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The vertical bar is used as a mathematical symbol in numerous ways. If used as a pair of brackets, it suggests the notion of the word "size". These are: absolute value: | |, read "the absolute value of x" [2] cardinality: | |, read "the cardinality of the set S" or "the length of a string S"
The real absolute value function is an example of a continuous function that achieves a global minimum where the derivative does not exist. The subdifferential of | x | at x = 0 is the interval [−1, 1]. [14] The complex absolute value function is continuous everywhere but complex differentiable nowhere because it violates the Cauchy–Riemann ...
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
For example, saying "the absolute value is denoted by | · |" is perhaps clearer than saying that it is denoted as | |. ± (plus–minus sign) 1. Denotes either a plus sign or a minus sign. 2. Denotes the range of values that a measured quantity may have; for example, 10 ± 2 denotes an unknown value that lies between 8 and 12.
The absolute value | | is a norm on the vector space formed by the real or complex numbers. The complex numbers form a one-dimensional vector space over themselves and a two-dimensional vector space over the reals; the absolute value is a norm for these two structures.
The standard absolute value on the integers. The standard absolute value on the complex numbers.; The p-adic absolute value on the rational numbers.; If R is the field of rational functions over a field F and () is a fixed irreducible polynomial over F, then the following defines an absolute value on R: for () in R define | | to be , where () = () and ((), ()) = = ((), ()).
The absolute value of a real number r is defined by: [4] | | =, | | =, < Absolute value may also be thought of as the number's distance from zero on the real number line. For example, the absolute value of both 70 and −70 is 70.
This template may be used to enclose text between two vertical bars (U+007C | VERTICAL LINE), such as to denote the absolute value. It adds padding (of width 0.1 em) on each side inside the bars. It adds padding (of width 0.1 em) on each side inside the bars.