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The indicator function of A is the Iverson bracket of the property of belonging to A; that is, = [ ] . For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers.
Such indicators have some special properties. For example, the following statements are all true for an indicator function that is trigonometrically convex at least on an interval (,): [1]: 55–57 [2]: 54–61
In mathematics, the Dirichlet function [1] [2] is the indicator function ... The Dirichlet function is an archetypal example of the Blumberg theorem.
Indicator function: maps x to either 1 or 0, depending on whether or not x belongs to some subset. Step function: A finite linear combination of indicator functions of half-open intervals. Heaviside step function: 0 for negative arguments and 1 for positive arguments. The integral of the Dirac delta function. Sawtooth wave; Square wave ...
To put it more simply, the indicator vector of T is a vector with one element for each element in S, with that element being one if the corresponding element of S is in T, and zero if it is not. [1] [2] [3] An indicator vector is a special (countable) case of an indicator function.
For example, let M be the space of all linear functions of Y and let denote this ... Any simple function is a finite linear combination of indicator functions.
The same fact can be stated as the indicator function (denoted here by ) of the symmetric difference, being the XOR (or addition mod 2) of the indicator functions of its two arguments: () = or using the Iverson bracket notation [] = [] [].
One example of such a function is the indicator function of the rational numbers, also known as the Dirichlet function. This function is denoted as 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} and has domain and codomain both equal to the real numbers .