Iverson bracket

In mathematics, the Iverson bracket, named after Kenneth E. Iverson, is a notation that generalises the Kronecker delta. It converts any logical proposition into a number that is 1 if the proposition is satisfied, and 0 otherwise, and is generally written by putting the proposition inside square brackets:

where P is a statement that can be true or false.

In the context of summation, the notation can be used to write any sum as an infinite sum without limits: If ${\displaystyle P(k)}$ is any property of the integer ${\displaystyle k}$,

Note that by this convention, a summand ${\displaystyle f(k)[{\textbf {false}}]}$ must evaluate to 0 regardless of whether ${\displaystyle f(k)}$ is defined. Likewise for products:

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