Vertical bar

This is the sighted version that was marked on May 18, 2021. There is 1 pending change that needs to be sighted.

The title of this article is ambiguous. For other meanings, see Vertical line (disambiguation).

| ¦

The vertical bar (often called pipe in programming jargon) is mainly used in computing and mathematics. The character is represented either as a continuous ( | ) or in the middle interrupted ( ¦ ) vertical bar.

On PCs with the operating systems DOS, Windows and Linux, it is generated with the German keyboard layout via the key combination Alt Gr + < or Alt + 0124. The Swiss keyboard layout provides the key combination Alt Gr + 1 for the interrupted stroke and Alt Gr + 7 for the continuous stroke.

On a Mac, you create it on both the German and Swiss keyboards by pressing the key combination ⌥+7.

On a Mac with a Windows distribution via Boot Camp (software) you create it on the German as well as on the Swiss keyboard by the key combination cmd + alt + <.

Usage

Mathematics

  • The single vertical line stands for
    • the relation "divides" between integers
    • the conditional probability in probability theory
    • the restriction of the domain of definition of a given function: if are A\subseteq Btwo sets and fa function with domain of definition B, then f|_Adenotes the function which on Afcoincides with and is otherwise undefined.
    • the function evaluation at one point. f(x)\vert_{x=1} = f(1)
    • the difference of two function values at two points, for example in integral calculus: F(x) \Big\vert_{a}^{b} = F(b) - F(a)
    • "with the property:" or "to which applies:" in the intensional notation of sets:

{\displaystyle \{2z\mid z\in \mathbb {Z} \}}is the set of even integers,

{\displaystyle \{(x,\,y)\in \mathbb {R} ^{2}\mid x^{2}+y^{2}=1\}}is the unit circle

    • the Sheffer's line in logic A | B := \neg (A \wedge B) \equiv \overline{A \wedge B}
  • A pair of simple vertical strokes (like parentheses) denotes
    • the absolute amount of a number
    • the determinant of a matrix
    • the power of a set
  • The double vertical line denotes parallelism: g \parallel h
  • A pair of double vertical bars (like brackets) denotes a standard

Physics

  • In Dirac notation in physics, ⟨is \langle\phi|\mathcal{O}|\psi\ranglea matrix element.

Data processing and programming languages

  • In shells, a vertical line indicates a pipe. Pipes can be used to chain the input and output streams of two programs. (Ex.: ls | more)
  • In some markup languages, the vertical bar represents the border of a table cell
  • In various databases (e.g. Informix) the vertical bar is used as a default separator of data fields for exported tables.
  • In some search engines, such as Google, the vertical bar - placed without spaces between search terms - can replace the OR function (the operator "OR")
  • In many programming languages (e.g. C, Perl, PHP, and Java), two vertical bars in a row denote the logical OR, and a single vertical bar denotes the bitwise OR.
  • Two vertical bars one after the other denote the concatenation of two strings in various programming languages (e.g. Rexx)

Other uses

  • In lexicons and dictionaries, such as the Duden, the vertical line indicates possible separators of a word; alternatively, a midpoint is sometimes used.
  • In textual sciences, the vertical stroke is often used to mark a page turn.
  • On the menus of gourmet restaurants, the vertical line is used when only the three main ingredients are indicated by the dishes to separate them.
  • In the International Phonetic Alphabet (IPA) and in Khoisan languages, a similar click sound letter indicates the dental click.

Since the vertical stroke is not used in normal text, it is not considered a punctuation mark.

Coding

The vertical bars are defined and coded as follows:

International character encoding standard Unicode
and encoding in HTML web document format

Characters

Unicode

German designation

HTML

 

Position

Name

hexadecimal

decimal

named

 

|

U+007C

Vertical line

Vertical stroke

&#x007C;

&#124;

(not available)

 

¦

U+00A6

Broken bar

Interrupted stroke

&#x00A6;

&#166;

& brvbar;

 

U+2223

Divides

Divide-Stroke

&#x2223;

&#8739;

 

U+23AE

Integral extension

Integral line

&#x23AE;

&#9134;

 

U+2502

Box drawings light vertical

Element thin top-bottom

&#x2502;

&#9474;

 

U+2503

Box drawings heavy vertical

Element thick top-bottom

&#x2503;

&#9475;

 

U+2506

Box drawings light triple dash vertical

Element thin dashed top-bottom

&#x2506;

&#9476;

 

U+2507

Box drawings heavy triple dash vertical

Element thick dashed top-bottom

&#x2507;

&#9479;

 

U+250A

Box drawings light quadruple dash vertical

Element thin dotted top-bottom

&#x250A;

&#9482;

 

U+250B

Box drawings heavy quadruple dash vertical

Element thick dotted top-bottom

&#x250B;

&#9483;

 

U+254E

Box drawings light double dash vertical

Element thin large dashed top-bottom

&#x254E;

&#9550;

 

U+254F

Box drawings heavy double dash vertical

Element thick large dashed top-bottom

&#x254F;

&#9551;

 

ǀ

U+01C0

Latin letter dental click

Latin letter Dental click

&#x1C0;

&#448;

 

The current version of the ASCII character set contains the vertical stroke, but not the interrupted stroke. This occurs, however, in equally old character sets of the company IBM. However, the ASCII extensions ISO 6937 and ISO 8859-1 (also known as Latin-1) already contain both stroke variants in 1986. Almost all modern computers with Latin fonts use an ISO 8859 variant or the Unicode standard and can therefore process and display both characters without any problems.

There was originally a reason for the two variants of the vertical stroke (continuous and interrupted): In the older fonts, there were those which represented the vertical stroke confusingly in the same way as the lowercase letter l (small L) and the uppercase letter I (capital i). In more sophisticated documents, this resulted in three characters with an (almost) identical representation.


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