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Iverson’s bracket

The Iverson’s bracket is defined as follows

[P] = {1, if P is true, 0, otherwise,

where P is a proposition, that is a statement that is either true or false.

For instance, the Kronecker delta

δ _ (i, j) = {1, if i = j, 0, if i != j,

can be written using Iverson’s bracket as typeset structure, or sum of squares of primes less than 100 can be written as  typeset structure

It is named after Kenneth E. Iverson who introduced it in early 60’s in the form [1] , [2]:  If typeset structure is a relation defined on a set typeset structure, then the relational statement typeset structure is a logical variable which is true (and consequently equal to 1) if and only if typeset structure stands in the relation  typeset structure to typeset structure. Then if  typeset structure is a real number then the sign function typeset structure can be defines as typeset structure.

References

[1]  Iverson, K. E. (1962). A Programming Language. New York: Wiley.

[2]  Knuth, D. E. (1992). Two notes on notation. American Mathematical Monthly, 99 (5), 403-422.

Cite this web-page as:

Štefan Porubský: Iverson’s bracket .

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