Vertical bar
| | |
---|---|
Vertical bar | |
In Unicode | U+007C | VERTICAL LINE (|, |, |) |
Related | |
See also | U+00A6 ¦ BROKEN BAR (¦) U+2016 ‖ DOUBLE VERTICAL LINE (‖, ‖) DIVIDES |
The vertical bar, |, is a glyph with various uses in mathematics, computing, and typography. It has many names, often related to particular meanings: Sheffer stroke (in logic), pipe, bar, or (literally the word "or"), vbar, and others.[1]
Usage
Mathematics
The vertical bar is used as a
- absolute value: , read "the absolute value of x"[2]
- cardinality: , read "the cardinality of the set S" or "the length of a string S".
- determinant: , read "the determinant of the matrix A".[2] When the matrix entries are written out, the determinant is denoted by surrounding the matrix entries by vertical bars instead of the usual brackets or parentheses of the matrix, as in .
- order: , read "the order of the group G", or , "the order of the element "
Likewise, the vertical bar is also used singly in many different ways:
- conditional probability: , read "the probability of X given Y"
- distance: , denoting the shortest distance between point to line , so line is perpendicular to line
- divisibility: , read "a divides b" or "a is a factor of b", though Unicode also provides special 'divides' and 'does not divide' symbols (U+2223 and U+2224: ∣, ∤)[2]
- function evaluation: , read "f of x, evaluated at x equals 4" (see subscripts at Wikibooks)
- restriction: , denoting the restriction of the function , with a domain that is a superset of , to just
- set-builder notation: , read "the set of x such that x is less than two". Often, a colon':' is used instead of a vertical bar
- the Sheffer stroke in logic: , read "a nand b"
- subtraction: , read "f(x) from a to b", denoting . Used in the context of a definite integral with variable x.
- A vertical bar can be used to separate variables from fixed parameters in a function, for example , or in the notation for elliptic integrals.
The double vertical bar, , is also employed in mathematics.
- parallelism: , read "the line is parallel to the line "
- norm: , read "the norm (length, size, magnitude etc.) of the matrix ". The norm of a one-dimensional vector is the absolute value and single bars are used.[3]
- Propositional truncation (a mere proposition in homotopy type theory): for any (read "term of type ") we have [4] (here reads "image of in " and reads "propositional truncation of ")[5]
In LaTeX mathematical mode, the ASCII vertical bar produces a vertical line, and \|
creates a double vertical line (a | b \| c
is set as ). This has different spacing from \mid
and \parallel
, which are relational operators: a \mid b \parallel c
is set as . See below about LaTeX in text mode.
Chemistry
In chemistry, the vertical line is used in cell notation of electrochemical cells.
Example,
Zn | Zn2+ || Cu2+ | Cu
Single vertical lines show components of the cell which do not mix, usually being in different phases. The double vertical line ( || ) is used to represent salt bridge; which is used to allow free moving ions to move.
Physics
The vertical bar is used in
- : the quantum physical state
- : the dual state corresponding to the state above
- : the inner productof states and
- Grassmann dimensions.[6]
Computing
Pipe
A
grep -i 'blair' filename.log | more
where the output from the grep process (all lines containing 'blair') is piped to the more process (which allows a command line user to read through results one page at a time).
The same "pipe" feature is also found in later versions of DOS and Microsoft Windows.
This usage has led to the character itself being called "pipe".
Disjunction
In many programming languages, the vertical bar is used to designate the
Specifically, in
??!
, which, outside string literals, is equivalent to the |
character.
In regular expression syntax, the vertical bar again indicates logical or (alternation). For example: the Unix command grep -E 'fu|bar'
matches lines containing 'fu' or 'bar'.
Concatenation
The double vertical bar operator "||" denotes
Delimiter
Although not as common as commas or tabs, the vertical bar can be used as a
Similarly, the vertical bar may see use as a delimiter for regular expression operations (e.g. in sed). This is useful when the regular expression contains instances of the more common forward slash (/
) delimiter; using a vertical bar eliminates the need to escape all instances of the forward slash. However, this makes the bar unusable as the regular expression "alternative" operator.
Backus–Naur form
In Backus–Naur form, an expression consists of sequences of symbols and/or sequences separated by '|', indicating a choice, the whole being a possible substitution for the symbol on the left.
<personal-name> ::= <name> | <initial>
Concurrency operator
In calculi of communicating processes (like
APL
The pipe in APL is the modulo or residue function between two operands and the absolute value function next to one operand.
List comprehensions
The vertical bar is used for list comprehensions in some functional languages, e.g.
Text markup
The vertical bar is used as a special character in
In LaTeX text mode, the vertical bar produces an
\textbar
command can be used to produce a vertical bar.
Phonetics and orthography
In the
Some Northwest and Northeast Caucasian languages written in the Cyrillic script have a vertical bar called palochka (Russian: палочка, lit. 'little stick'), indicating the preceding consonant is an ejective.
Longer single and double vertical bars are used to mark prosodic boundaries in the IPA.
Literature
In medieval European manuscripts, a single vertical bar was a common variant of the
In Sanskrit and other Indian languages, a single vertical mark, a danda, has a similar function as a period (full stop). Two bars || (a 'double danda') is the equivalent of a pilcrow in marking the end of a stanza, paragraph or section. The danda has its own Unicode code point, U+0964.
Poetry
A double vertical bar ⟨||⟩ or ⟨ǁ⟩ is the standard caesura mark in English
Notation
In the Geneva Bible and early printings of the King James Version, a double vertical bar is used to mark margin notes that contain an alternative translation from the original text. These margin notes always begin with the conjunction "Or". In later printings of the King James Version, the double vertical bar is irregularly used to mark any comment in the margins.
A double vertical bar symbol may be used to call out a
Music scoring
In music, when writing chord sheets, single vertical bars associated with a colon (|: A / / / :|) represents the beginning and end of a section (e.g. Intro, Interlude, Verse, Chorus) of music.[citation needed] Single bars can also represent the beginning and end of measures (|: A / / / | D / / / | E / / / :|). A double vertical bar associated with a colon can represent the repeat of a given section (||: A / / / :|| - play twice).[citation needed]
Encoding
Solid vertical bar versus broken bar
Many early video terminals and
An initial draft for a 7-bit character set that was published by the X3.2 subcommittee for Coded Character Sets and Data Format on June 8, 1961, was the first to include the vertical bar in a standard set. The bar was intended to be used as the representation for the
It may be desirable to employ distinctive styling to facilitate their use for specific purposes as, for example, to stylize the graphics in code positions 2/1 and 5/14 to those frequently associated with logical OR (|) and logical NOT (¬) respectively.
— X3.2 document X3.2/475[11]
The original vertical bar encoded at 0x7C in the original May 12, 1966 draft was then broken as ¦, so it could not be confused with the unbroken logical OR. In the 1967 revision of ASCII, along with the equivalent ISO 464 code published the same year, the code point was defined to be a broken vertical bar, and the exclamation mark character was allowed to be rendered as a solid vertical bar.[12][13] However, the 1977 revision (ANSI X.3-1977) undid the changes made in the 1967 revision, enforcing that the circumflex could no longer be stylised as a logical NOT symbol, the exclamation mark likewise no longer allowing stylisation as a vertical bar, and defining the code point originally set to the broken bar as a solid vertical bar instead;[12] the same changes were also reverted in ISO 646-1973 published four years prior.
Some variants of EBCDIC included both versions of the character as different code points. The broad implementation of the extended ASCII ISO/IEC 8859 series in the 1990s also made a distinction between the two forms. This was preserved in Unicode as a separate character at U+00A6 BROKEN BAR (the term "parted rule" is used sometimes in Unicode documentation). Some fonts draw the characters the same (both are solid vertical bars, or both are broken vertical bars).[14][failed verification] The broken bar does not appear to have any clearly identified uses distinct from those of the vertical bar.[15] In non-computing use — for example in mathematics, physics and general typography — the broken bar is not an acceptable substitute for the vertical bar.
Many keyboards with US or US-International layout display the broken bar on a keycap even though the solid vertical bar character is produced in modern operating systems. This includes many German
key.The broken bar character can be typed (depending on the layout) as ¦
In some dictionaries, the broken bar is used to mark stress that may be either primary or secondary. That is, [¦ba] covers the pronunciations [ˈba] and [ˌba].[16]
Unicode code points
These glyphs are encoded in Unicode as follows:
- U+007C | VERTICAL LINE (|, |, |) (single vertical line)
- U+00A6 ¦ BROKEN BAR (¦) (single broken line)
- U+2016 ‖ DOUBLE VERTICAL LINE (‖, ‖) (double vertical line ( ): used in pairs to indicate norm)
- U+FF5C | FULLWIDTH VERTICAL LINE (Fullwidth form)
- U+FFE4 ¦ FULLWIDTH BROKEN BAR
- U+2225 ∥ PARALLEL TO (∥, ∥, ∥, ∥, ∥)
- U+01C0 ǀ LATIN LETTER DENTAL CLICK
- U+01C1 ǁ LATIN LETTER LATERAL CLICK
- U+2223 ∣ DIVIDES (∣, ∣, ∣, ∣)
- U+2502 │ BOX DRAWINGS LIGHT VERTICAL(│) (and various other box drawing characters in the range U+2500 to U+257F)
- U+0964 । DEVANAGARI DANDA
- U+0965 ॥ DEVANAGARI DOUBLE DANDA
Code pages and other historical encodings
Code pages, ASCII, ISO/IEC, EBCDIC, Shift-JIS, etc. | Vertical bar (| )
|
Broken bar (¦ )
|
---|---|---|
CP991
|
124 (7Ch) | none |
CP775
|
167 (A7h) | |
CP858
|
221 (DDh) | |
CP863
|
160 (A0h) | |
CP864
|
219 (DBh) | |
CP1258
|
166 (A6h) | |
ISO/IEC 8859-2, -3, -4, -5, -6, -10, -11, -14, -15, -16 | none | |
EBCDIC CCSID 37 | 79 (4Fh) | 106 (6Ah) |
EBCDIC CCSID 500 | 187 (BBh) | |
JIS X 0208, JIS X 0213 | EUC: A1C3h)[a]
|
none |
See also
- Bar (diacritic) – Diacritic used in some languages
- Triple bar – Symbol with multiple meanings
Notes
- ISO-2022-JP(allowing switching to and from ASCII).
References
- ^ Raymond, Eric S. "ASCII". The Jargon File. Archived from the original on Oct 30, 2023.
- ^ a b c Weisstein, Eric W. "Single Bar". Wolfram MathWorld. Retrieved 2020-08-24.
- ^ Weisstein, Eric W. "Matrix Norm". Wolfram MathWorld. Retrieved 2020-08-24.
- ^ Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics (GitHub version) (PDF). Institute for Advanced Study. p. 108. Archived from the original (PDF) on 2017-07-07. Retrieved 2017-07-01.
- ^ Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics (print version). Institute for Advanced Study. p. 450.
- ^ Larus Thorlacius, Thordur Jonsson (eds.), M-Theory and Quantum Geometry, Springer, 2012, p. 263.
- ^ a b "Virgule". Oxford English Dictionary. Vol. XII (Corrected reissue ed.). Oxford University Press. 1933. p. 235..
- ^ Bringhurst, Robert (2005). The Elements of Typographic Style (ver. 3.1 ed.). Point Roberts, Washington: Hartley and Marks. pp. 68–69.
But beyond the ... double dagger, this order is not familiar to most readers, and never was.
- ^ CiteSeerX 10.1.1.96.678. Retrieved July 10, 2020.
- ^ H. W. Nelson, letter to Thomas B. Steel, June 8, 1966, Honeywell Inc. X3.2 Standards Subcommittee Records, 1961-1969 (CBI 67), Charles Babbage Institute, University of Minnesota, Minneapolis, box 1, folder 23.
- ^ X3.2 document X3.2/475, December 13, 1966, Honeywell Inc. X3.2 Standards Subcommittee Records, 1961-1969 (CBI 67), Charles Babbage Institute, University of Minnesota, Minneapolis, box 1, folder 22.
- ^ from the original on 2016-06-13. Retrieved 2016-06-13.
- ^ Korpela, Jukka. "Character histories - notes on some Ascii code positions". Archived from the original on 2020-03-11. Retrieved 2020-05-31.
- ^ Jim Price (2010-05-24). "ASCII Chart: IBM PC Extended ASCII Display Characters". Retrieved 2012-02-23.
- ^ Jukka "Yucca" Korpela (2006-09-20). "Detailed descriptions of the characters". Retrieved 2012-02-23.
- ^ For example, "Balearic". Merriam-Webster.com Dictionary..