Floor function

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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


[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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098