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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 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"
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
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 norm of a vector is represented with double bars on both sides of the vector. The norm of a vector v can be represented as: ‖ ‖ The norm is also sometimes represented with single bars, like | |, but this can be confused with absolute value (which is a type of norm).
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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.
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