Namespaces
Variants
Actions

Floor function

From Encyclopedia of Mathematics
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

entier function, greatest integer function, integral part function

The function of a real variable that assigns to a real number $x$ the largest integer $\leq x$. The modern notation is $\lfloor x\rfloor$; the classical notation is $[x]$. In computer science and computer languages it is often denoted by $\operatorname{int}(x)$.

The related ceiling function $\lceil x\rceil$ gives the smallest integer $\geq x$. The fractional part function is defined as

$$\operatorname{frac}(x)=\begin{cases}x-\lfloor x\rfloor&\text{for }x\geq0,\\x-\lfloor x\rfloor-1&\text{for }x<0.\end{cases}$$

The nearest integer function is

$$\operatorname{nint}(x)=\operatorname{round}(x)=x-\operatorname{frac}(x).$$

References

[a1] R.L. Graham, D.E. Knuth, O. Patashnik, "Concrete mathematics: a foundation for computer science" , Addison-Wesley (1990)
[a2] S. Wolfram, "Mathematica: Version 3" , Addison-Wesley (1996) pp. 718–719
How to Cite This Entry:
Floor function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Floor_function&oldid=33154
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article