Iverson bracket

In mathematics, the Iverson bracket, named after Kenneth E. Iverson, is defined as follows

Related Topics:
Mathematics - Kenneth E. Iverson

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: = left{egin{matrix} 1 &mathrm{if} P mathrm{is true} \ 0 &mathrm{otherwise}end{matrix} ight.

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where P is a proposition.

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For example, the Kronecker delta notation is a specific case of Iverson notation, that is,

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: delta_{ij} = ,

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The notation is useful especially in simplifying sums or integrals, for example

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: sum_{0le i le 10} i^2 = sum_{i} i^2

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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.

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See also: Indicator function.

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