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Indicator function
Overview
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, an indicator function or a characteristic function is a function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
defined on a set
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-1.gif)
Subset
In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment...
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-2.gif)
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-3.gif)
The indicator function of a subset
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-4.gif)
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-5.gif)
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-6.gif)
defined as
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-7.gif)
The Iverson bracket allows the equivalent notation,
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-8.gif)
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-9.gif)
The function
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-10.gif)
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-11.gif)
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-12.gif)
![](http://image.absoluteastronomy.com/images/formulas/7/7/1776968-13.gif)
Unanswered Questions