2731:. 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.
9240:
979:
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.
8047:
2832:. 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.
31:
1480:
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,
7270:
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
7800:
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
6221:
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
1446:
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
3790:
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
1881:
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
6209:
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,
978:
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
1315:
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
950:
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
2794:
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,
1877:
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
1067:
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.
7336:
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
4201:
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,
5545:. 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
1882:
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.
3879:
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.
3821:
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
6893:
5322:
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
1919:. 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
7811:) 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
6586:
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:
900:
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).
6255:
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:
1335:
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
3033:, 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.
1471:. 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.
1272:
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
8575:
2811:
157:
8127:
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.
1327:
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
2921:
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
3506:
1212:
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.
8078:
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.
7093:
9043:
669:
3842:, 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
909:
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
6106:
5976:
8911:
8906:
7795:
544:
534:
5066:
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
3163:
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
4893:
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 "
6628:
1866:
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
5618:
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
3934:
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
3622:
4181:
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
2798:
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
3107:
8481:
8073:
1309:
6852:
4611:
6970:
3159:
8966:
6723:
2904:, 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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9126:
9053:
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8864:
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679:
609:
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and related articles attempt to cover both unital rings and non-unital rings: they do not consistently implement this interpretation. This attempt to cover multiple meanings violates
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9033:
8976:
8931:
3722:
735:
659:
604:
559:
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8951:
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Readers have differing levels of experience and knowledge. When in doubt, articles should define the notation they use. For example, some readers will immediately recognize that Δ(
696:
589:
584:
3767:
7549:
7518:
1133:) 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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8602:
7735:
7706:
7673:
7641:
7609:
7577:
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2601:
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184:
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6004:
815:
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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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6338:
2515:
2449:
8896:
8833:
2688:
524:
452:
202:
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1060:, 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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152:
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5234:
4874:
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5809:) 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:
4788:
2661:
664:
622:
517:
339:
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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
7959:
3318:
2997:
before implementation. If there is no positive response, or if planned changes affect more than one article, consider notifying an appropriate Wikiproject, such as
2541:
1852:. Both are acceptable, but an article should be internally consistent. In an already consistent article, editors should refrain from changing one style to another.
9276:
647:
497:
135:
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6026:
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tag, described in the next subsection) or, in certain cases, using other means of formatting that render in HTML; both are acceptable and widely used, except for
9002:
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8633:
7845:
4970:
714:
634:
287:
252:
219:
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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
9151:
9060:
9048:
8880:
8124:
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.
686:
674:
504:
366:
322:
63:
4596:) and its adjacent characters should be avoided at present, since these characters are not yet universally supported and may have an inconsistent appearance.
3958:
also helps some spell checkers and screen readers treat math markup properly. Note that certain special characters (equal signs, absolute value bars) require
8783:
8715:
8653:
8648:
8628:
8582:
402:
391:
309:
239:
234:
214:
164:
6183:, 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.
5586:"–". 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
9093:
8956:
8736:
8607:
8169:
2799:
731:
579:
334:
189:
4468:
are intended for compatibility with legacy character sets, and Unicode-capable environments (like Knowledge (XXG)) should use the Greek letters instead (
4348:
Italicize lower-case Greek letters when they are variables or constants (in line with the general advice to italicize variables): the example expression
3892:
1262:
1113:
Use standard notation when possible. If an article requires non-standard or uncommon notation, they should be defined. For example, an article that uses
8859:
8854:
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8623:
8560:
5312:
3165:
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Providing further reading enables other editors to verify and to extend the given information, as well as to discuss the quality of a particular source.
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470:
224:
209:
142:
3220:
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.
1216:
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:
8508:
1100:
1092:
8705:
2795:
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.
931:
299:
8828:
8823:
8587:
5606:
Square brackets have two problems; they can occasionally cause problems with wiki markup, and editors sometimes 'fix' the brackets in asymmetrical
3433:
447:
442:
169:
4859:
4827:
2491:
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,
1447:
bare lists of facts and formulae, and relying too much on addressing the reader directly and referring to "we". Also avoid contentless clichés as
922:? 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.
9166:
9081:
8818:
8813:
8767:
8529:
4624:
tags, respectively, with no other formatting info. Font sizes and such should be entrusted to be handled with stylesheets. For example, to write
843:
721:
437:
432:
378:
3227:
The font size can be slightly larger than that of the surrounding text on some browsers, making text containing inline formulae harder to read.
2255:
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.
9206:
9201:
9028:
8592:
8565:
8298:
This style, adopted by Knowledge (XXG), is shared by Higham (1998), Halmos (1970), the Chicago Manual of Style, and many mathematics journals.
4073:
templates (which will set a serif font but not italics), use the wikitext markup of double apostrophes to make variables italic. For example:
1878:
conventions common in that area. Thus the act of changing an article from one set of conventions to another should not be undertaken lightly.
830:
825:
654:
174:
147:
7012:
1319:
If not included in the introduction, a history section can provide additional context and details on the topic's motivation and connections.
9244:
9141:
8669:
8643:
8536:
848:
259:
229:
3630:
renders exponents lower, especially under square roots, often resulting in a smaller square root which fits better in inline text: compare
9086:
8597:
8164:
2998:
2915:
Some notions are defined differently depending on context or author. Articles should contain some references that support the given usage.
725:
179:
39:
7824:), which is more common anyway. If absolutely necessary (e.g. when discussing the notation itself), use the Unicode character (e.g. 𝟙).
4677:
2982:
which should use HTML only, as LaTeX markup might cause uneven spacing in the table of contents, as well as the appearance of illegible
8808:
8793:
8788:
8710:
8700:
8684:
5046:, and is typical when used as a postfix. This character also appears on keyboards, and is thus easier to type and search for. Example:
1337:
427:
412:
407:
304:
294:
274:
8849:
8762:
8731:
8679:
461:
373:
329:
269:
8461:
8436:
8375:
5549:(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
2105:
9176:
8798:
8147:
6067:
5937:
4831:
2993:
from LaTeX to HTML, nor from non-LaTeX to LaTeX without a clear improvement. Proposed changes should generally be discussed on the
2989:
Large-scale formatting changes to an article or group of articles are likely to be controversial. One should not change formatting
1340:. Lastly, a well-written and complete article should have a "References" section. This topic is discussed in detail in the section
1289:. It may also be edifying to list non-examples, which almost-but-not-quite satisfy the definition. In keeping with the purpose and
805:
417:
4877:
are very likely to be displayed correctly, a significant number of viewers will have problems seeing all the characters listed at
9266:
5888:
markup is incompatible with the Media Viewer (used for full-screen image viewing on mobile devices), so until that is fixed, the
1140:
should provide an exact definition of the object, perhaps in a "Definition" section after section(s) of motivation. For example:
1078:, which can illuminate the use of the topic and its connections to other areas of mathematics or other non-mathematical subjects.
3112:
8286:
7744:
7266:. Changes from one style to another should be done only to make an article consistent with itself. Formatting changes should
879:
9181:
5439:
the formula for a general audience (not just mathematicians), or giving examples of its application, it is prudent to use the
3014:, the community of mathematical editors of English Knowledge (XXG) currently has no consensus about preferred formatting; see
810:
8414:
8214:
4231:
8803:
6593:
422:
344:
1742:. In addition to compromising the encyclopedic tone, these abbreviations are a form of jargon that may confuse the reader.
8501:
7292:. But this guide is rarely followed in reliable mathematical sources, and it is contradicted by other style guides, like
8674:
3550:
264:
51:
7916:); non-metric units can be either type of fraction, but the fraction style should be consistent throughout the article.
4823:
2839:
1481:
not an equation involving a previously known object. Also identify the nature of the entity being defined. Don't write:
9271:
8517:
7822:, LaTeX blackboard bold currently does not work with numerals. Use bold instead (e.g. {{math|'''1'''}} or <math: -->
4528:
tag for making text bold. Bold notation has been largely replaced by blackboard bold, which may be encoded in LaTeX as
893:
111:
43:
17:
4942:
9136:
9131:
9121:
8152:
3241:
If an inline formula needs to be typeset in LaTeX, keep the height down by using text-style or horizontal fractions:
3075:
3015:
780:
775:
765:
2918:
Important theorems should cite historical papers as an additional information (not necessarily for looking them up).
1095:, but others will never have encountered the notation. The latter group will be helped by an aside like "...where Δ(
3030:
8251:"-" as a valid representation of the minus sign. Except situations where "-" has to represent the minus sign in a
8142:
6914:
6766:
3066:
3050:
3026:
2969:
2912:
is for). Also, often one might want to find out more details (like the proof of a theorem stated in the article).
1029:
9223:
9221:
9116:
6923:
5563:
as an operator symbol is also discouraged except in abstract contexts (e.g. to denote an unspecified operator).
2930:
760:
119:
8494:
8476:
7883:
and with the baseline of the numbers aligned with the baseline of the surrounding text (as in 1/2). The use of
6673:
5752:
3830:
at the beginning. Such formatting can be removed if a formula is edited and need not be added to new formulae.
7853:
4055:
template to enclose a simple mention of a variable by name. This helps distinguish certain characters such as
1302:
7340:
Today, either blackboard bold or ordinary bold letters can be used interchangeably to represent the standard
4045:
Use italic text for variables, but never for numbers or symbols. To ensure an italic serif typeface, use the
1645:
If it is reasonable to do so, rephrase the sentence to avoid the use of the word "if" entirely. For example,
1312:
contains some details on how to create graphs and other pictures as well as how to include them in articles.
7337:
mathematical printing to denote certain common objects in a style distinct from other uses of bold letters.
6464:
6417:
5840:
4870:
1944:. A structure satisfying all the ring axioms except the existence of a multiplicative identity is called a
1274:
1261:
Other times, it may be better to separate the statement into its own section, as for long theorems like the
9196:
9161:
9156:
5901:
The use of √ with no overline is acceptable for simple expressions, as long as the operand is unambiguous.
3888:
The following sections cover the way of presenting simple inline formulae in HTML, instead of using LaTeX.
2994:
936:
Articles should start with a short introductory section, called the "lead". The purpose of the lead is to
820:
795:
790:
8102:
for a point. This allows easy use in LaTeX markup. However, older books tend to use upright letters as in
6398:
5652:
5607:
5460:
3683:
2409:
The context should clearly state that this is a semidirect product and should state which group is normal.
1161:
9186:
8543:
7850:
In mathematics articles, fractions should always be written either with a horizontal fraction bar (as in
6210:
comma, semicolon, or other punctuation at that place, the formula must have that punctuation at the end.
2933:
article has more information on this and also several examples for how the cited literature should look.
1308:
A picture can really bring home a point, and can often precede the mathematical discussion of a concept.
896:
contains guidelines for writing and editing clear, encyclopedic, attractive, and interesting articles on
853:
59:
7980:
For simple fractional subscripts or superscripts, the horizontal style is visually the least confusing:
5610:
to make them symmetrical. The nowiki tag can be used as a general solution to problems like this, as in
2090:
9171:
7315:
6192:
5910:
5768:
5710:
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4805:
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1823:
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73:
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7617:
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3255:
2829:
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2029:
1285:. Occasionally, it is appropriate to give a large number of computationally-flavored examples, as in
1239:
701:
9146:
2990:
2606:
785:
7880:
6394:
5440:
4946:
4851:
4796:. Formulae formatted without using TeX should use the same syntax to maintain the same appearance.
3858:
3777:, is adequate for articles that use only simple inline formulae and better for text-only browsers.
3514:
generates a smaller summation symbol and moves the limits to its right side. The rewritten formula
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might be given as the hypothesis of a theorem whose conclusion is obviously true in the case that
1377:
There are several issues of writing style that are particularly relevant in mathematical writing.
8190:
8105:
7248:
for a variable. Upright fonts are sometimes used for standard, nearly universal constants, as in
6156:
6114:
6033:
5987:
5789:√ can be used when written on its own, but when part of a larger expression, can be problematic.
5642:
5062:(∗) for subscripts and when the bottom of the character should roughly align with the
2318:
2126:
1933:
1286:
1282:
1038:
1017:
9226:
4685:) for squares. This does not combine well with other powers, as the following comparison shows:
3935:
3237:
is fixed, it will not work in image captions when readers click through to see full-size images.
2454:
125:
6302:
6288:(parentheses may be omitted here, as the argument consists of a single term only; typeset from
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2434:
1266:
8458:
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8372:
7909:
6401:; if there is any risk that a term could become ambiguous for our readership, use parentheses.
5747:. As of December 2010, this character is not interpreted correctly by screen readers such as
2666:
2118:
2102:
2015:
1896:
1153:
8194:
2546:
2474:
1290:
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8006:
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2812:
Knowledge (XXG):WikiProject Computer science/Manual of style (computer science) § Algorithms
2258:
2069:
2054:
1989:
915:
121:
5275:
5219:
4881:. One way to guarantee that an uncommon symbol is rendered correctly for all readers is to
3839:
8354:
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6350:
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5021:
4766:
4493:
2694:
2639:
2275:
2112:
2047:
1975:
1900:
8358:
7828:
7801:
discouraged in English Knowledge (XXG); instead, either the LaTeX rendering (for example
5880:
3926:
font to display a formula (whether as SVG or HTML). HTML math expressions should use the
3234:
7936:
6393:
Note: For potential pitfalls of forms not understood consistently across the board, see
5518:
and reachable in the "Math and logic" drop-down list below the edit box or via template
5007:
is appropriate; do not use the ASCII apostrophe (') or double quote (") in these cases.
3295:
2520:
8325:
6910:
6222:
does not line up with that of the running text—the punctuation can be placed after the
5892:
5793:
5786:
5589:
5450:
5011:
5004:
4938:
4431:
4414:
3805:
2772:
2311:
2235:
2222:
2212:
2194:
2094:
2086:
1941:
1570:
When defining a term, do not use the phrase "if and only if". For example, instead of
1021:
995:
865:
8085:
7997:
7972:
6136:
6011:
4741:
Moreover, the TeX engine used on Knowledge (XXG) may format simple superscripts using
2986:
to sections. Some of the issues presented by using LaTeX or HTML are discussed below.
1068:
Include a physical or geometric analogy or diagram if it can help introduce the topic.
951:
formulae displayed when hovering, they must be written in raw html (without templates
9260:
9225:
8471:
8240:
8217:, not a well-known language so generally not a good choice when showing an algorithm.
7983:
7964:
7886:
7341:
6180:
5803:
5695:
5521:
5151:
4504:
Commonly used sets of numbers are typeset in boldface, as in the set of real numbers
4195:
4185:
4067:
4049:
3959:
3952:
3942:
3929:
3899:
2749:
2062:
2058:
2043:
2022:
1945:
965:
123:
6226:
tag and then the whole formula (including the punctuation) can be enclosed with the
1380:
In the interest of clarity, sentences should not begin with a symbol. Do not write:
8425:
8248:
8226:
7812:
7676:
7580:
7293:
7272:
6405:
When operator (function) names do not have a pre-defined abbreviation, we may use
5829:
This method should be avoided whenever technically possible to do so. Instead, use
5488:
4962:
4958:
4869:
Not all of the symbols in these lists are displayed correctly on all browsers (see
3025:
the preferred formatting is the LaTeX markup, with a possible exception for simple
2379:
2177:
2136:
2082:
1770:
1697:
1692:
1687:
1574:
1485:
1468:
1464:
1460:
1456:
1452:
1448:
1397:
1384:
1232:
1228:
955:
919:
5327:
when writing the less-than sign, just like in HTML and XML. For example, to write
4854:(with notable exception of "+", "=", "|", as well as ",", ":", and three sorts of
973:). In the latter case the LaTeX source is displayed without the tags <math: -->
50:
It is a generally accepted standard that editors should attempt to follow, though
5047:
4954:
4950:
3230:
The download speed of a page is negatively affected if it contains many formulas.
3041:
Knowledge (XXG) allows editors to typeset mathematical formulae in (a subset of)
1802:
1786:
1716:
1711:
1649:
1611:
1514:
1428:
1419:
982:
The lead sentence should informally define or describe the subject. For example:
8452:
8390:
8308:
8252:
8244:
5744:
5542:
5043:
2825:
2735:
1937:
1224:
987:
897:
7797:). Font preferences vary from one mathematical author or publisher to another.
6057:
should be written as prose, to avoid using more vertical space than necessary:
8265:
7644:
7300:. This makes the more common practice to use an italic face for the constant
6906:
5578:
The correct encoding of the minus sign "−" is different from all varieties of
5313:
Knowledge (XXG):Manual of Style/Abbreviations § Unicode abbreviation ligatures
5249:
4839:
3914:
3501:{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {\pi ^{2}}{6}}.}
2821:
1971:
1957:
1953:
1278:
4965:. (The only exception is when discussing the Unicode characters themselves.)
2908:
Knowledge (XXG) articles cannot be a substitute for a textbook (that is what
8368:
8312:
8198:
6519:
includes correct spacing that would not be present with other means such as
5468:
4246:
for functions in other cases; for example when we define the function as in
2909:
2817:
2567:
2412:
The bar notation is discouraged because it is not supported by all browsers.
1964:
1949:
1475:
2115:
need not be bounded. In a bounded lattice, 0 and 1 are allowed to be equal.
8046:
7912:
reasons among others. Metric units are given in decimal fractions (e.g.,
7282:. For example, the ISO 80000-2 recommends that the mathematical constant
2402:(with the bar on the side of the non-normal subgroup) with or without the
8082:
Recent geometry books tend to use an italic serif font in diagrams as in
5538:
5464:
5159:
5068:
2283:
1243:
1192:
1181:
8406:
8255:(including wiki code), it should not be seen in a rendered page, though.
8172:—advice on providing references for mathematical and scientific articles
7240:
Some authors prefer to use an upright (Roman) font for operators, as in
7088:{\displaystyle {\frac {dz}{dx}}={\frac {dz}{dy}}\cdot {\frac {dy}{dx}},}
1874:, as well as notation, such as the correct symbols to use for a subset.
7902:
4855:
4843:
4585:
4212:
3895:. Not all templates are recommended for use; in particular, use of the
3062:
2846:
primes = sieve sieve (p : xs) = p : sieve </syntaxhighlight: -->
2279:
1982:
1703:
The reader might not find what you write obvious. Instead, try to hint
1046:
8328:(¼, ½, and ¾) work with screen readers, but others, like ⅐, might not.
6179:
An exception would be if some of the definitions are very long (as in
1316:
should be highlighted with words such as "is defined by" in the text.
8446:
General style manuals often include advice on mathematics, including
8363:(second ed.), SIAM (Society for Industrial and Applied Mathematics),
5579:
3905:
template to format fractions is discouraged in mathematics articles.
3054:
2428:
5566:
Metric units often embed the notion of multiplication and division.
5558:
5412:
Standard algebraic notation is best for formulae, so two variables
1734:(if and only if), as well as quantifier symbols ∀ and ∃ instead of
8486:
8045:
6917:, Knowledge (XXG) articles usually use an italic font. One writes
6905:
For single-letter variables, constants, and operators such as the
5203:
for set substraction. (Either Unicode character can be used where
5163:
4847:
3923:
3042:
8074:
Knowledge (XXG):How to create charts for Knowledge (XXG) articles
6894:
An opinion: Why you should never use \mbox within Knowledge (XXG)
5570:
endorses the half-high dot (⋅) or a bare space for this purpose.
2382:
defining the product. The semidirect product may also be written
2068:
Separation axioms for topological spaces are as described on the
2032:
is not assumed to be separated. The term "prescheme" is not used.
5583:
5567:
3223:
Having LaTeX-based formulae inline has the following drawbacks:
3065:), depending on user preferences. For more details on this, see
3058:
8490:
8276:
Knowledge (XXG) talk:WikiProject Mathematics/Archive 68#ƒ or f?
6213:
If the formula is written in LaTeX, that is, surrounded by the
5898:
method or √ with no overline should be used in image captions.
1769:
when verbalizing quantifiers since it is ambiguous. Instead of
9227:
6101:{\displaystyle \mathbf {F} =\mathbf {b} \times a\mathbf {r} ,}
5971:{\displaystyle \mathbf {F} =\mathbf {b} \times a\mathbf {r} ,}
3046:
2310:) (and with the implied convention that the category is not a
1722:
Articles should avoid common blackboard abbreviations such as
1281:. Multiple related examples may also be given together, as in
918:, is it best to assume that a reader is already familiar with
126:
25:
8227:
Unicode Technical Report #25: Unicode Support for Mathematics
7846:
Knowledge (XXG):Manual of Style/Dates and numbers § Fractions
7819:
5248:(which on some systems is too small and can be confused with
4862:
includes markup for LaTeX and HTML, and Unicode code points.
4612:
Knowledge (XXG):Manual of Style (superscripts and subscripts)
4275:
Sets are usually written in upper case italics; for example:
5027:
can be useful to prevent overlap with italicized characters.
3801:. Take care of some necessary substitutions documented for
1717:
By a straightforward, if lengthy, algebraic calculation, ...
6340:(parentheses are required to clarify the intended argument)
5304:, which on some systems renders as two separate characters.
3168:). Instead, formulas may be placed on their own line using
3166:
Knowledge (XXG):Manual of Style/Accessibility § Indentation
3049:); the formulae are, for a default reader, translated into
1338:
Knowledge (XXG):Manual of Style/Layout § "See also" section
7790:{\displaystyle \mathbb {H} ^{i}(X,\Omega _{X}^{\bullet })}
4510:. Again, typically we use wiki markup: three apostrophes (
4242:, are not in italic font, but we use italic names such as
4945:(ASCII) letters should be used instead of the equivalent
1563:
In definitions, the symbol "=" is preferred over "≡" or "
1275:
Algebraic number theory § Failure of unique factorization
1265:, or to present multiple equivalent formulations, as for
7579:) and for certain other mathematical objects, including
5526:), which produces a symmetrically spaced centered dot: "
5455:. Do not use the letter "x" to indicate multiplication.
1948:. There is an exception for rings of operators, such as
1862:
Knowledge (XXG):WikiProject Logic/Standards for notation
1341:
8211:
7323:
6623:{\displaystyle x_{\text{this one}}=y_{\text{that one}}}
6200:
5918:
5776:
5718:
5403:
4927:
4911:" in an elementary article may make it more accessible.
4813:
4420:
For consistency with the LaTeX style, do not italicize
3072:
The LaTeX formulae can be displayed inline (like this:
2959:
2952:
1831:
1756:
1554:
1368:
1361:
95:
88:
81:
7901:) is discouraged in mathematics articles. The use of
7857:
4790:
will be an image, and for others it will be HTML like
3791:(optionally excluding the adjacent punctuation), e.g.
3731:
3553:
3260:
8108:
8088:
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3078:
2669:
2642:
2609:
2580:
2549:
2523:
2497:
2477:
2457:
2437:
8349:
A style guide specifically written for mathematics:
5701:
template to avoid line breaks and use the TeX font.
4763:
depending on user preferences. Thus, for some users
4444:
According to the Unicode Consortium, the characters
3891:Templates supporting HTML formatting are listed in
3617:{\textstyle \sum _{n=1}^{\infty }1/n^{2}=\pi ^{2}/6}
3189:. For instance, the formula above was typeset using
2415:
If the bar notation is used it should be entered as
2193:, or in contexts where there may be confusion with
1683:
Avoid, as far as possible, useless phrases such as:
1277:, while others may deserve their own section, as in
9215:
9109:
9074:
9011:
8990:
8889:
8873:
8842:
8776:
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3658:
3633:
3627:
3517:
3372:
3345:
3323:
3287:
3244:
3192:
3169:
1053:The lead section should include, when appropriate:
8420:Some finer points of typography are discussed in:
8116:
8094:
8030:
7953:
7871:
7789:
7729:
7700:
7667:
7635:
7603:
7571:
7543:
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7481:
7457:
7433:
7409:
7385:
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6717:
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3716:
3616:
3500:
3312:
3276:
3153:
3101:
2682:
2655:
2624:
2595:
2563:symbol should be explicitly explained in the text.
2555:
2535:
2509:
2483:
2463:
2443:
946:and summarize the article's most important points.
8360:Handbook of Writing for the Mathematical Sciences
4971:Knowledge (XXG):Manual of Style/Dates and numbers
4834:may be useful when editing mathematics articles.
4616:Superscripts and subscripts should be wrapped in
3797:, or by replacing the tags with a template, e.g.
1712:It follows directly from this definition that ...
1310:How to create graphs for Knowledge (XXG) articles
1009:, 'study') is concerned with the properties of a
5834:tags and \sqrt{}, even if inline. For example:
3102:{\displaystyle \mathbf {x} \in \mathbb {R} ^{2}}
8451:University of Chicago Press Staff, ed. (2010),
7244:, for the differential operator, as opposed to
6891:, but this is now considered undesirable. See
4969:For when to use or not use Roman numerals, see
2738:of vectors should be denoted with a centre-dot
2570:, use superscript non-italic capital letter T:
8170:Knowledge (XXG):Scientific citation guidelines
2800:Knowledge (XXG):WikiProject Mathematics/Proofs
2221:is used (this does not affect the notation of
8502:
7836:markup should not be used in image captions.
5208:markup cannot be used for technical reasons.)
4879:Mathematical operators and symbols in Unicode
3428:is too large to be used inline, rendering as
3344:Often better formatting can be achieved with
2896:Including citations and literature references
873:
8:
8337:Not all fractions are available precomposed.
7288:should be typeset in an upright Roman font:
6847:{\displaystyle r=x_{predicted}-x_{observed}}
1028:, crumpling and bending, but not tearing or
932:Knowledge (XXG):Manual of Style/Lead section
9127:Categories, lists, and navigation templates
6965:{\displaystyle \int _{0}^{\pi }\sin x\,dx,}
5424:when presented in a formula. That is, when
4873:). Although the symbols that correspond to
3154:{\displaystyle \int _{0}^{\pi }\sin x\,dx.}
1283:Adjunction formula § Applications to curves
1004:
998:
771:Categories, lists, and navigation templates
42:is a part of the English Knowledge (XXG)'s
8509:
8495:
8487:
8432:, Reading, Massachusetts: Addison-Wesley,
7260:; other authors use Roman boldface, as in
6883:For several years this manual recommended
6718:{\displaystyle \sum _{i=1}^{n}{y_{i}^{2}}}
3913:By default, regular text is rendered in a
3893:Category:Mathematical formatting templates
1424:may be decomposed into cosets, as follows.
1393:can be decomposed into cosets, as follows.
880:
866:
396:
360:
107:
9277:Knowledge (XXG) Manual of Style (science)
8457:(16th ed.), University of Chicago Press,
8311:before the punctuation instead, but it's
8109:
8107:
8087:
8018:
8014:
8008:
7943:
7938:
7908:(such as ½) is discouraged entirely, for
7872:{\displaystyle \textstyle {\frac {1}{2}}}
7858:
7855:
7778:
7773:
7754:
7750:
7749:
7746:
7721:
7717:
7716:
7713:
7692:
7688:
7687:
7684:
7659:
7655:
7654:
7651:
7627:
7623:
7622:
7619:
7595:
7591:
7590:
7587:
7563:
7559:
7558:
7555:
7532:
7528:
7527:
7524:
7501:
7497:
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7472:
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7469:
7448:
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7424:
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7399:
7397:
7376:
7375:
7373:
7352:
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7349:
7198:
7192:
7153:
7062:
7039:
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7014:
6936:
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6780:
6768:
6708:
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6698:
6692:
6681:
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6352:
6304:
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6118:
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6090:
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2586:
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2548:
2522:
2496:
2476:
2456:
2436:
2211:; when written multiplicatively, e.g. as
2187:, when written additively, has notation Z
1817:, depending on what you wish to express.
5541:(*) as a multiplication sign outside of
5042:when the character should render like a
4836:Almost all mathematical operator symbols
4492:). This is also required for "micro" by
3838:Images generated from LaTeX markup have
1963:The ring with one element is called the
8480:) is being considered for merging. See
8182:
8165:Knowledge (XXG):WikiProject Mathematics
6951:
6489:{\displaystyle a\operatorname {tr} (A)}
6436:{\displaystyle 2\operatorname {csch} x}
5869:{\displaystyle {\sqrt {9}},{\sqrt{27}}}
5615:to have the ] treated as literal text.
5162:) in mathematical expressions, because
4883:force the symbol to display as an image
4860:list of mathematical symbols by subject
4828:list of mathematical symbols by subject
3140:
2845:<syntaxhighlight lang="Haskell": -->
2234:The standard notation for the abstract
1293:of an encyclopedia, examples should be
460:
110:
6238:This shows that {{nowrap|<math: -->
4961:, and not precomposed characters like
4947:Unicode characters in the U+21XX range
3826:) added at the end of the formula, or
3626:which fits much better inline. Adding
2974:One may set formulae using LaTeX (the
2616:
1960:, which we do not assume to be unital.
943:provide context regarding the subject,
62:. When in doubt, discuss first on the
5420:being multiplied are best written as
5264:(which on some systems is too large).
5164:tilde has other mathematical meanings
3852:<math alt="Square root of pi": -->
3717:{\displaystyle {\sqrt {x^{2}+y^{2}}}}
3053:images. They may also be rendered as
1342:§ Including literature and references
1129:to denote exponentiation (instead of
7:
8393:(1970), "How to Write Mathematics",
8307:It is technically possible to use a
8148:Knowledge (XXG):Mathematical symbols
5177:... \smallsetminus ...</math: -->
4832:Knowledge (XXG):Mathematical symbols
4600:
2937:Typesetting of mathematical formulae
971:), or in LaTeX (inside <math: -->
7995:
7970:
7832:
6061:Example 2: The foocity is given by
5931:Example 1: The foocity is given by
5884:
5830:
5727:There is a special Unicode symbol,
5204:
4886:
4675:Do not use special characters like
3918:
2975:
8110:
7770:
7675:, the additive and multiplicative
6544:
6541:
6538:
5905:Explanation of symbols in formulae
3762:{\textstyle {\sqrt {x^{2}+y^{2}}}}
3570:
3453:
2675:
2587:
2139:follows the Serre convention that
1730:(without loss of generality), and
1049:to three given circles in a plane.
24:
8238:Note that, aside of <math: -->
7544:{\displaystyle \mathbb {Z} _{p},}
7513:{\displaystyle \mathbb {F} _{q},}
4103:is a value on the horizontal axis
4091:is a value on the horizontal axis
3109:), as well as on their own line:
1433:be the corresponding subgroup of
1402:be the corresponding subgroup of
1287:Lambert W function § Applications
1045:is to construct circles that are
58:edit to this page should reflect
9239:
9238:
8137:Help for those writing a formula
7730:{\displaystyle \mathbb {G} _{m}}
7701:{\displaystyle \mathbb {G} _{a}}
7668:{\displaystyle \mathbb {A} _{K}}
7636:{\displaystyle \mathbb {P} ^{n}}
7604:{\displaystyle \mathbb {A} ^{n}}
7572:{\displaystyle \mathbb {Q} _{p}}
6239:\tfrac{1}{2} = 0.5</math: -->
6161:
6153:is the bazness coefficient, and
6119:
6091:
6080:
6072:
6038:
5992:
5961:
5950:
5942:
3277:{\displaystyle {\tfrac {1}{2}}x}
3080:
2900:Per the Knowledge (XXG) policy,
2596:{\displaystyle X^{\mathrm {T} }}
940:describe and define the subject,
29:
5172:... \setminus ...</math: -->
4025:The relationship is defined as
3966:The relationship is defined as
3774:
3773:HTML-generating formatting, as
2625:{\displaystyle X^{\mathsf {T}}}
1415:Instead, write something like:
18:Knowledge (XXG):Manual of Style
8153:Knowledge (XXG):Rendering math
7784:
7760:
6483:
6477:
6327:
6315:
5737:LATIN SMALL LETTER F WITH HOOK
4413:(It is also possible to enter
3872:{\displaystyle {\sqrt {\pi }}}
2838:Source code should always use
1707:something must hold, such as:
1263:Poincaré–Birkhoff–Witt theorem
1242:(number of elements) of every
1093:discriminant of a number field
1:
9044:References and external links
7482:{\displaystyle \mathbb {H} ,}
7458:{\displaystyle \mathbb {C} ,}
7434:{\displaystyle \mathbb {R} ,}
7410:{\displaystyle \mathbb {Q} ,}
7386:{\displaystyle \mathbb {Z} ,}
7362:{\displaystyle \mathbb {N} ,}
7213:{\displaystyle e^{i\theta }.}
6555:{\displaystyle 2{\rm {sin}}x}
5154:to mean "approximately" (and
4577:{\displaystyle \mathbb {R} .}
3365:tag, which translates to the
3004:For inline formulae, such as
670:References and external links
8484:to help reach a consensus. ›
8313:seldom respected by browsers
8229:, §2.5 Duplicated Characters
8117:{\displaystyle \mathrm {A} }
6887:as a workaround for lack of
6168:{\displaystyle \mathbf {r} }
6126:{\displaystyle \mathbf {b} }
6045:{\displaystyle \mathbf {r} }
5999:{\displaystyle \mathbf {b} }
5270:... \ngtr ...</math: -->
4824:list of mathematical symbols
3657:<math display=inline: -->
3516:<math display=inline: -->
2931:Knowledge (XXG):Cite sources
2423:(⋊) for maximum portability.
1348:Writing style in mathematics
8897:Specific naming conventions
8454:The Chicago Manual of Style
8395:Enseignements Mathématiques
6028:is the bazness coefficient,
5214:... \circ ...</math: -->
4606:Superscripts and subscripts
4592:(plain text ℝ or math font
3341:is too tall to fit inline.
3191:<math display=block: -->
3001:for mathematical articles.
2842:. For example this markup:
2781:, never with juxtaposition
2464:{\displaystyle \subsetneq }
2363:is the normal subgroup and
1903:" has two common meanings:
525:Specific naming conventions
9293:
8576:Organizing by subject area
8071:
7843:
7313:
6333:{\displaystyle 2\sin(x+1)}
6190:
6187:Punctuation after formulae
5908:
5766:
5708:
5582:"-‐‑", as well as from en-
5393:
5310:
4968:
4917:
4803:
4609:
4598:
4490:GREEK CAPITAL LETTER OMEGA
4362:would then be typeset by:
3029:of Latin letters, digits,
2967:
2942:
2809:
2510:{\displaystyle A\subset B}
2444:{\displaystyle \subseteq }
1859:
1821:
1746:
1688:It is easily seen that ...
1544:
1473:
1461:It must be emphasized that
1351:
1279:Chain rule § First example
929:
71:
9234:
9202:Wikimedia sister projects
8524:
8195:WP:DICT#Major differences
8143:Help:Displaying a formula
5879:Because of Mediawiki bug
5743:), sometimes used as the
4376:''λ'' + ''y''
3067:Help:Displaying a formula
2970:Help:Displaying a formula
2849:generates the following:
2683:{\displaystyle X^{\top }}
2543:). All other uses of the
1915:which may also be called
1907:which may also be called
1457:It must be mentioned that
1013:that are preserved under
1005:
999:
826:Wikimedia sister projects
8482:templates for discussion
8210:This example, from here
7804:\mathbb{Z}</math: -->
6175:is the quuxance vector.
5759:should be used instead.
5755:. An italicized letter
5753:NonVisual Desktop Access
5691:These templates use the
5447:in HTML or accessed via
3917:font. The TeX markup of
3853:\sqrt{\pi}</math: -->
3031:common punctuation marks
2995:talk page of the article
2851:
2697:, infima are written as
2556:{\displaystyle \subset }
2484:{\displaystyle \subset }
2421:{{unicode|⋊}}
2417:{{unicode|⋉}}
1923:if the context permits.
1856:Mathematical conventions
1039:Euclidean plane geometry
9267:WikiProject Mathematics
8369:10.1137/1.9780898719550
8031:{\displaystyle x^{1/2}}
7271:the same principles as
6281:{\displaystyle 2\sin x}
6133:is the barness vector,
6052:is the quuxance vector.
4871:Help:Special characters
4516:) rather than the HTML
2999:WikiProject Mathematics
2271:odd and greater than 1.
2089:with finite joins, not
1886:Terminology conventions
1453:It should be noted that
9272:Knowledge (XXG) how-to
8118:
8096:
8069:
8032:
7955:
7873:
7823:\bold{1}</math: -->
7791:
7731:
7702:
7669:
7637:
7605:
7573:
7545:
7514:
7483:
7459:
7435:
7411:
7387:
7363:
7214:
7174:
7089:
6997:—note the thin space (
6966:
6848:
6725:(correct—typeset from
6719:
6697:
6630:(correct—typeset from
6624:
6556:
6490:
6437:
6399:implied multiplication
6373:
6334:
6282:
6177:
6169:
6147:
6127:
6102:
6055:
6046:
6022:
6006:is the barness vector,
6000:
5972:
5870:
5745:Florin currency symbol
5286:
5285:{\displaystyle \ngtr }
5230:
5229:{\displaystyle \circ }
4784:
4578:
4500:Common sets of numbers
4215:are never italicized:
4211:is the mass of a foo.
3873:
3850:element. For example,
3763:
3718:
3618:
3574:
3502:
3457:
3314:
3278:
3155:
3103:
2684:
2657:
2626:
2597:
2557:
2537:
2511:
2485:
2465:
2445:
2171:Notational conventions
1259:
1231:, states that for any
1210:
1051:
1034:
8834:Writing about fiction
8385:More style guidance:
8119:
8097:
8049:
8033:
8001:x^{1/2}</math: -->
7956:
7923:in abstract algebra:
7919:Only "/" is used for
7906:precomposed fractions
7879:), or with a forward
7874:
7792:
7732:
7703:
7670:
7638:
7606:
7574:
7546:
7515:
7484:
7460:
7436:
7412:
7388:
7364:
7215:
7175:
7173:{\displaystyle x+iy,}
7090:
6967:
6849:
6720:
6677:
6625:
6557:
6491:
6438:
6374:
6372:{\displaystyle 2sinx}
6335:
6283:
6170:
6148:
6128:
6103:
6059:
6047:
6023:
6001:
5973:
5929:
5871:
5537:Do not use the ASCII
5428:a formula, don't use
5287:
5231:
5071:for a canonical list.
4785:
4783:{\displaystyle x^{2}}
4599:Further information:
4584:However, the special
4579:
4478:GREEK SMALL LETTER MU
4424:Greek letters; e.g.
3874:
3815:Deprecated formatting
3793:({{nobr|<math: -->
3764:
3719:
3619:
3554:
3503:
3437:
3315:
3279:
3156:
3104:
2685:
2658:
2656:{\displaystyle X^{T}}
2627:
2598:
2558:
2538:
2512:
2486:
2466:
2446:
2314:unless that is said).
2046:is not assumed to be
1909:non-negative integers
1253:divides the order of
1218:
1142:
1065:informal introduction
1058:Historical motivation
1035:
984:
453:Writing about fiction
158:Organizing by subject
112:Manual of Style (MoS)
52:occasional exceptions
9177:Talk page guidelines
8865:Stringed instruments
8571:Disambiguation pages
8106:
8086:
8007:
7937:
7854:
7745:
7712:
7683:
7650:
7618:
7586:
7554:
7523:
7492:
7468:
7444:
7420:
7396:
7372:
7348:
7191:
7152:
7013:
6924:
6767:
6674:
6594:
6530:
6465:
6418:
6386:2sin x</math: -->
6351:
6303:
6263:
6157:
6137:
6115:
6068:
6034:
6012:
5988:
5938:
5841:
5276:
5220:
5069:Asterisk#Mathematics
4838:have their specific
4767:
4588:characters, such as
4563:
3859:
3729:
3684:
3551:
3434:
3296:
3256:
3113:
3076:
2830:programming language
2816:An article about an
2667:
2640:
2607:
2578:
2547:
2521:
2495:
2475:
2455:
2435:
2018:is assumed to be an
1204:) is an open set in
1043:Apollonius's problem
926:Article introduction
892:This subpage of the
806:Talk page guidelines
481:Stringed instruments
153:Disambiguation pages
8982:Trinidad and Tobago
8912:France (and French)
8907:China (and Chinese)
8407:10.5169/seals-43857
8355:Higham, Nicholas J.
8159:General information
8042:Graphs and diagrams
7976:R / A</math: -->
7954:{\displaystyle R/A}
7783:
7183:x+iy,</math: -->
6941:
6901:Roman versus italic
6713:
6395:order of operations
5441:multiplication sign
5390:Multiplication sign
4852:General Punctuation
4559:, which renders as
3855:generates an image
3313:{\displaystyle x/2}
3130:
2840:syntax highlighting
2536:{\displaystyle A=B}
2451:, proper subset by
2267:, and are zero for
1726:(with respect to),
1138:mathematical object
1136:An article about a
610:Trinidad and Tobago
545:France (and French)
535:China (and Chinese)
9182:Template namespace
8264:Latin Extended-B,
8191:ring (mathematics)
8114:
8092:
8070:
8028:
7951:
7869:
7868:
7787:
7769:
7727:
7698:
7665:
7633:
7601:
7569:
7541:
7510:
7479:
7455:
7431:
7407:
7383:
7359:
7210:
7170:
7085:
6995:dx ,</math: -->
6962:
6952:
6927:
6844:
6715:
6699:
6620:
6552:
6486:
6433:
6369:
6330:
6278:
6251:Multi-letter names
6165:
6143:
6123:
6098:
6042:
6018:
5996:
5968:
5919:MOS:EXPLAINSYMBOLS
5866:
5483:An alternative to
5478:−42 = 9 × (−5) + 3
5463:26 by 4, 6 is the
5282:
5226:
4890:with LaTeX markup.
4780:
4574:
4298:would be written:
4232:standard functions
3869:
3846:attribute for the
3759:
3714:
3614:
3498:
3310:
3274:
3269:
3151:
3141:
3116:
3099:
3037:Using LaTeX markup
2680:
2653:
2622:
2593:
2553:
2533:
2507:
2481:
2461:
2441:
2329:should be written
2319:semidirect product
2302:) rather than Mor(
2119:Elliptic functions
2061:for our notion of
2009:Algebraic geometry
1905:{0, 1, 2, 3, ...},
1555:MOS:MATH#DEFSYMBOL
1323:Concluding matters
1221:Lagrange's theorem
1154:topological spaces
974:and </math: -->
914:in the context of
811:Template namespace
755:Related guidelines
9254:
9253:
9192:Understandability
9054:Structure drawing
9003:Latter Day Saints
8804:Lyrics and poetry
8747:Stand-alone lists
8634:Dates and numbers
8095:{\displaystyle A}
7866:
7834:...</math: -->
7080:
7057:
7034:
6617:
6604:
6510:(A)</math: -->
6146:{\displaystyle a}
6021:{\displaystyle a}
5886:...</math: -->
5864:
5849:
5832:...</math: -->
5613:]</nowiki: -->
5206:...</math: -->
5060:ASTERISK OPERATOR
4888:...</math: -->
4601:§ Blackboard bold
3960:special attention
3920:...</math: -->
3867:
3799:({{tmath|1=...}})
3794:...</math: -->
3788:...</math: -->
3757:
3712:
3493:
3473:
3268:
3045:markup (see also
3016:WP:Rendering math
2980:section headings,
2824:or in some cases
2259:Bernoulli numbers
2248:in geometry and D
2016:algebraic variety
1990:Clifford algebras
1936:is assumed to be
1917:positive integers
972:...</math: -->
890:
889:
816:Understandability
746:
745:
680:Structure drawing
635:Latter Day Saints
488:
487:
423:Lyrics and poetry
345:Stand-alone lists
220:Dates and numbers
106:
105:
9284:
9242:
9241:
9228:
9152:Military history
9061:Computer science
9034:Compound classes
8881:Military history
8511:
8504:
8497:
8488:
8466:
8441:
8426:Knuth, Donald E.
8409:
8380:
8338:
8335:
8329:
8322:
8316:
8305:
8299:
8296:
8290:
8287:October 2020 RfC
8284:
8278:
8273:
8267:
8262:
8256:
8245:parser functions
8236:
8230:
8224:
8218:
8208:
8202:
8187:
8123:
8121:
8120:
8115:
8113:
8101:
8099:
8098:
8093:
8067:
8063:
8057:
8053:
8037:
8035:
8034:
8029:
8027:
8026:
8022:
8002:
7993:
7989:
7987:1/2</sup: -->
7977:
7968:
7967:|''R'' / ''A''}}
7960:
7958:
7957:
7952:
7947:
7932:
7921:quotient objects
7915:
7900:
7899:
7895:
7890:
7878:
7876:
7875:
7870:
7867:
7859:
7835:
7810:
7809:\Z</math: -->
7805:
7796:
7794:
7793:
7788:
7782:
7777:
7759:
7758:
7753:
7736:
7734:
7733:
7728:
7726:
7725:
7720:
7707:
7705:
7704:
7699:
7697:
7696:
7691:
7674:
7672:
7671:
7666:
7664:
7663:
7658:
7642:
7640:
7639:
7634:
7632:
7631:
7626:
7613:projective space
7610:
7608:
7607:
7602:
7600:
7599:
7594:
7578:
7576:
7575:
7570:
7568:
7567:
7562:
7550:
7548:
7547:
7542:
7537:
7536:
7531:
7519:
7517:
7516:
7511:
7506:
7505:
7500:
7488:
7486:
7485:
7480:
7475:
7464:
7462:
7461:
7456:
7451:
7440:
7438:
7437:
7432:
7427:
7416:
7414:
7413:
7408:
7403:
7392:
7390:
7389:
7384:
7379:
7368:
7366:
7365:
7360:
7355:
7326:
7305:
7291:
7287:
7264:
7259:
7255:
7251:
7247:
7243:
7235:
7233:
7230:
7226:
7219:
7217:
7216:
7211:
7206:
7205:
7184:
7179:
7177:
7176:
7171:
7145:
7143:
7139:
7135:
7132:
7129:
7126:
7122:
7118:
7115:
7111:
7107:
7103:
7100:
7094:
7092:
7091:
7086:
7081:
7079:
7071:
7063:
7058:
7056:
7048:
7040:
7035:
7033:
7025:
7017:
7006:
7002:
7001:
6996:
6994:
6990:
6987:
6984:
6980:
6977:
6971:
6969:
6968:
6963:
6940:
6935:
6890:
6886:
6878:
6876:
6872:
6868:
6864:
6853:
6851:
6850:
6845:
6843:
6842:
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6753:
6749:
6745:
6741:
6737:
6733:
6730:
6724:
6722:
6721:
6716:
6714:
6712:
6707:
6696:
6691:
6662:
6660:
6656:
6653:
6650:
6646:
6642:
6639:
6636:
6629:
6627:
6626:
6621:
6619:
6618:
6615:
6606:
6605:
6602:
6581:
6579:
6575:
6572:
6561:
6559:
6558:
6553:
6548:
6547:
6522:
6518:
6511:
6509:
6505:
6502:
6495:
6493:
6492:
6487:
6458:
6456:
6452:
6449:
6442:
6440:
6439:
6434:
6410:
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6387:
6378:
6376:
6375:
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6339:
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6336:
6331:
6296:
6294:
6287:
6285:
6284:
6279:
6241:
6236:template, as in
6235:
6229:
6225:
6220:
6216:
6203:
6174:
6172:
6171:
6166:
6164:
6152:
6150:
6149:
6144:
6132:
6130:
6129:
6124:
6122:
6107:
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6099:
6094:
6083:
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6051:
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6048:
6043:
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6027:
6025:
6024:
6019:
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6003:
6002:
5997:
5995:
5977:
5975:
5974:
5969:
5964:
5953:
5945:
5921:
5897:
5891:
5887:
5875:
5873:
5872:
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5865:
5863:
5855:
5850:
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5833:
5825:
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5742:
5738:
5735:
5732:
5731:
5721:
5700:
5694:
5686:
5676:
5675:
5671:
5668:
5665:
5658:. For instance:
5657:
5651:
5647:
5641:
5637:
5631:
5627:
5621:
5614:
5597:
5593:
5561:
5557:
5554:
5553:
5548:
5525:
5517:
5516:
5513:
5510:
5507:
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5498:
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5479:
5474:
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5446:
5443:: "×", coded as
5431:
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5384:
5383:
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5373:
5370:
5358:
5357:
5353:
5350:
5347:
5344:
5341:
5333:
5326:
5303:
5302:NOT GREATER-THAN
5300:
5297:
5296:
5291:
5289:
5288:
5283:
5271:
5263:
5260:
5257:
5256:
5247:
5244:
5241:
5240:
5235:
5233:
5232:
5227:
5215:
5207:
5202:
5199:
5196:
5195:
5190:
5187:
5184:
5183:
5178:
5173:
5157:
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5146:
5143:
5142:
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5134:
5131:
5130:
5123:
5120:
5117:
5116:
5111:
5108:
5105:
5104:
5097:
5094:
5091:
5090:
5085:
5082:
5079:
5078:
5061:
5058:
5055:
5054:
5049:
5041:
5038:
5035:
5034:
5026:
5020:
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4996:
4995:
4990:
4987:
4984:
4983:
4964:
4960:
4956:
4952:
4930:
4910:
4889:
4830:and the list at
4816:
4795:
4789:
4787:
4786:
4781:
4779:
4778:
4762:
4761:
4758:
4755:
4751:
4748:
4745:
4736:
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4710:
4706:
4684:
4680:
4670:
4669:
4665:
4662:
4658:
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4652:
4649:
4646:
4643:
4640:
4632:
4623:
4619:
4595:
4591:
4583:
4581:
4580:
4575:
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4558:
4557:
4554:
4551:
4548:
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4541:
4538:
4535:
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4527:
4526:
4523:
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4514:
4509:
4491:
4488:
4485:
4484:
4479:
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4464:
4461:
4460:
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4452:
4449:
4448:
4441:
4439:
4410:
4409:
4405:
4402:
4398:
4395:
4392:
4389:
4386:
4383:
4380:
4377:
4374:
4371:
4368:
4361:
4338:
4336:
4331:
4327:
4323:
4320:
4317:
4314:
4311:
4308:
4305:
4293:
4267:
4265:
4245:
4241:
4237:
4221:
4210:
4200:
4194:
4190:
4184:
4177:
4160:
4159:
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4152:
4149:
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4132:
4129:
4126:
4123:
4120:
4117:
4114:
4102:
4092:
4090:
4086:
4083:
4080:
4072:
4066:
4062:
4058:
4054:
4048:
4035:
4021:will result in:
4016:
4015:
4011:
4008:
4005:
4001:
3998:
3995:
3992:
3988:
3985:
3982:
3979:
3976:
3973:
3970:
3957:
3951:
3947:
3941:
3933:
3921:
3904:
3898:
3878:
3876:
3875:
3870:
3868:
3863:
3854:
3849:
3845:
3829:
3825:
3810:
3804:
3800:
3796:
3789:
3770:, respectively.
3769:
3768:
3766:
3765:
3760:
3758:
3756:
3755:
3743:
3742:
3733:
3723:
3721:
3720:
3715:
3713:
3711:
3710:
3698:
3697:
3688:
3680:which render as
3679:
3677:
3676:
3672:
3668:
3664:
3661:
3654:
3652:
3651:
3647:
3643:
3639:
3636:
3629:
3625:
3623:
3621:
3620:
3615:
3610:
3605:
3604:
3592:
3591:
3582:
3573:
3568:
3545:
3543:
3541:
3538:
3534:
3530:
3527:
3523:
3520:
3513:
3507:
3505:
3504:
3499:
3494:
3489:
3488:
3479:
3474:
3472:
3471:
3459:
3456:
3451:
3427:
3425:
3424:
3420:
3416:
3413:
3410:
3407:
3403:
3399:
3395:
3391:
3388:
3385:
3382:
3378:
3375:
3368:
3364:
3363:
3360:
3357:
3354:
3351:
3348:
3340:
3338:
3337:
3333:
3329:
3326:
3319:
3317:
3316:
3311:
3306:
3291:
3289:
3283:
3281:
3280:
3275:
3270:
3261:
3251:
3249:
3247:
3216:
3214:
3212:
3208:
3205:
3202:
3198:
3195:
3188:
3187:
3184:
3181:
3178:
3175:
3172:
3160:
3158:
3157:
3152:
3129:
3124:
3108:
3106:
3105:
3100:
3098:
3097:
3092:
3083:
3013:
2977:
2962:
2955:
2891:
2888:
2885:
2882:
2879:
2876:
2873:
2870:
2867:
2864:
2861:
2858:
2855:
2762:
2747:
2730:
2720:
2707:or as a product
2706:
2689:
2687:
2686:
2681:
2679:
2678:
2662:
2660:
2659:
2654:
2652:
2651:
2631:
2629:
2628:
2623:
2621:
2620:
2619:
2602:
2600:
2599:
2594:
2592:
2591:
2590:
2562:
2560:
2559:
2554:
2542:
2540:
2539:
2534:
2516:
2514:
2513:
2508:
2490:
2488:
2487:
2482:
2470:
2468:
2467:
2462:
2450:
2448:
2447:
2442:
2422:
2418:
2401:
2391:
2377:
2358:
2343:
2261:are denoted by B
2099:General Topology
2070:separation axiom
1914:
1906:
1834:
1816:
1800:
1784:
1759:
1718:
1713:
1699:
1694:
1689:
1679:
1641:
1603:
1557:
1539:
1510:Instead, write:
1506:
1470:
1466:
1462:
1458:
1454:
1450:
1442:
1425:
1411:
1394:
1371:
1364:
1267:Nakayama's lemma
1199:
1011:geometric object
1008:
1007:
1002:
1001:
970:
964:
960:
954:
916:abstract algebra
882:
875:
868:
687:Computer science
660:Compound classes
505:Military history
397:
361:
127:
108:
98:
91:
84:
33:
32:
26:
9292:
9291:
9287:
9286:
9285:
9283:
9282:
9281:
9257:
9256:
9255:
9250:
9230:
9229:
9224:
9211:
9105:
9070:
9007:
8986:
8885:
8869:
8838:
8784:Anime and manga
8772:
8751:
8720:
8716:Trivia sections
8689:
8675:Image placement
8658:
8654:Titles of works
8649:Text formatting
8612:
8603:Self-references
8583:Gender identity
8549:
8520:
8518:Manual of Style
8515:
8485:
8477:Manual of Style
8464:
8450:
8439:
8424:
8410:. Reprinted in
8389:
8378:
8353:
8347:
8345:Further reading
8342:
8341:
8336:
8332:
8323:
8319:
8306:
8302:
8297:
8293:
8285:
8281:
8274:
8270:
8263:
8259:
8237:
8233:
8225:
8221:
8209:
8205:
8188:
8184:
8179:
8161:
8139:
8134:
8104:
8103:
8084:
8083:
8076:
8065:
8061:
8055:
8051:
8044:
8010:
8005:
8004:
7991:
7981:
7962:
7935:
7934:
7924:
7913:
7897:
7893:
7892:
7884:
7852:
7851:
7848:
7842:
7820:a rendering bug
7807:
7802:
7748:
7743:
7742:
7739:hypercohomology
7715:
7710:
7709:
7686:
7681:
7680:
7653:
7648:
7647:
7621:
7616:
7615:
7589:
7584:
7583:
7557:
7552:
7551:
7526:
7521:
7520:
7495:
7490:
7489:
7466:
7465:
7442:
7441:
7418:
7417:
7394:
7393:
7370:
7369:
7346:
7345:
7334:blackboard bold
7330:
7329:
7322:
7318:
7312:
7310:Blackboard bold
7301:
7289:
7283:
7262:
7257:
7253:
7249:
7245:
7241:
7234:.</math: -->
7231:
7228:
7224:
7194:
7189:
7188:
7150:
7149:
7144:,</math: -->
7141:
7137:
7133:
7130:
7127:
7124:
7120:
7116:
7113:
7109:
7105:
7101:
7098:
7072:
7064:
7049:
7041:
7026:
7018:
7011:
7010:
6999:
6992:
6988:
6985:
6982:
6978:
6975:
6922:
6921:
6903:
6888:
6884:
6874:
6870:
6866:
6862:
6813:
6776:
6765:
6764:
6751:
6747:
6743:
6739:
6735:
6731:
6728:
6672:
6671:
6658:
6654:
6651:
6648:
6644:
6640:
6637:
6634:
6610:
6597:
6592:
6591:
6580:x</math: -->
6577:
6573:
6570:
6528:
6527:
6520:
6516:
6507:
6503:
6500:
6463:
6462:
6457:x</math: -->
6454:
6450:
6447:
6416:
6415:
6407:
6349:
6348:
6301:
6300:
6295:x</math: -->
6292:
6261:
6260:
6253:
6248:
6237:
6233:
6227:
6223:
6218:
6214:
6207:
6206:
6199:
6195:
6189:
6155:
6154:
6135:
6134:
6113:
6112:
6066:
6065:
6032:
6031:
6010:
6009:
5986:
5985:
5936:
5935:
5925:
5924:
5917:
5913:
5907:
5895:
5889:
5839:
5838:
5822:
5820:
5815:
5813:
5806:
5800:
5799:(often seen as
5796:
5790:
5783:
5782:
5775:
5771:
5765:
5756:
5740:
5736:
5733:
5729:
5728:
5725:
5724:
5717:
5713:
5707:
5705:Function symbol
5698:
5692:
5684:
5673:
5669:
5666:
5663:
5655:
5649:
5645:
5639:
5635:
5629:
5625:
5619:
5612:<nowiki: -->
5611:
5604:
5602:Square brackets
5595:
5587:
5576:
5559:
5555:
5551:
5550:
5546:
5519:
5514:
5511:
5508:
5505:
5502:
5499:
5496:
5491:
5484:
5477:
5473:26 = 6 × 4 + 2.
5472:
5448:
5444:
5429:
5410:
5409:
5402:
5398:
5392:
5381:
5377:
5374:
5371:
5368:
5355:
5351:
5348:
5345:
5342:
5339:
5328:
5324:
5320:
5315:
5301:
5298:
5294:
5293:
5274:
5273:
5268:
5261:
5258:
5254:
5253:
5245:
5242:
5238:
5237:
5218:
5217:
5212:
5201:REVERSE SOLIDUS
5200:
5197:
5193:
5192:
5188:
5185:
5181:
5180:
5175:
5170:
5155:
5147:
5144:
5140:
5139:
5135:
5132:
5128:
5127:
5121:
5118:
5114:
5113:
5109:
5106:
5102:
5101:
5095:
5092:
5088:
5087:
5083:
5080:
5076:
5075:
5059:
5056:
5052:
5051:
5039:
5036:
5032:
5031:
5024:
5018:
5014:
5008:
5000:
4997:
4993:
4992:
4988:
4985:
4981:
4980:
4974:
4949:. For example,
4934:
4933:
4926:
4922:
4902:
4901:" rather than "
4820:
4819:
4814:MOS:MATHSPECIAL
4812:
4808:
4802:
4800:Special symbols
4791:
4770:
4765:
4764:
4759:
4756:
4753:
4749:
4746:
4743:
4733:
4714:
4708:
4689:
4682:
4676:
4666:
4663:
4660:
4656:
4653:
4650:
4647:
4644:
4641:
4638:
4631:
4625:
4621:
4617:
4614:
4608:
4603:
4593:
4589:
4561:
4560:
4555:
4552:
4549:
4546:
4542:
4539:
4536:
4533:
4530:
4524:
4521:
4518:
4512:
4505:
4502:
4494:MOS:UNITSYMBOLS
4489:
4486:
4482:
4481:
4477:
4474:
4470:
4469:
4465:
4462:
4458:
4457:
4453:
4450:
4446:
4445:
4426:
4425:
4406:
4403:
4400:
4396:
4393:
4390:
4387:
4384:
4381:
4378:
4375:
4372:
4369:
4366:
4349:
4346:
4334:
4329:
4325:
4321:
4318:
4315:
4312:
4309:
4306:
4303:
4279:
4273:
4248:
4247:
4243:
4239:
4235:
4228:
4216:
4209:
4203:
4198:
4192:
4188:
4182:
4168:
4157:
4153:
4150:
4147:
4143:
4140:
4137:
4134:
4130:
4127:
4124:
4121:
4118:
4115:
4112:
4100:
4088:
4084:
4081:
4078:
4070:
4064:
4060:
4056:
4052:
4046:
4043:
4026:
4013:
4009:
4006:
4003:
3999:
3996:
3993:
3990:
3986:
3983:
3980:
3977:
3974:
3971:
3968:
3955:
3949:
3945:
3939:
3927:
3911:
3909:Font formatting
3902:
3896:
3886:
3857:
3856:
3851:
3847:
3843:
3836:
3827:
3823:
3817:
3808:
3802:
3798:
3792:
3786:
3785:Directly using
3783:
3775:described below
3747:
3734:
3727:
3726:
3725:
3702:
3689:
3682:
3681:
3674:
3670:
3666:
3662:
3659:
3656:
3649:
3645:
3641:
3637:
3634:
3631:
3596:
3583:
3549:
3548:
3547:
3539:
3536:
3532:
3528:
3525:
3521:
3518:
3515:
3511:
3508:
3480:
3463:
3432:
3431:
3422:
3418:
3414:
3411:
3408:
3405:
3401:
3397:
3393:
3389:
3386:
3383:
3380:
3376:
3373:
3370:
3366:
3361:
3358:
3355:
3352:
3349:
3346:
3335:
3331:
3327:
3324:
3321:
3294:
3293:
3285:
3254:
3253:
3245:
3242:
3210:
3206:
3203:
3200:
3196:
3193:
3190:
3185:
3182:
3179:
3176:
3173:
3170:
3111:
3110:
3087:
3074:
3073:
3039:
3023:on its own line
3005:
2972:
2966:
2965:
2958:
2951:
2947:
2939:
2898:
2893:
2892:
2889:
2886:
2883:
2880:
2877:
2874:
2871:
2868:
2865:
2862:
2859:
2856:
2853:
2847:
2814:
2808:
2792:
2752:
2739:
2722:
2712:
2698:
2670:
2665:
2664:
2643:
2638:
2637:
2610:
2605:
2604:
2581:
2576:
2575:
2545:
2544:
2519:
2518:
2493:
2492:
2473:
2472:
2453:
2452:
2433:
2432:
2420:
2416:
2393:
2383:
2364:
2354:
2345:
2339:
2330:
2276:category theory
2266:
2254:
2247:
2230:
2223:isometry groups
2220:
2192:
2173:
2121:are written in
2087:preordered sets
2079:
2039:
2011:
1974:is not assumed
1929:
1921:natural numbers
1913:{1, 2, 3, ...},
1912:
1904:
1901:natural numbers
1893:
1891:Natural numbers
1888:
1864:
1858:
1838:
1837:
1832:MOS:MATH#PLURAL
1830:
1826:
1763:
1762:
1755:
1751:
1583:if and only if
1561:
1560:
1553:
1549:
1537:
1504:
1478:
1410:is then finite.
1375:
1374:
1367:
1360:
1356:
1350:
1325:
1195:
1085:
1003:, 'place', and
968:
962:
958:
952:
934:
928:
907:
894:Manual of Style
886:
836:
835:
756:
748:
747:
742:
741:
717:
707:
706:
650:
640:
639:
625:
615:
614:
520:
510:
509:
500:
490:
489:
403:Anime and manga
394:
384:
383:
369:
358:
350:
349:
325:
315:
314:
310:Trivia sections
290:
280:
279:
265:Image placement
255:
245:
244:
240:Titles of works
235:Text formatting
205:
195:
194:
185:Self-references
165:Gender identity
138:
128:
122:
102:
101:
94:
87:
80:
76:
68:
67:
54:may apply. Any
44:Manual of Style
30:
22:
21:
20:
12:
11:
5:
9290:
9288:
9280:
9279:
9274:
9269:
9259:
9258:
9252:
9251:
9249:
9248:
9235:
9232:
9231:
9222:
9220:
9219:
9217:
9213:
9212:
9210:
9209:
9204:
9199:
9194:
9189:
9184:
9179:
9174:
9169:
9164:
9159:
9154:
9149:
9144:
9139:
9137:Citing sources
9134:
9132:Categorization
9129:
9124:
9122:Article titles
9119:
9113:
9111:
9107:
9106:
9104:
9103:
9102:
9101:
9094:Figure skating
9091:
9090:
9089:
9078:
9076:
9072:
9071:
9069:
9068:
9063:
9058:
9057:
9056:
9051:
9046:
9041:
9036:
9026:
9021:
9015:
9013:
9009:
9008:
9006:
9005:
9000:
8994:
8992:
8988:
8987:
8985:
8984:
8979:
8974:
8969:
8964:
8959:
8954:
8949:
8944:
8939:
8934:
8929:
8924:
8919:
8914:
8909:
8904:
8899:
8893:
8891:
8887:
8886:
8884:
8883:
8877:
8875:
8871:
8870:
8868:
8867:
8862:
8857:
8852:
8846:
8844:
8840:
8839:
8837:
8836:
8831:
8826:
8821:
8816:
8811:
8806:
8801:
8796:
8791:
8786:
8780:
8778:
8774:
8773:
8771:
8770:
8765:
8759:
8757:
8753:
8752:
8750:
8749:
8744:
8742:Road junctions
8739:
8737:Lists of works
8734:
8728:
8726:
8722:
8721:
8719:
8718:
8713:
8708:
8703:
8697:
8695:
8691:
8690:
8688:
8687:
8682:
8677:
8672:
8666:
8664:
8660:
8659:
8657:
8656:
8651:
8646:
8641:
8636:
8631:
8629:Capitalization
8626:
8620:
8618:
8614:
8613:
8611:
8610:
8608:Words to watch
8605:
8600:
8595:
8590:
8585:
8580:
8579:
8578:
8568:
8563:
8557:
8555:
8551:
8550:
8548:
8547:
8540:
8533:
8525:
8522:
8521:
8516:
8514:
8513:
8506:
8499:
8491:
8469:
8468:
8467:
8462:
8444:
8443:
8437:
8418:
8417:
8383:
8382:
8376:
8346:
8343:
8340:
8339:
8330:
8326:ISO/IEC 8859-1
8324:Characters in
8317:
8300:
8291:
8279:
8268:
8257:
8231:
8219:
8203:
8181:
8180:
8178:
8175:
8174:
8173:
8167:
8160:
8157:
8156:
8155:
8150:
8145:
8138:
8135:
8133:
8130:
8112:
8091:
8060:The length of
8059:
8043:
8040:
8025:
8021:
8017:
8013:
7986:|x<sup: -->
7950:
7946:
7942:
7865:
7862:
7841:
7838:
7786:
7781:
7776:
7772:
7768:
7765:
7762:
7757:
7752:
7724:
7719:
7695:
7690:
7662:
7657:
7630:
7625:
7598:
7593:
7566:
7561:
7540:
7535:
7530:
7509:
7504:
7499:
7478:
7474:
7454:
7450:
7430:
7426:
7406:
7402:
7382:
7378:
7358:
7354:
7342:number systems
7328:
7327:
7319:
7314:
7311:
7308:
7238:
7237:
7220:(typeset from
7209:
7204:
7201:
7197:
7186:
7180:(typeset from
7169:
7166:
7163:
7160:
7157:
7147:
7095:(typeset from
7084:
7078:
7075:
7070:
7067:
7061:
7055:
7052:
7047:
7044:
7038:
7032:
7029:
7024:
7021:
7008:
6972:(typeset from
6961:
6958:
6955:
6950:
6947:
6944:
6939:
6934:
6930:
6915:Euler's number
6911:imaginary unit
6902:
6899:
6881:
6880:
6877:</math: -->
6858:—typeset from
6841:
6838:
6835:
6832:
6829:
6826:
6823:
6820:
6816:
6812:
6807:
6804:
6801:
6798:
6795:
6792:
6789:
6786:
6783:
6779:
6775:
6772:
6758:
6757:
6754:</math: -->
6711:
6706:
6702:
6695:
6690:
6687:
6684:
6680:
6665:
6664:
6661:</math: -->
6613:
6609:
6600:
6584:
6583:
6566:—typeset from
6551:
6546:
6543:
6540:
6535:
6514:
6513:
6496:(typeset from
6485:
6482:
6479:
6476:
6473:
6470:
6460:
6443:(typeset from
6432:
6429:
6426:
6423:
6403:
6402:
6390:
6389:
6383:—typeset from
6368:
6365:
6362:
6359:
6356:
6342:
6341:
6329:
6326:
6323:
6320:
6317:
6314:
6311:
6308:
6298:
6277:
6274:
6271:
6268:
6252:
6249:
6247:
6244:
6224:</math: -->
6219:</math: -->
6205:
6204:
6196:
6191:
6188:
6185:
6163:
6142:
6121:
6109:
6108:
6097:
6093:
6089:
6086:
6082:
6078:
6074:
6054:
6053:
6040:
6029:
6017:
6007:
5994:
5979:
5978:
5967:
5963:
5959:
5956:
5952:
5948:
5944:
5923:
5922:
5914:
5909:
5906:
5903:
5877:
5876:
5862:
5858:
5853:
5848:
5827:
5826:
5787:radical symbol
5781:
5780:
5772:
5767:
5764:
5763:Radical symbol
5761:
5723:
5722:
5714:
5709:
5706:
5703:
5689:
5688:
5678:
5677:
5603:
5600:
5594:) or use the "
5575:
5572:
5494:(also encoded
5481:
5480:
5475:
5435:However, when
5408:
5407:
5399:
5394:
5391:
5388:
5387:
5386:
5361:
5360:
5319:
5318:Less-than sign
5316:
5308:
5306:
5305:
5281:
5265:
5225:
5209:
5167:
5148:TILDE OPERATOR
5124:
5098:
5096:DIVISION SLASH
5072:
5028:
4977:
4976:
4975:
4939:Roman numerals
4932:
4931:
4923:
4918:
4915:
4913:
4912:
4891:
4875:named entities
4865:Keep in mind:
4818:
4817:
4809:
4804:
4801:
4798:
4777:
4773:
4739:
4738:
4735:2</sup: -->
4712:
4673:
4672:
4629:
4607:
4604:
4573:
4569:
4501:
4498:
4345:
4342:
4341:
4340:
4296:
4295:
4272:
4269:
4227:
4224:
4207:
4179:
4178:
4162:
4161:
4105:
4104:
4094:
4093:
4042:
4039:
4038:
4037:
4019:
4018:
3910:
3907:
3885:
3882:
3866:
3835:
3832:
3816:
3813:
3782:
3779:
3754:
3750:
3746:
3741:
3737:
3709:
3705:
3701:
3696:
3692:
3678:</math: -->
3653:</math: -->
3628:display=inline
3613:
3609:
3603:
3599:
3595:
3590:
3586:
3581:
3577:
3572:
3567:
3564:
3561:
3557:
3544:</math: -->
3512:display=inline
3497:
3492:
3487:
3483:
3477:
3470:
3466:
3462:
3455:
3450:
3447:
3444:
3440:
3430:
3426:</math: -->
3339:</math: -->
3309:
3305:
3301:
3290:</math: -->
3273:
3267:
3264:
3250:</math: -->
3239:
3238:
3231:
3228:
3215:</math: -->
3150:
3147:
3144:
3139:
3136:
3133:
3128:
3123:
3119:
3096:
3091:
3086:
3082:
3038:
3035:
3021:For a formula
2964:
2963:
2956:
2948:
2943:
2938:
2935:
2927:
2926:
2923:
2919:
2916:
2913:
2897:
2894:
2852:
2844:
2807:
2804:
2791:
2788:
2787:
2786:
2773:matrix product
2734:The scalar or
2732:
2691:
2677:
2673:
2650:
2646:
2618:
2613:
2589:
2584:
2564:
2552:
2532:
2529:
2526:
2506:
2503:
2500:
2480:
2460:
2440:
2431:is denoted by
2426:
2425:
2424:
2413:
2410:
2350:
2335:
2315:
2312:small category
2272:
2262:
2256:
2249:
2243:
2236:dihedral group
2232:
2226:
2216:
2213:roots of unity
2198:-adic integers
2188:
2172:
2169:
2168:
2167:
2130:
2116:
2109:
2091:partial orders
2078:
2075:
2074:
2073:
2066:
2038:
2035:
2034:
2033:
2026:
2010:
2007:
2006:
2005:
1986:
1968:
1961:
1928:
1925:
1892:
1889:
1887:
1884:
1857:
1854:
1840:The plural of
1836:
1835:
1827:
1822:
1761:
1760:
1752:
1747:
1720:
1719:
1714:
1701:
1700:
1695:
1690:
1681:
1680:
1654:is a function
1643:
1642:
1605:
1604:
1559:
1558:
1550:
1545:
1541:
1540:
1535:
1519:by the vector
1508:
1507:
1502:
1444:
1443:
1426:
1413:
1412:
1395:
1373:
1372:
1365:
1357:
1352:
1349:
1346:
1324:
1321:
1305:for details).
1303:WP:NOTTEXTBOOK
1180:if, for every
1084:
1081:
1080:
1079:
1069:
1061:
948:
947:
944:
941:
927:
924:
906:
903:
888:
887:
885:
884:
877:
870:
862:
859:
858:
857:
856:
851:
846:
838:
837:
834:
833:
828:
823:
818:
813:
808:
803:
798:
793:
788:
783:
781:Citing sources
778:
776:Categorization
773:
768:
766:Article titles
763:
757:
754:
753:
750:
749:
744:
743:
740:
739:
732:Figure skating
729:
718:
713:
712:
709:
708:
705:
704:
699:
694:
689:
684:
683:
682:
677:
672:
667:
662:
651:
646:
645:
642:
641:
638:
637:
632:
626:
621:
620:
617:
616:
613:
612:
607:
602:
597:
592:
587:
582:
577:
572:
567:
562:
557:
552:
547:
542:
537:
532:
527:
521:
516:
515:
512:
511:
508:
507:
501:
496:
495:
492:
491:
486:
485:
484:
483:
478:
473:
465:
464:
458:
457:
456:
455:
450:
445:
440:
435:
430:
425:
420:
415:
410:
405:
395:
390:
389:
386:
385:
382:
381:
376:
370:
365:
364:
359:
356:
355:
352:
351:
348:
347:
342:
340:Road junctions
337:
335:Lists of works
332:
326:
321:
320:
317:
316:
313:
312:
307:
302:
297:
291:
286:
285:
282:
281:
278:
277:
272:
267:
262:
256:
251:
250:
247:
246:
243:
242:
237:
232:
227:
222:
217:
215:Capitalization
212:
206:
201:
200:
197:
196:
193:
192:
190:Words to watch
187:
182:
177:
172:
167:
162:
161:
160:
150:
145:
139:
134:
133:
130:
129:
124:
120:
118:
115:
114:
104:
103:
100:
99:
92:
85:
77:
72:
69:
49:
48:
36:
34:
23:
15:
14:
13:
10:
9:
6:
4:
3:
2:
9289:
9278:
9275:
9273:
9270:
9268:
9265:
9264:
9262:
9247:
9246:
9237:
9236:
9233:
9218:
9214:
9208:
9205:
9203:
9200:
9198:
9195:
9193:
9190:
9188:
9185:
9183:
9180:
9178:
9175:
9173:
9170:
9168:
9165:
9163:
9160:
9158:
9155:
9153:
9150:
9148:
9145:
9143:
9140:
9138:
9135:
9133:
9130:
9128:
9125:
9123:
9120:
9118:
9115:
9114:
9112:
9108:
9100:
9097:
9096:
9095:
9092:
9088:
9085:
9084:
9083:
9080:
9079:
9077:
9073:
9067:
9064:
9062:
9059:
9055:
9052:
9050:
9047:
9045:
9042:
9040:
9037:
9035:
9032:
9031:
9030:
9027:
9025:
9022:
9020:
9017:
9016:
9014:
9010:
9004:
9001:
8999:
8996:
8995:
8993:
8989:
8983:
8980:
8978:
8975:
8973:
8970:
8968:
8965:
8963:
8960:
8958:
8955:
8953:
8950:
8948:
8945:
8943:
8940:
8938:
8935:
8933:
8930:
8928:
8925:
8923:
8920:
8918:
8915:
8913:
8910:
8908:
8905:
8903:
8900:
8898:
8895:
8894:
8892:
8888:
8882:
8879:
8878:
8876:
8872:
8866:
8863:
8861:
8860:Record charts
8858:
8856:
8855:Music samples
8853:
8851:
8848:
8847:
8845:
8841:
8835:
8832:
8830:
8827:
8825:
8822:
8820:
8817:
8815:
8812:
8810:
8807:
8805:
8802:
8800:
8797:
8795:
8792:
8790:
8787:
8785:
8782:
8781:
8779:
8775:
8769:
8766:
8764:
8761:
8760:
8758:
8754:
8748:
8745:
8743:
8740:
8738:
8735:
8733:
8730:
8729:
8727:
8723:
8717:
8714:
8712:
8709:
8707:
8704:
8702:
8699:
8698:
8696:
8692:
8686:
8683:
8681:
8678:
8676:
8673:
8671:
8668:
8667:
8665:
8661:
8655:
8652:
8650:
8647:
8645:
8642:
8640:
8639:Pronunciation
8637:
8635:
8632:
8630:
8627:
8625:
8624:Abbreviations
8622:
8621:
8619:
8615:
8609:
8606:
8604:
8601:
8599:
8596:
8594:
8591:
8589:
8586:
8584:
8581:
8577:
8574:
8573:
8572:
8569:
8567:
8564:
8562:
8561:Accessibility
8559:
8558:
8556:
8552:
8546:
8545:
8541:
8539:
8538:
8534:
8532:
8531:
8527:
8526:
8523:
8519:
8512:
8507:
8505:
8500:
8498:
8493:
8492:
8489:
8483:
8479:
8478:
8473:
8465:
8463:9780226104201
8460:
8456:
8455:
8449:
8448:
8447:
8440:
8438:0-201-13448-9
8435:
8431:
8427:
8423:
8422:
8421:
8416:
8413:
8408:
8404:
8400:
8396:
8392:
8388:
8387:
8386:
8379:
8377:0-89871-420-6
8374:
8370:
8366:
8362:
8361:
8356:
8352:
8351:
8350:
8344:
8334:
8331:
8327:
8321:
8318:
8314:
8310:
8304:
8301:
8295:
8292:
8288:
8283:
8280:
8277:
8272:
8269:
8266:
8261:
8258:
8254:
8250:
8246:
8242:
8235:
8232:
8228:
8223:
8220:
8216:
8212:
8207:
8204:
8200:
8196:
8192:
8186:
8183:
8176:
8171:
8168:
8166:
8163:
8162:
8158:
8154:
8151:
8149:
8146:
8144:
8141:
8140:
8136:
8131:
8129:
8125:
8089:
8080:
8075:
8048:
8041:
8039:
8023:
8019:
8015:
8011:
7999:
7985:
7978:
7974:
7966:
7948:
7944:
7940:
7931:
7927:
7922:
7917:
7911:
7910:accessibility
7907:
7904:
7888:
7882:
7863:
7860:
7847:
7839:
7837:
7833:<math: -->
7830:
7825:
7821:
7816:
7814:
7808:<math: -->
7803:<math: -->
7798:
7779:
7774:
7766:
7763:
7755:
7740:
7722:
7693:
7678:
7677:group schemes
7660:
7646:
7628:
7614:
7596:
7582:
7564:
7538:
7533:
7507:
7502:
7476:
7452:
7428:
7404:
7380:
7356:
7343:
7338:
7335:
7325:
7321:
7320:
7317:
7309:
7307:
7304:
7299:
7295:
7286:
7281:
7276:
7274:
7269:
7265:
7222:<math: -->
7207:
7202:
7199:
7195:
7187:
7182:<math: -->
7167:
7164:
7161:
7158:
7155:
7148:
7097:<math: -->
7082:
7076:
7073:
7068:
7065:
7059:
7053:
7050:
7045:
7042:
7036:
7030:
7027:
7022:
7019:
7009:
6974:<math: -->
6959:
6956:
6953:
6948:
6945:
6942:
6937:
6932:
6928:
6920:
6919:
6918:
6916:
6912:
6908:
6900:
6898:
6897:
6895:
6860:<math: -->
6857:
6839:
6836:
6833:
6830:
6827:
6824:
6821:
6818:
6814:
6810:
6805:
6802:
6799:
6796:
6793:
6790:
6787:
6784:
6781:
6777:
6773:
6770:
6763:
6762:
6761:
6727:<math: -->
6709:
6704:
6700:
6693:
6688:
6685:
6682:
6678:
6670:
6669:
6668:
6632:<math: -->
6611:
6607:
6598:
6590:
6589:
6588:
6568:<math: -->
6565:
6549:
6533:
6526:
6525:
6524:
6517:\operatorname
6501:\operatorname
6498:<math: -->
6480:
6474:
6471:
6468:
6461:
6448:\operatorname
6445:<math: -->
6430:
6427:
6424:
6421:
6414:
6413:
6412:
6408:\operatorname
6400:
6396:
6392:
6391:
6385:<math: -->
6382:
6366:
6363:
6360:
6357:
6354:
6347:
6346:
6345:
6324:
6321:
6318:
6312:
6309:
6306:
6299:
6290:<math: -->
6275:
6272:
6269:
6266:
6259:
6258:
6257:
6250:
6245:
6243:
6232:
6215:<math: -->
6211:
6202:
6201:MOS:MATH#PUNC
6198:
6197:
6194:
6186:
6184:
6182:
6181:Heat equation
6176:
6140:
6095:
6087:
6084:
6076:
6064:
6063:
6062:
6058:
6030:
6015:
6008:
5984:
5983:
5982:
5965:
5957:
5954:
5946:
5934:
5933:
5932:
5928:
5927:A list as in
5920:
5916:
5915:
5912:
5904:
5902:
5899:
5894:
5885:<math: -->
5882:
5860:
5856:
5851:
5846:
5837:
5836:
5835:
5831:<math: -->
5812:
5811:
5810:
5805:
5795:
5788:
5778:
5774:
5773:
5770:
5762:
5760:
5754:
5750:
5746:
5720:
5716:
5715:
5712:
5704:
5702:
5697:
5683:
5682:
5681:
5661:
5660:
5659:
5654:
5653:closed-closed
5644:
5634:
5624:
5616:
5609:
5601:
5599:
5591:
5585:
5581:
5573:
5571:
5569:
5564:
5562:
5544:
5540:
5535:
5533:
5529:
5523:
5490:
5476:
5470:
5467:and 2 is the
5466:
5462:
5458:
5457:
5456:
5452:
5442:
5438:
5433:
5427:
5423:
5419:
5415:
5405:
5401:
5400:
5397:
5389:
5366:
5365:
5364:
5337:
5336:
5335:
5331:
5317:
5314:
5309:
5292:) instead of
5279:
5269:<math: -->
5266:
5251:
5246:RING OPERATOR
5236:) instead of
5223:
5213:<math: -->
5210:
5205:<math: -->
5176:<math: -->
5171:<math: -->
5168:
5165:
5161:
5153:
5152:other symbols
5125:
5099:
5073:
5070:
5065:
5045:
5029:
5023:
5013:
5006:
4978:
4972:
4967:
4966:
4948:
4944:
4940:
4936:
4935:
4929:
4925:
4924:
4921:
4916:
4909:
4905:
4900:
4896:
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4415:Greek letters
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4344:Greek letters
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4096:displays as:
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3919:<math: -->
3916:
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3883:
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3828:\displaystyle
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3807:
3787:<math: -->
3781:Line wrapping
3780:
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3048:
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3036:
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3024:
3019:
3018:for details.
3017:
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3000:
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2987:
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2976:<math: -->
2971:
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2751:
2750:inner product
2746:
2742:
2737:
2733:
2729:
2725:
2719:
2715:
2711:, suprema as
2710:
2705:
2701:
2696:
2692:
2671:
2648:
2644:
2635:
2611:
2582:
2573:
2569:
2566:For a matrix
2565:
2550:
2530:
2527:
2524:
2504:
2501:
2498:
2478:
2471:. The symbol
2458:
2438:
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2414:
2411:
2408:
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2400:
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2207:
2203:
2199:
2197:
2191:
2186:
2183:
2179:
2176:The abstract
2175:
2174:
2170:
2165:
2161:
2157:
2153:
2150:
2146:
2142:
2138:
2135:
2131:
2128:
2124:
2120:
2117:
2114:
2110:
2107:
2106:0-387-90125-6
2104:
2100:
2096:
2093:as in, e.g.,
2092:
2088:
2084:
2083:Directed sets
2081:
2080:
2077:Miscellaneous
2076:
2071:
2067:
2064:
2060:
2059:quasi-compact
2056:
2053:
2049:
2045:
2044:compact space
2041:
2040:
2036:
2031:
2027:
2024:
2023:algebraic set
2021:
2017:
2013:
2012:
2008:
2003:
1999:
1995:
1991:
1987:
1984:
1981:
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1698:Obviously ...
1696:
1691:
1686:
1685:
1684:
1677:
1673:
1669:
1665:
1661:
1657:
1653:
1652:even function
1648:
1647:
1646:
1639:
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1631:
1627:
1623:
1619:
1615:
1610:
1609:
1608:
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1513:
1512:
1511:
1501:
1497:
1493:
1489:
1484:
1483:
1482:
1477:
1472:
1465:Consider that
1440:
1436:
1432:
1427:
1423:
1418:
1417:
1416:
1409:
1405:
1401:
1396:
1392:
1388:
1385:Suppose that
1383:
1382:
1381:
1378:
1370:
1369:MOS:MATH#NOWE
1366:
1363:
1362:MOS:MATH#TONE
1359:
1358:
1355:
1347:
1345:
1343:
1339:
1333:
1331:
1322:
1320:
1317:
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1306:
1304:
1300:
1299:instructional
1296:
1292:
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1258:
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1248:
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1234:
1230:
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1203:
1198:
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1190:
1186:
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1167:
1163:
1159:
1155:
1151:
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1141:
1139:
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1128:
1124:
1120:
1116:
1111:
1109:
1106:
1102:
1098:
1094:
1090:
1082:
1077:
1073:
1070:
1066:
1062:
1059:
1056:
1055:
1054:
1050:
1048:
1044:
1040:
1033:
1031:
1027:
1023:
1019:
1016:
1012:
997:
993:
989:
983:
980:
976:
967:
957:
945:
942:
939:
938:
937:
933:
925:
923:
921:
917:
913:
904:
902:
899:
895:
883:
878:
876:
871:
869:
864:
863:
861:
860:
855:
852:
850:
847:
845:
842:
841:
840:
839:
832:
829:
827:
824:
822:
819:
817:
814:
812:
809:
807:
804:
802:
799:
797:
794:
792:
789:
787:
784:
782:
779:
777:
774:
772:
769:
767:
764:
762:
759:
758:
752:
751:
737:
733:
730:
727:
723:
720:
719:
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711:
710:
703:
700:
698:
695:
693:
690:
688:
685:
681:
678:
676:
673:
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668:
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663:
661:
658:
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652:
649:
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643:
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633:
631:
628:
627:
624:
619:
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611:
608:
606:
603:
601:
598:
596:
593:
591:
588:
586:
583:
581:
578:
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573:
571:
568:
566:
563:
561:
558:
556:
553:
551:
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543:
541:
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536:
533:
531:
528:
526:
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522:
519:
514:
513:
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503:
502:
499:
494:
493:
482:
479:
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476:Record charts
474:
472:
471:Music samples
469:
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459:
454:
451:
449:
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411:
409:
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404:
401:
400:
399:
398:
393:
388:
387:
380:
377:
375:
372:
371:
368:
363:
362:
357:By topic area
354:
353:
346:
343:
341:
338:
336:
333:
331:
328:
327:
324:
319:
318:
311:
308:
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263:
261:
258:
257:
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249:
248:
241:
238:
236:
233:
231:
228:
226:
225:Pronunciation
223:
221:
218:
216:
213:
211:
210:Abbreviations
208:
207:
204:
199:
198:
191:
188:
186:
183:
181:
178:
176:
173:
171:
168:
166:
163:
159:
156:
155:
154:
151:
149:
146:
144:
143:Accessibility
141:
140:
137:
132:
131:
117:
116:
113:
109:
97:
93:
90:
86:
83:
79:
78:
75:
70:
65:
61:
57:
53:
47:
45:
41:
35:
28:
27:
19:
9243:
9207:WikiProjects
9117:Article size
9018:
8706:Lead section
8542:
8535:
8528:
8475:
8453:
8445:
8429:
8419:
8398:
8394:
8391:Halmos, P.R.
8384:
8359:
8348:
8333:
8320:
8303:
8294:
8282:
8271:
8260:
8249:hyphen-minus
8234:
8222:
8206:
8185:
8126:
8081:
8077:
7979:
7929:
7925:
7918:
7849:
7826:
7817:
7813:MOS:STYLERET
7799:
7581:affine space
7339:
7331:
7302:
7297:
7294:Donald Knuth
7284:
7277:
7273:MOS:STYLERET
7267:
7261:
7239:
6907:differential
6904:
6892:
6882:
6855:
6759:
6666:
6585:
6563:
6515:
6404:
6380:
6343:
6254:
6212:
6208:
6178:
6110:
6060:
6056:
5980:
5930:
5926:
5900:
5878:
5828:
5784:
5726:
5690:
5679:
5617:
5605:
5577:
5565:
5547:·
5536:
5531:
5527:
5489:dot operator
5482:
5436:
5434:
5425:
5421:
5417:
5413:
5411:
5362:
5329:
5321:
5307:
5262:WHITE CIRCLE
5005:prime symbol
5001:DOUBLE PRIME
4928:MOS:ROMANNUM
4914:
4907:
4903:
4898:
4894:
4885:, using the
4864:
4821:
4792:
4740:
4734:<sup: -->
4728:
4724:
4720:
4716:
4703:
4699:
4695:
4691:
4674:
4626:
4622:<sub: -->
4618:<sup: -->
4615:
4506:
4503:
4443:
4435:
4427:
4421:
4419:
4412:
4364:
4358:
4354:
4350:
4347:
4297:
4288:
4284:
4280:
4274:
4261:
4257:
4253:
4249:
4229:
4217:
4204:
4180:
4173:
4169:
4164:results in:
4163:
4106:
4095:
4044:
4031:
4027:
4020:
3912:
3890:
3887:
3837:
3820:
3818:
3784:
3772:
3509:
3343:
3240:
3222:
3219:
3162:
3071:
3040:
3022:
3020:
3010:
3006:
3003:
2988:
2984:anchor links
2979:
2973:
2960:MOS:FORMULAE
2940:
2928:
2899:
2848:
2837:
2834:
2820:may include
2815:
2797:
2793:
2782:
2778:
2775:
2768:
2764:
2758:
2754:
2744:
2740:
2727:
2723:
2721:or as a sum
2717:
2713:
2708:
2703:
2699:
2633:
2571:
2403:
2398:
2394:
2388:
2384:
2380:homomorphism
2373:
2369:
2365:
2360:
2355:
2351:
2346:
2340:
2336:
2331:
2326:
2322:
2307:
2303:
2299:
2295:
2291:
2287:
2268:
2263:
2251:
2244:
2239:
2227:
2217:
2208:
2205:
2201:
2195:
2189:
2184:
2178:cyclic group
2163:
2159:
2155:
2151:
2148:
2144:
2140:
2137:modular form
2133:
2122:
2098:
2051:
2019:
2001:
1997:
1993:
1979:
1920:
1916:
1908:
1894:
1880:
1876:
1871:
1867:
1865:
1849:
1845:
1841:
1839:
1819:
1812:
1808:
1804:
1796:
1792:
1788:
1780:
1776:
1772:
1766:
1764:
1757:MOS:MATH#ANY
1744:
1740:there exists
1739:
1735:
1731:
1727:
1723:
1721:
1704:
1702:
1682:
1675:
1671:
1667:
1663:
1659:
1655:
1651:
1644:
1637:
1633:
1629:
1625:
1621:
1617:
1613:
1606:
1600:
1596:
1592:
1588:
1584:
1580:
1576:
1569:
1564:
1562:
1542:
1532:
1528:
1524:
1520:
1516:
1515:Multiplying
1509:
1499:
1495:
1491:
1487:
1486:Multiplying
1479:
1445:
1438:
1434:
1430:
1421:
1414:
1407:
1403:
1399:
1390:
1389:is a group.
1386:
1379:
1376:
1334:
1326:
1318:
1314:
1307:
1298:
1297:rather than
1294:
1271:
1260:
1254:
1250:
1246:
1235:
1233:finite group
1229:group theory
1220:
1219:
1215:
1211:
1205:
1201:
1196:
1188:
1184:
1177:
1173:
1169:
1165:
1157:
1149:
1145:
1143:
1135:
1130:
1126:
1122:
1118:
1114:
1112:
1107:
1101:discriminant
1096:
1091:) means the
1088:
1086:
1083:Article body
1076:applications
1075:
1071:
1064:
1057:
1052:
1042:
1036:
1018:deformations
991:
985:
981:
977:
949:
935:
920:group theory
908:
891:
831:WikiProjects
761:Article size
691:
300:Lead section
55:
37:
9099:Terminology
9019:Mathematics
8967:Philippines
8829:Visual arts
8824:Video games
8588:Hidden text
8430:The TeXbook
8401:: 123–152,
8309:word joiner
8253:source code
8247:accept the
8189:Currently,
7827:Due to bug
7645:adele rings
5777:MOS:RADICAL
5667:open-closed
5633:closed-open
5623:open-closed
5596:−
5590:subst:minus
5543:source code
5445:×
5179:instead of
5138:instead of
5112:instead of
5086:instead of
5044:superscript
4943:Basic Latin
4840:code points
4610:Main page:
4417:directly.)
4191:or without
3546:renders as
2953:MOS:FORMULA
2826:source code
2771:), or as a
2736:dot product
2127:half-period
2063:compactness
2057:, who uses
2020:irreducible
1958:C* algebras
1954:B* algebras
1938:associative
1693:Clearly ...
1612:A function
1575:A function
1523:defined by
1469:We see that
1295:informative
1225:mathematics
988:mathematics
930:Main page:
898:mathematics
736:Terminology
692:Mathematics
595:Philippines
448:Visual arts
443:Video games
170:Hidden text
56:substantive
9261:Categories
9197:User pages
9162:Signatures
9157:Notability
9082:Cue sports
8819:Television
8814:Philosophy
8768:Trademarks
8617:Formatting
8415:0821800558
8199:homographs
8072:See also:
8050:The angle
7961:– markup:
7844:See also:
6246:Font usage
5741:ƒ
5598:" entity.
5574:Minus sign
5492:⋅
5471:, because
5437:explaining
5311:See also:
5250:interpunct
5048:C*-algebra
5003:where the
4709:²
4683:²
4454:MICRO SIGN
4234:, such as
4230:Names for
3915:sans serif
3884:Using HTML
3367:\textstyle
3233:Until bug
2968:See also:
2822:pseudocode
2810:See also:
2806:Algorithms
2632:, and not
2321:of groups
2238:of order 2
1976:noetherian
1972:local ring
1950:* algebras
1860:See also:
1844:is either
1807:satisfies
1791:satisfies
1775:satisfies
1674:) for all
1658:such that
1636:) for all
1599:) for all
1474:See also:
1441:is finite.
1178:continuous
1176:is called
1156:, and let
1072:Motivation
1022:stretching
1020:, such as
1015:continuous
994:(from the
821:User pages
796:Signatures
791:Notability
722:Cue sports
438:Television
433:Philosophy
379:Trademarks
203:Formatting
9039:Chemicals
9029:Chemistry
8977:Singapore
8957:Macedonia
8932:Indonesia
8593:Infoboxes
8566:Biography
8537:Directory
8241:templates
7891:(such as
7840:Fractions
7280:WP:WEIGHT
7003:) before
6865:predicted
6856:incorrect
6564:incorrect
6381:incorrect
5680:produces
5643:open-open
5608:intervals
5469:remainder
5189:SET MINUS
4226:Functions
4063:. Within
4041:Variables
3292:produces
3252:produces
2945:Shortcuts
2910:Wikibooks
2902:WP:VERIFY
2818:algorithm
2568:transpose
2294:, as Hom(
2284:morphisms
2132:A weight
2048:Hausdorff
1965:zero ring
1787:if every
1476:MOS:NOTED
1449:Note that
1354:Shortcuts
1223:, in the
1099:) is the
905:Structure
665:Chemicals
655:Chemistry
605:Singapore
580:Macedonia
560:Indonesia
175:Infoboxes
148:Biography
96:MOS:MATHS
74:Shortcuts
64:talk page
60:consensus
40:guideline
9245:Category
9172:Subpages
9167:Overview
9147:Hatnotes
9142:Contents
9066:Taxonomy
9024:Medicine
8991:Religion
8962:Pakistan
8952:Malaysia
8890:Regional
8670:Captions
8644:Spelling
8530:Overview
8472:template
8428:(1984),
8357:(1998),
8213:, is in
8132:See also
7316:Shortcut
6873:observed
6760:but not
6657:that one
6643:this one
6616:that one
6603:this one
6344:but not
6193:Shortcut
5911:Shortcut
5769:Shortcut
5719:MOS:FNOF
5711:Shortcut
5539:asterisk
5465:quotient
5461:dividing
5396:Shortcut
5352:<
5325:<
5160:negation
5064:baseline
5040:ASTERISK
4920:Shortcut
4897:divides
4856:brackets
4806:Shortcut
4711:) versus
4466:OHM SIGN
4385:π
4256:) = sin(
4213:SI units
3938:. Using
3840:alt text
3834:Alt text
2828:in some
2748:, as an
2280:Hom-sets
2278:, write
2225:called C
2055:Bourbaki
2037:Topology
1850:formulas
1846:formulae
1824:Shortcut
1803:if some
1785:, write
1749:Shortcut
1547:Shortcut
1437:. Then
1420:A group
1244:subgroup
1193:preimage
1182:open set
1162:function
1026:twisting
992:topology
849:Contents
844:Overview
801:Subpages
786:Hatnotes
702:Taxonomy
697:Medicine
623:Religion
590:Pakistan
585:Malaysia
518:Regional
260:Captions
230:Spelling
89:MOS:MATH
9110:Related
9087:Snooker
9012:Science
8937:Ireland
8874:History
8794:Blazons
8598:Linking
8554:Content
8474:below (
8239:, many
8215:Haskell
7903:Unicode
7829:T263572
7818:Due to
7741:(e.g.,
7737:), and
7324:MOS:BBB
7298:TeXbook
5881:T263572
5685:(−π, π]
5487:is the
5084:SOLIDUS
4858:). The
4844:Unicode
4586:Unicode
4540:\mathbb
4422:capital
3922:uses a
3510:Adding
3353:display
3235:T263572
3177:display
3063:MathJax
3061:(using
3027:strings
2695:lattice
2419:(⋉) or
2378:is the
2158:), and
2113:lattice
1983:Zariski
1927:Algebra
1868:compact
1842:formula
1771:if any
1736:for all
1172:. Then
1103:of the
1047:tangent
726:Snooker
648:Science
565:Ireland
498:History
413:Blazons
180:Linking
136:Content
9216:Search
9075:Sports
9049:Safety
8972:Poland
8922:Hawaii
8902:Canada
8809:Novels
8789:Comics
8711:Tables
8701:Layout
8694:Layout
8685:Images
8663:Images
8470:‹ The
7914:5.2 cm
7256:, and
7229:\theta
7185:), and
6913:, and
6231:nowrap
6111:where
5981:where
5730:U+0192
5580:hyphen
5560:BULLET
5552:U+2022
5426:citing
5380:< 3
5334:, use
5332:< 3
5295:U+226F
5255:U+25CB
5239:U+2218
5194:U+005C
5182:U+2216
5150:. Use
5141:U+223C
5129:U+007E
5115:U+2236
5103:U+003A
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5077:U+002F
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5050:. Use
5033:U+002A
5022:pprime
4994:U+2033
4982:U+2032
4957:, not
4732:(with
4707:(with
4633:, use
4590:U+211D
4483:U+03A9
4471:U+03BC
4459:U+2126
4447:U+00B5
4260:) cos(
4220:= 5 cm
3529:\infty
3384:\infty
3359:inline
3320:, but
3246:\tfrac
3055:MathML
2991:boldly
2922:topic.
2854:primes
2790:Proofs
2429:Subset
2372:→ Aut(
2359:where
2129:style.
2095:Kelley
2052:contra
2030:scheme
1980:contra
1942:unital
1911:, and
1765:Avoid
1607:write
1467:, and
1330:fields
1238:, the
1191:, the
1030:gluing
715:Sports
675:Safety
600:Poland
550:Hawaii
530:Canada
428:Novels
408:Comics
305:Tables
295:Layout
288:Layout
275:Images
253:Images
82:WP:MSM
8998:Islam
8947:Korea
8942:Japan
8927:India
8917:Egypt
8850:Music
8843:Music
8763:Legal
8756:Legal
8732:Lists
8725:Lists
8680:Icons
8177:Notes
8000:: -->
7994:) or
7975:: -->
7881:slash
7131:\frac
7128:\cdot
7114:\frac
7099:\frac
6889:\text
6885:\mbox
6861:r = x
6652:\text
6638:\text
5893:radic
5794:radic
5672:−π, π
5515:: -->
5509:</
5506:\cdot
5503:: -->
5459:When
5451:times
5378:''x''
5349:''x''
5252:) or
5136:TILDE
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5110:COLON
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4989:PRIME
4848:ASCII
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3186:: -->
3183:block
3043:LaTeX
2890:sieve
2863:sieve
2860:sieve
2693:In a
2663:, or
2286:from
2282:, or
2182:order
2072:page.
1895:"The
1815:) = 0
1801:, or
1799:) = 0
1783:) = 0
1538:, ...
1505:, ...
1301:(see
1240:order
1164:from
1160:be a
1105:field
1006:λόγος
1000:τόπος
996:Greek
912:field
630:Islam
575:Korea
570:Japan
555:India
540:Egypt
462:Music
374:Legal
367:Legal
330:Lists
323:Lists
270:Icons
38:This
16:<
9187:Tips
8799:Film
8777:Arts
8544:Tips
8459:ISBN
8434:ISBN
8412:ISBN
8373:ISBN
8243:and
7998:math
7996:<
7984:math
7973:math
7971:<
7965:math
7887:frac
7708:and
7332:The
7275:.
6989:\sin
6976:\int
6729:\sum
6667:and
6453:csch
6425:csch
6397:and
6293:\sin
6217:and
5804:sqrt
5785:The
5751:and
5749:JAWS
5696:math
5584:dash
5568:NIST
5522:sdot
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5372:math
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5211:Use
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5158:for
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4953:and
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4176:+ 2)
4172:= −(
4156:+ 2)
4138:<
4116:math
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4068:math
4059:and
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4034:+ 2)
4030:= −(
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3994:<
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3207:\sin
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2325:and
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2103:ISBN
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1992:use
1988:For
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1934:ring
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1870:and
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1398:Let
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1148:and
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966:math
854:Tips
418:Film
392:Arts
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7969:or
7933:or
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6986:\pi
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6869:- x
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6647:= y
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6574:\rm
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6240:.}}
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3608:/
3602:2
3594:=
3589:2
3585:n
3580:/
3576:1
3566:1
3563:=
3560:n
3540:^
3533:^
3496:.
3491:6
3486:2
3476:=
3469:2
3465:n
3461:1
3449:1
3446:=
3443:n
3423:}
3421:6
3417:2
3415:^
3409:{
3402:}
3400:2
3398:^
3396:n
3392:1
3390:{
3356:=
3336:}
3334:2
3330:x
3328:{
3308:2
3304:/
3300:x
3272:x
3266:2
3263:1
3209:x
3201:^
3199:0
3197:_
3180:=
3149:.
3146:x
3143:d
3138:x
3122:0
3095:2
3090:R
3081:x
3011:b
3007:a
2887::
2884:p
2881:=
2878:)
2872::
2869:p
2866:(
2857:=
2785:.
2779:b
2776:a
2769:b
2767:,
2765:a
2761:⟩
2759:b
2757:,
2755:a
2753:⟨
2745:b
2741:a
2728:b
2724:a
2718:b
2714:a
2704:b
2700:a
2690:.
2672:X
2649:T
2645:X
2634:X
2617:T
2612:X
2588:T
2583:X
2572:X
2531:B
2528:=
2525:A
2505:B
2499:A
2404:φ
2399:K
2395:Q
2389:Q
2385:K
2376:)
2374:K
2370:Q
2366:φ
2361:K
2356:K
2352:φ
2349:×
2347:Q
2341:Q
2337:φ
2334:×
2332:K
2327:Q
2323:K
2308:B
2306:,
2304:A
2300:B
2298:,
2296:A
2292:B
2288:A
2269:n
2264:n
2252:n
2250:2
2245:n
2240:n
2228:n
2218:n
2209:Z
2206:n
2204:/
2202:Z
2196:p
2190:n
2185:n
2166:.
2164:e
2160:q
2156:τ
2154:(
2152:f
2149:τ
2145:τ
2141:f
2134:k
2123:ω
2097:(
2050:(
2025:.
2002:v
2000:(
1998:Q
1994:v
1978:(
1967:.
1813:x
1811:(
1809:F
1805:x
1797:x
1795:(
1793:F
1789:x
1781:x
1779:(
1777:F
1773:x
1678:.
1676:x
1672:x
1670:(
1668:f
1664:x
1660:f
1656:f
1640:.
1638:x
1634:x
1632:(
1630:f
1626:x
1622:f
1614:f
1601:x
1597:x
1595:(
1593:f
1589:x
1585:f
1577:f
1565::
1536:0
1533:v
1529:v
1525:u
1521:u
1517:M
1503:0
1500:v
1496:v
1492:u
1488:M
1439:H
1435:G
1431:H
1422:G
1408:H
1404:G
1400:H
1391:G
1387:G
1255:G
1251:G
1247:H
1236:G
1206:S
1202:O
1200:(
1197:f
1189:T
1185:O
1174:f
1170:T
1166:S
1158:f
1150:T
1146:S
1131:x
1127:n
1123:x
1119:n
1117:^
1115:x
1108:K
1097:K
1089:K
1032:.
881:e
874:t
867:v
738:)
734:(
728:)
724:(
66:.
46:.
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