Indicator Function - Definition

Definition

The indicator function of a subset of a set is a function

defined as

\mathbf{1}_A(x) =
\begin{cases}
1 &\text{if } x \in A, \\
0 &\text{if } x \notin A.
\end{cases}

The Iverson bracket allows the equivalent notation, to be used instead of

The function is sometimes denoted or or even just . (The Greek letter χ appears because it is the initial letter of the Greek word characteristic.)

Read more about this topic:  Indicator Function

Famous quotes containing the word definition:

    No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.
    Florence Nightingale (1820–1910)

    One definition of man is “an intelligence served by organs.”
    Ralph Waldo Emerson (1803–1882)

    Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.
    The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)