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Concept
Vertical bar
Summary
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.
The vertical bar is used as a mathematical symbol in numerous ways:
absolute value: , read "the absolute value of x"
cardinality: , read "the cardinality of the set S" or "the length of a string S".
conditional probability: , read "the probability of X given Y"
determinant: , read "the determinant of the matrix A". 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 .
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: ∣, ∤)
function evaluation: , read "f of x, evaluated at x equals 4" (see subscripts at Wikibooks)
order: , read "the order of the group G", or , "the order of the element "
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.
Official source
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