Definition:Iverson's Convention
 | This page has been identified as a candidate for refactoring of bases complexity. In particular: multiple definitions Until this has been finished, please leave {{Refactor}} in the code.
New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$.To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Refactor}} from the code. |
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: $(16)$