
3242:T263572
3184:display
3070:MathJax
3068:(using
3034:strings
2702:lattice
2426:(⋉) or
2385:is the
2165:), and
2120:lattice
1990:Zariski
1934:Algebra
1875:compact
1849:formula
1778:if any
1743:for all
1179:. Then
1110:of the
1054:tangent
733:Snooker
655:Science
572:Ireland
505:History
420:Blazons
187:Linking
143:Content
9223:Search
9082:Sports
9056:Safety
8979:Poland
8929:Hawaii
8909:Canada
8816:Novels
8796:Comics
8718:Tables
8708:Layout
8701:Layout
8692:Images
8670:Images
8477:‹ The
7921:5.2 cm
7263:, and
7236:\theta
7192:), and
6920:, and
6238:nowrap
6118:where
5988:where
5737:U+0192
5587:hyphen
5567:BULLET
5559:U+2022
5433:citing
5387:< 3
5341:, use
5339:< 3
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5262:U+25CB
5246:U+2218
5201:U+005C
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5148:U+223C
5136:U+007E
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5040:U+002A
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4989:U+2032
4964:, not
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4454:U+00B5
4267:) cos(
4227:= 5 cm
3536:\infty
3391:\infty
3366:inline
3327:, but
3253:\tfrac
3062:MathML
2998:boldly
2929:topic.
2861:primes
2797:Proofs
2436:Subset
2379:→ Aut(
2366:where
2136:style.
2102:Kelley
2059:contra
2037:scheme
1987:contra
1949:unital
1918:, and
1772:Avoid
1614:write
1474:, and
1337:fields
1245:, the
1198:, the
1037: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
9005:Islam
8954:Korea
8949:Japan
8934:India
8924:Egypt
8857:Music
8850:Music
8770:Legal
8763:Legal
8739:Lists
8732:Lists
8687:Icons
8184:Notes
8007:: -->
8001:) or
7982:: -->
7888:slash
7138:\frac
7135:\cdot
7121:\frac
7106:\frac
6896:\text
6892:\mbox
6868:r = x
6659:\text
6645:\text
5900:radic
5801:radic
5679:−π, π
5522:: -->
5516:</
5513:\cdot
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5466:When
5458:times
5385:''x''
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3190:block
3050:LaTeX
2897:sieve
2870:sieve
2867:sieve
2700:In a
2670:, or
2293:from
2289:, or
2189:order
2079:page.
1902:"The
1822:) = 0
1808:, or
1806:) = 0
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1545:, ...
1512:, ...
1308:(see
1247:order
1171:from
1167:be a
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1013:λόγος
1007:τόπος
1003:Greek
919: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:<
9194:Tips
8806:Film
8784:Arts
8551:Tips
8466:ISBN
8441:ISBN
8419:ISBN
8380:ISBN
8250:and
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7715:and
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7282:.
6996:\sin
6983:\int
6736:\sum
6674:and
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6432:csch
6404:and
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6224:and
5811:sqrt
5792:The
5758:and
5756:JAWS
5703:math
5591:dash
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5218:Use
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4179:= −(
4163:+ 2)
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4066:and
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4037:= −(
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2110:ISBN
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3655:2
3653:^
3649:^
3647:x
3645:{
3631:,
3619:6
3615:/
3609:2
3601:=
3596:2
3592:n
3587:/
3583:1
3573:1
3570:=
3567:n
3547:^
3540:^
3503:.
3498:6
3493:2
3483:=
3476:2
3472:n
3468:1
3456:1
3453:=
3450:n
3430:}
3428:6
3424:2
3422:^
3416:{
3409:}
3407:2
3405:^
3403:n
3399:1
3397:{
3363:=
3343:}
3341:2
3337:x
3335:{
3315:2
3311:/
3307:x
3279:x
3273:2
3270:1
3216:x
3208:^
3206:0
3204:_
3187:=
3156:.
3153:x
3150:d
3145:x
3129:0
3102:2
3097:R
3088:x
3018:b
3014:a
2894::
2891:p
2888:=
2885:)
2879::
2876:p
2873:(
2864:=
2792:.
2786:b
2783:a
2776:b
2774:,
2772:a
2768:⟩
2766:b
2764:,
2762:a
2760:⟨
2752:b
2748:a
2735:b
2731:a
2725:b
2721:a
2711:b
2707:a
2697:.
2679:X
2656:T
2652:X
2641:X
2624:T
2619:X
2595:T
2590:X
2579:X
2538:B
2535:=
2532:A
2512:B
2506:A
2411:φ
2406:K
2402:Q
2396:Q
2392:K
2383:)
2381:K
2377:Q
2373:φ
2368:K
2363:K
2359:φ
2356:×
2354:Q
2348:Q
2344:φ
2341:×
2339:K
2334:Q
2330:K
2315:B
2313:,
2311:A
2307:B
2305:,
2303:A
2299:B
2295:A
2276:n
2271:n
2259:n
2257:2
2252:n
2247:n
2235:n
2225:n
2216:Z
2213:n
2211:/
2209:Z
2203:p
2197:n
2192:n
2173:.
2171:e
2167:q
2163:τ
2161:(
2159:f
2156:τ
2152:τ
2148:f
2141:k
2130:ω
2104:(
2057:(
2032:.
2009:v
2007:(
2005:Q
2001:v
1985:(
1974:.
1820:x
1818:(
1816:F
1812:x
1804:x
1802:(
1800:F
1796:x
1788:x
1786:(
1784:F
1780:x
1685:.
1683:x
1679:x
1677:(
1675:f
1671:x
1667:f
1663:f
1647:.
1645:x
1641:x
1639:(
1637:f
1633:x
1629:f
1621:f
1608:x
1604:x
1602:(
1600:f
1596:x
1592:f
1584:f
1572::
1543:0
1540:v
1536:v
1532:u
1528:u
1524:M
1510:0
1507:v
1503:v
1499:u
1495:M
1446:H
1442:G
1438:H
1429:G
1415:H
1411:G
1407:H
1398:G
1394:G
1262:G
1258:G
1254:H
1243:G
1213:S
1209:O
1207:(
1204:f
1196:T
1192:O
1181:f
1177:T
1173:S
1165:f
1157:T
1153:S
1138:x
1134:n
1130:x
1126:n
1124:^
1122:x
1115:K
1104:K
1096:K
1039:.
888:e
881:t
874:v
745:)
741:(
735:)
731:(
73:.
53:.
26:)
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