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In many cases, such as order theory, the inverse of the indicator function may be defined. This is commonly called the generalized Möbius function, as a generalization of the inverse of the indicator function in elementary number theory, the Möbius function. (See paragraph below about the use of the inverse in classical recursion theory.)
Those indicator functions which are of the form = + are called -trigonometrically convex (and are real constants). If ρ = 1 {\displaystyle \rho =1} , we simply say, that h {\displaystyle h} is trigonometrically convex.
In mathematics, the Dirichlet function [1] [2] is the indicator function of the set of rational numbers, i.e. () = if x is a rational number and () = if x is not a rational number (i.e. is an irrational number).
Another use of the Iverson bracket is to simplify equations with special cases. For example, the formula (,) = = is valid for n > 1 but is off by 1 / 2 for n = 1.To get an identity valid for all positive integers n (i.e., all values for which () is defined), a correction term involving the Iverson bracket may be added: (,) = = (() + [=])
In mathematics, the term "characteristic function" can refer to any of several distinct concepts: The indicator function of a subset , that is the function 1 A : X → { 0 , 1 } , {\displaystyle \mathbf {1} _{A}\colon X\to \{0,1\},} which for a given subset A of X , has value 1 at points of A and 0 at points of X − A .
Thus the surface delta prime function (a.k.a. Dirac δ'-function) exists on a piecewise smooth surface, and is equivalent to the Laplacian of the indicator function of the domain D encompassed by that piecewise smooth surface. Naturally, the difference between a point and a surface disappears in one dimension.
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 ...
Indicator function of a subset of the domain, a concept in mathematics Indicator net , nets anchored at various depths to the sea bed around Allied naval bases during World War II intended to entangle U-boat traffic of the enemy