# 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 the Excluded Middle does not apply.

In each case, $0$ is the very strong zero which results in $0$ when multiplied by every quantity, even indeterminate ones.

## 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: $(16)$