MR1163629 (93f:05001)
Knuth, Donald E.
Two notes on notation.
Amer. Math. Monthly 99 (1992), no. 5, 403–422.

Two notational schemas, with all their advantages, disadvantages and even pitfalls, are discussed. The first goes back to K. E. Iverson and creates a kind of characteristic function by enclosing a (mathematical) statement within square brackets. The resulting term returns 1 if the statement is true and 0 otherwise. Example:[$n$ is prime]. This is useful, among other things, for manipulating sums. The other is a notation for Stirling numbers of both kinds using square brackets and braces, respectively. With it, many formulae become more perspicuous and the two types of combinatorial numbers receive a unified treatment. The author exhibits many historical relationships and points to the effects the choice of a specific notation may have.
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Reviewed by W. Dörfler