Definition:Iverson's Convention
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Definition
Iverson's Convention is a notation which allows a compact means of assigning a value of $1$ or $0$ to a proposition $P$, depending on whether $P$ is true or false:
- $\sqbrk P = \begin{cases}
1 & : \text {$P$ is true} \\ 0 & : \text {$P$ is false} \end{cases}$
It is sometimes seen specified as:
- $\sqbrk P = \begin{cases}
1 & : \text {$P$ is true} \\ 0 & : \text {$P$ otherwise} \end{cases}$
which can be useful in fields of mathematics where the Law of Excluded Middle does not apply.
In each case, $0$ is the very strong zero.
Also known as
Iverson's convention is also known as the Iverson bracket notation.
Also see
Source of Name
This entry was named for Kenneth Eugene Iverson.
Historical Note
The Iverson's convention was invented by Kenneth Eugene Iverson in $1962$.
The specific use of square brackets was advocated by Donald Knuth to avoid ambiguity in parenthesized logical expressions.
Sources
- 1992: Donald E. Knuth: Two Notes on Notation (Amer. Math. Monthly Vol. 99: pp. 403 – 422) www.jstor.org/stable/2325085
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.3$: Sums and Products: $(16)$