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.

Also see

 * Definition:Kronecker Delta