In mathematics, the Iverson bracket, named after Kenneth E. Iverson, is defined as follows
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![[P] = \left\{\begin{matrix} 1 &\mathrm{if}\ P\ \mathrm{is\ true} \\ 0 &\mathrm{otherwise}\end{matrix}\right.](a/../upload/math/190c0c6097a8b75d331c7b090a24fae6.png)
where P is a proposition.
For example, the Kronecker delta notation is a specific case of Iverson notation, that is,
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![\delta_{ij} = [i=j]\,](a/../upload/math/045e0f10cc2146482b18605e0c9402e0.png)
The notation is useful especially in simplifying sums or integrals, for example
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![\sum_{0\le i \le 10} i^2 = \sum_{i} i^2[0 \le i \le 10]](a/../upload/math/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.