Definition:Iverson's Convention

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.

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.