# Definition:Floor Function/Notation

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## Definition

Before around $1970$, the usual symbol for the **floor function** was $\left[{x}\right]$.

The notation $\floor x$ for the **floor function** is a relatively recent development.

Compare the notation for the corresponding ceiling function, $\ceiling x$, which in the context of discrete mathematics is used almost as much.

Some sources use $\operatorname {fl} \paren x$ for the **floor function** of $x$. However, this notation is clumsy, and will not be used on $\mathsf{Pr} \infty \mathsf{fWiki}$.

## Historical Note

The notation $\floor x$ for the floor function was introduced in the $1960$s by Kenneth Eugene Iverson and made popular by Donald Ervin Knuth.

## Sources

- 1997: Donald E. Knuth:
*The Art of Computer Programming: Volume 1: Fundamental Algorithms*(3rd ed.) ... (previous) ... (next): $\S 1.2.4$: Integer Functions and Elementary Number Theory