be taken off to form it. This has been, and we imagine always will be, the cause either of abandonment or abbreviation. The question is, whether a new and easy notation could not be substituted; and it is desirable that it should be derived from analogy, such as (accidentally, we believe) does exist in >, =, and <. If we look at × and +, and observe that the first is made by turning the second through half a right angle, denoting multiplication, which is primarily an extension of addition in like manner as division is an extension of subtraction, we may thus invent the symbol / or \ to denote division, which is also the symbol of subtraction turned through half a right angle. If a/b were used to denote a divided by b, and (a+b)/(c+d) to denote a + b divided by c + d, all necessity for increased spacing would be avoided; but this alteration should not be introduced into completely mathematical expressions, though it would be convenient in particular cases.

Quotient of set

A quotient of a set is informally a new set obtained by identifying some elements of the original set. This is denoted as a fraction (sometimes even as a built fraction), where the numerator is the original set (often equipped with some algebraic structure). What is appropriate as denominator depends on the context.

In the most general case, the denominator is an equivalence relation on the original set , and elements are to be identified in the quotient if they are equivalent according to ; this is technically achieved by making the set of all equivalence classes of .

In group theory, the slash is used to mark quotient groups. The general form is , where is the original group and is the normal subgroup; this is read " mod ", where "mod" is short for "modulo". Formally this is a special case of quotient by an equivalence relation, where iff for some . Since many algebraic structures (rings, vector spaces, etc.) in particular are groups, the same style of quotients extend also to these, although the denominator may need to satisfy additional closure properties for the quotient to preserve the full algebraic structure of the original (e.g. for the quotient of a ring to be a ring, the denominator must be an ideal).

When the original set is the set of integers , the denominator may alternatively be just an integer: . This is an alternative notation for the set of integers modulo ''n'' (needed because is also notation for the very different ring of ''n''-adic integers). is an abbreviation of or , which both are ways of writing the set in question as a quotient of groups.

Combining slash

Slashes may also be used as a combining character in mathematical formulae. The most important use of this is that combining a slash with a relation negates it, producing e.g. 'not equal' as negation of or 'not in' as negation of ; these slashed relation symbols are always implicitly defined in terms of the non-slashed base symbol. The graphical form of the negation slash is mostly the same as for a division slash, except in some cases where that would look odd; the negation of (divides) and negation of (various meanings) customarily both have their negations slashes less steep and in particular shorter than the usual one.

The Feynman slash notation is an unrelated use of combining slashes, mostly seen in quantum field theory. This kind of combining slash takes a vector base symbol and converts it to a matrix quantity. Technically this notation is a shorthand for contracting the vector with the Dirac gamma matrices, so ; what one gains is not only a more compact formula, but also not having to allocate a letter as the contracted index.

Computing

The slash, sometimes distinguished as "forward slash", is used in computing in a number of ways, primarily as a separator among levels in a given hierarchy, for example in the path of a filesystem.

File paths

The slash is used as the path component separator in many computer operating systems (e.g., Unix's ). In Unix and Unix-like systems, such as macOS and Linux, the slash is also used for the volume root directory (e.g., the initial slash in ). Confusion of the slash with the backslash largely arises from the use of the latter as the path component separator in the widely used MS-DOS and Windows systems.

Networking

The slash is used in a similar fashion in internet URLs (e.g., ). Often this portion of such URLs corresponds with files on a Unix server with the same name, and this is where this convention for internet URLs comes from.

The slash in an IP address (e.g., ) indicates the prefix size in CIDR notation. The number of addresses of a subnet may be calculated as 2, in which the address size is 128 for IPv6 and 32 for IPv4. For example, in IPv4, the prefix size/29 gives: 2 = 2 = 8 addresses.

Programming

The slash is used as a division operator in most programming languages while APL uses it for reduction (fold) and compression (filter). The double slash is used by Rexx as a modulo operator, and Python (starting in version 2.2) uses a double slash for division which rounds (using floor) to an integer. In Raku the double slash is used as a "defined-or" alternative to ||. A dot and slash is used in MATLAB and GNU Octave to indicate an element-by-element division of matrices.

Comments that begin with (a slash and an asterisk) and end with were introduced in PL/I and subsequently adopted by SAS, C, Rexx, C++, Java, JavaScript, PHP, CSS, and C. A double slash is also used by C99, C++, C#, PHP, Java, Swift, Pascal and JavaScript to start a single line comment.

In SGML and derived languages such as HTML and XML, a slash is used in closing tags. For example, in HTML, begins a section of text and closes it. In XHTML, slashes are also necessary for "self-closing" elements such as the newline command {{mono}} where HTML has simply {{mono}}.

In a style originating in the Digital Equipment Corporation line of operating systems (OS/8, RT-11, TOPS-10, et cetera), Windows, MS-DOS, some CP/M programs, OpenVMS, and OS/2 all use the slash to indicate command-line options. For example, the command is understood as using the command dir ("directory") with the "wide" option. No space is required between the command and the switch; this was the reason for the choice to use backslashes as the path separator since one would otherwise be unable to run a program in a different directory.

Slashes are used as the standard delimiters for regular expressions, although other characters can be used instead.

IBM JCL uses a double slash to start each line in a batch job stream except for /* and /&.

Programs

IRC and many in-game chat clients use the slash to mark commands, such as joining and leaving a chat room or sending private messages. For example, in IRC, is a command to join the channel "services" and is a command to format the following message as though it were an action instead of a spoken message. In Minecrafts chat function, the slash is used for executing console and plugin commands. In Second Lifes chat function, the slash is used to select the "communications channel", allowing users to direct commands to virtual objects "listening" on different channels. For example, if a virtual house's lights were set to use channel 42, the command "/42 on" would turn them on. In Discord, slash commands are used to send special messages and execute commands, like sending a shrug emoji (¯\_(?)_/¯) or a table flip emoji ((?°?°)?( ???), or changing one's nickname using "/nick". Slash commands can also be used to use Discord bots.

The Gedcom standard for exchanging computerized genealogical data uses slashes to delimit surnames; an example would be Bill /Smith/ Jr. Slashes around surnames are also used in Personal Ancestral File.

Electronics

A leading slash is one of several common conventions for indicating an active-low digital signal, which performs the named function when at a low voltage level. For example, dynamic random-access memory has active-low Chip Select, Row Address Strobe and Column Address Strobe signals, commonly written , , and . This extends to signals which select between two options, such as "", which indicates that the function is "read" when high and "write" when low. (Sometimes written as for greater clarity.

Currency

The slash (as the "shilling mark" or "solidus") was an abbreviation for the shilling, a former coin of the United Kingdom and its former colonies. Before the decimalisation of currency in Britain, its currency abbreviations (collectively £sd) represented their Latin names, derived from a medieval French modification of the late Roman libra, solidus, and denarius. Thus, one penny less than two pounds was written £1 19s 11d or £1 19s 11d. During the period when English orthography included the long s, or ', (abbreviating shilling) the s came to be written as a single slash. The d. might be omitted, and "2s6" ("two shillings and sixpence") became simplified as 2/6. Amounts in full pounds, shillings and pence could be written in many different ways, for example: £1 9s 6d, £1.9.6, £1-9-6, and even £1/9/6d (with a slash used also to separate pounds and shillings). The same style was also used under the British Raj and early independent India for the predecimalization rupee/anna/pie system.

In five East African countries (Kenya, Tanzania, Uganda, Somalia, and the de facto country of Somaliland), where the national currencies are denominated in shillings, the decimal separator is a slash mark (e.g., ). Where the minor unit is zero, an equals sign is used (e.g., 5/=).

Dates

Slashes are a common calendar date separator used across many countries and by some standards such as the Common Log Format used by web servers. Depending on context, it may be in the form Day/Month/Year, Month/Day/Year, or Year/Month/Day. If only two elements are present, they typically denote a day and month in some order. For example, 9/11 is a common American way of writing the date 11 September; Britons write this as 11/9. Owing to the ambiguity across cultures, the practice of using only two elements to denote a date is sometimes proscribed.

Because of the world's many varying conventional date and time formats, ISO 8601 advocates the use of a Year-Month-Day system separated by hyphens (e.g., Victory in Europe Day occurred on 1945-05-08). In the ISO 8601 system, slashes represent date ranges: "1939/1945" represents what is more commonly written in Anglophone countries as "1939-1945". The autumn term of a northern-hemisphere school year might be marked "2010-09-01/12-22".

In English, a range marked by a slash often has a separate meaning from one marked by a dash or hyphen. "24/25 December" would mark the time shared by both days (i.e., the night from Christmas Eve to Christmas morning) rather than the time made up by both days together, which would be written "24-25 December". Similarly, a historical reference to "1066/67" might imply an event occurred during the winter of late 1066 and early 1067, whereas a reference to 1066-67 would cover the entirety of both years. The usage was particularly common in British English during World War II, where such slash dates were used for night-bombing air raids. It is also used by some police forces in the United States.

Numbering

The slash is used in numbering to note totals. For example, "page 17/35" indicates that the relevant passage is on the 17th page of a 35-page document. Similarly, the marking "#333/500" on a product indicates it is the 333rd out of 500 identical products or out of a batch of 500 such products. For scores on schoolwork, in games, and so on, "85/100" indicates 85 points were attained out of a possible 100.

Slashes are also sometimes used to mark ranges in numbers that already include hyphens or dashes. One example is the ISO treatment of dating. Another is the US Air Force's treatment of aircraft serial numbers, which are normally written to note the fiscal year and aircraft number. For example, "85-1000" notes the thousandth aircraft ordered in fiscal year 1985. To indicate the next fifty subsequent aircraft, a slash is used in place of a hyphen or dash: "85-1001/1050".

Linguistic transcription

A pair of slashes (as "slants") are used in the transcription of speech to enclose pronunciations (i.e., phonetic transcriptions). For example, the IPA transcription of the English pronunciation of "solidus" is written . Properly, slashes mark broad or phonemic transcriptions, whereas narrow, allophonic transcriptions are enclosed by square brackets. For example, the word little may be broadly rendered as but a careful transcription of the velarization of the second L would be written .

In sociolinguistics, a double or triple slash may also be used in the transcription of a traditional sociolinguistic interview or in other type of linguistic elicitation to represent simultaneous speech, interruptions, and certain types of speech disfluencies.

Single and double slashes are often used as typographic substitutes for the click letters ?, ?.

A diaphonemic transcription may be marked in several ways, e.g. with a pair of slash marks .

Poetry

The slash is used in various scansion notations for representing the metrical pattern of a line of verse, typically to indicate a stressed syllable.

Line breaks

The slash (as a "virgule") offset by spaces to either side is used to mark line breaks when transcribing text from a multi-line format into a single-line one. It is particularly common in quoting poetry, song lyrics, and dramatic scripts, formats where omitting the line breaks risks losing meaningful context. For example, here is a part of Hamlet's soliloquy:

If someone wanted to quote the above soliloquy in a prose paragraph, it is standard to mark the line breaks as follows: "To be, or not to be, that is the question: / Whether 'tis nobler in the mind to suffer / The slings and arrows of outrageous [[Fortune (goddess) Or to take arms against a sea of troubles, / And by opposing end them..." Less often, virgules are used in marking paragraph breaks when quoting a prose passage. Some style guides, such as New Hart's, prefer to use a pipe in place of the slash to mark these line and paragraph breaks.

The virgule may be thinner than a standard slash when typeset. In computing contexts, it may be necessary to use a non-breaking space before the virgule to prevent it from being widowed on the next line.

Abbreviation

The slash has become standard in several abbreviations. Generally, it is used to mark two-letter initialisms such as A/C (short for "air conditioner"), w/o ("without"), b/w ("black and white" or, less often, "between"), w/e ("whatever" or, less often, "weekend" or "week ending"), i/o ("input/output"), r/w ("read/write"), and n/a ("not applicable" or, in aviation, "not authorized"). Other initialisms employing the slash include w/ ("with") and w/r/t ("with regard to"). Such slashed abbreviations are somewhat more common in British English and were more common around the Second World War (as with "S/E" to mean "single-engined"). The abbreviation 24/7 (denoting 24 hours a day, 7 days a week) describes a business that is always open or unceasing activity. The slash is occasionally used for general omission in abbreviations, as in G/town for Georgetown, Guyana, though usually an apostrophe is used instead (as in C'ville for Charlotteville).

The slash in derived units such as m/s (meters per second) is not an abbreviation slash, but a straight division. It is however in that position read as 'per' rather than e.g. 'over', which can be seen as analogous to units whose symbols are pure abbreviations such as mph (miles per hour), although in abbreviations 'per' is 'p' or dropped entirely (psi, pounds per square inch) rather than a slash.

In the US government, the names of offices within various departments are abbreviated using slashes, starting with the larger office and following with its subdivisions. For example, the Federal Aviation Administration's Office of Commercial Space Transportation is formally abbreviated FAA/AST.

Proofreading

The slash or vertical bar (as a "separatrix") is used in proofreading to mark the end of margin notes or to separate margin notes from one another. The slash is also sometimes used in various proofreading initialisms, such as l/c and u/c for changes to lower and upper case, respectively.

Business correspondence

In formal business correspondence, when a letter is typed by someone other than the person responsible for its contents, it is standard to add a suffix with the initials of the author (in upper-case), and typist (in lower-case) after the signature block, separated by a slash. For example, a letter typed by D.E. at the direction of A.B.C. would include the line "ABC/de".

Fiction

The slash is used in fan fiction to mark the romantic pairing a piece will focus upon (e.g., a K/S denoted a Star Trek story would focus on a sexual relationship between Kirk and Spock), a usage which developed in the 1970s from the earlier friendship pairings marked by ampersands (e.g., K&S). The genre as a whole is now known as slash fiction. Because it is more generally associated with homosexual male relationships, lesbian slash fiction is sometimes distinguished as femslash. In situations where other pairings occur, the genres may be distinguished as m/m, f/f, and so on.

Libraries

The slash is used under the Anglo-American Cataloguing Rules to separate the title of a work from its statement of responsibility (i.e., the listing of its author, director, etc.). Like a line break, this slash is surrounded by a single space on either side. For example:

* Gone with the Wind / by Margaret Mitchell.
* Star Trek II. The Wrath of Khan [videorecording] / Paramount Pictures.

The format is used in both card catalogs and online records.

Addresses

The slash is sometimes used as an abbreviation for building numbers. For example, in some contexts, 8/A Evergreen Gardens specifies Apartment 8 in Building A of the residential complex Evergreen Gardens. In the United States, however, such an address refers to the first division of Apartment 8 and is simply a variant of Apartment 8A or 8-A. Similarly in the United Kingdom, an address such as 12/2 Anywhere Road means flat (or apartment) 2 in the building numbered 12 on Anywhere Road.

The slash is also used in the United States in the postal abbreviation for "care of." For example, Judy Smith c/o Bob Smith could be used when Bob Smith is receiving mail on Judy's behalf. Typically, this would be used in a situation where someone is either out of town, in an institution or hotel, or temporarily staying at another's address.

In Spanish address writings, "c/" is used as the abbreviation of "calle" (or "carrer" in Catalan) meaning "street".

Music

Slashes are used in musical notation as an alternative to writing out specific notes where it is easier to read than traditional notation or where the player can improvise. They are commonly used to indicate chords either in place of or in combination with traditional notation, notably in the form of slash chords. For drummers, they find use as an indication to continue with a previously indicated style.

Sports

A slash is used to mark a spare (knocking down all ten pins in two throws) when scoring ten-pin and duckpin bowling.

Text messaging

In online messaging, a slash might be used to imitate the formatting of a chat command (e.g., writing "/fliptable" as though there were such a command) or the closing tags of languages such as HTML (e.g., writing "/endrant" to end a diatribe or "/s" to mark the preceding text as sarcastic). A pair of slashes is sometimes used as a way to mark italic text, where no special formatting is available (e.g., /italics/).

Before an e-signature

In legal writing, especially in a pleading, attorneys often sign their name with an "s" that is either enclosed by two slashes or followed by a single slash and preceding the attorney's name. An example would be the following:

As a letter

The Iraqw language of Tanzania uses the slash as a letter, representing the voiced pharyngeal fricative, as in /ameeni, "woman".

Spacing

There are usually no spaces either before or after a slash. According to New Hart's Rules: The Oxford Style Guide, a slash is usually written without spacing on either side when it connects single words, letters or symbols. Exceptions are in representing the start of a new line when quoting verse, or a new paragraph when quoting prose. The Chicago Manual of Style also allows spaces when either of the separated items is a compound that itself includes a space: "Our New Zealand / Western Australia trip". (Compare use of an en dash used to separate such compounds.) The Canadian Style: A Guide to Writing and Editing prescribes: "No space before or after an oblique when used between individual words, letters or symbols; one space before and after the oblique when used between longer groups which contain internal spacing", giving the examples "n/a" and "Language and Society / Langue et société".

According to The Chicago Manual of Style, when typesetting a URL or computer path, line breaks should occur before a slash but not in the text between two slashes.

Unicode

As a very common character, the slash (as "slant") was originally encoded in ASCII with the decimal code 47 or 0x2F. The same value was used in Unicode, which calls it "solidus" and also adds some more characters:

*
* (for strikethrough)
* (for strikethrough)
*
*
*
*
* (fullwidth version of solidus)
*

Unicode fraction slash

is supposed to reformat the preceding and succeeding digits as numerator and denominator glyphs (e.g., display of "1, , 2" as , and similarly "123, , 456" as 123/456). This is supported by an increasing number of environments and computer fonts. Because support is not yet universal (this browser, for instance, renders "123/456"), some authors still use Unicode subscripts and superscripts to compose fractions, and many computer fonts design these characters for this purpose. In addition, precomposed fractions of the multiples less than 1 of / for 2 <= n <= 6 and n = 8 (e.g. and , as well as , , and , are found in the Unicode Number Forms or Latin-1 Supplement blocks.

Alternative names

The slash may also be read out as and, or, and/or, to, or cum in some compounds separated by a slash; over or out of in fractions, division, and numbering; and per or a(n) in derived units (as km/h) and prices (as $~/kg), where the division slash stands for "each".