Iverson bracket
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In mathematics, the Iverson bracket, named after Kenneth E. Iverson, is defined as follows
![[P] = \left\{\begin{matrix} 1 &\mathrm{if}\ P\ \mathrm{is\ true} \\ 0 &\mathrm{otherwise}\end{matrix}\right.](../../../math/1/9/0/190c0c6097a8b75d331c7b090a24fae6.png)
where P is a proposition.
For example, the Kronecker delta notation is a specific case of Iverson notation, that is,
![\delta_{ij} = [i=j]\,](../../../math/0/4/5/045e0f10cc2146482b18605e0c9402e0.png)
The notation is useful especially in simplifying sums or integrals, for example
![\sum_{0\le i \le 10} i^2 = \sum_{i} i^2[0 \le i \le 10]](../../../math/7/6/c/76c6c6da892f9c48a3e55950e44f445a.png)
as where i is strictly less than 0 or strictly greater than 10, the summand is 0, contributing nothing to the sum. Such use of the Iverson bracket can permit easier manipulation of these expressions.
See also: Indicator function.
[edit] External links
- Donald Knuth, "Two Notes on Notation", American Mathematical Monthly, Volume 99, Number 5, May 1992, pp. 403-422. tex pdf
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