# Floor function

From Encyclopedia of Mathematics

*entier function, greatest integer function, integral part function*

The function of a real variable that assigns to a real number the largest integer . The modern notation is ; the classical notation is . In computer science and computer languages it is often denoted by .

The related ceiling function gives the smallest integer . The fractional part function is defined as

The nearest integer function is

#### 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. M. Hazewinkel (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Floor_function&oldid=17649

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098