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iversion
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There are 8 letters in IVERSION ( E1I1N1O1R1S1V4 )
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Iversion might refer to |
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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:* * * * [ * P * ] * = * * * { * * * * 1 * * * * if * * P * * is true; * * * * * * 0 * * * * otherwise, * * * * * * * * * * {\displaystyle [P]={\begin{cases}1&{\text{if }}P{\text{ is true;}}\\0&{\text{otherwise,}}\end{cases}}} * 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 * * * * P * ( * k * ) * * * {\displaystyle P(k)} * is any * property of the integer * * * * k * * * {\displaystyle k} * , * * * * * * ∑ * * k * * * f * ( * k * ) * * [ * P * ( * k * ) * ] * = * * ∑ * * P * ( * k * ) * * * f * ( * k * ) * . * * * {\displaystyle \sum _{k}f(k)\,[P(k)]=\sum _{P(k)}f(k).} * Note that by this convention, a summand * * * * f * ( * k * ) * [ * * * false * * * ] * * * {\displaystyle f(k)[{\textbf {false}}]} * must evaluate to 0 regardless of whether * * * * f * ( * k * ) * * * {\displaystyle f(k)} * is defined. * Likewise for products: * * * * * * ∏ * * k * * * f * ( * k * * ) * * [ * P * ( * k * ) * ] * * * = * * ∏ * * P * ( * k * ) * * * f * ( * k * ) * . * * * {\displaystyle \prod _{k}f(k)^{[P(k)]}=\prod _{P(k)}f(k).} * The notation was originally introduced by Kenneth E. Iverson in his programming language APL, though restricted to single relational operators enclosed in parentheses, while the generalisation to arbitrary statements, notational restriction to square brackets, and ... |