Floor Function

Pronunciation: /flɔr ˈfʌŋk ʃən/ ?

A graph showing the floor function.
Figure 1: Floor function.

The floor function is a function that returns the largest integer less than or equal to the argument. The floor function is denoted ⌊x⌋. A floor function is a type of step function.

Examples
x⌊x⌋
-4⌊-4⌋ = -4
-3.5⌊-3.5⌋ = -4
-0.5⌊-0.5⌋ = -1
0⌊0⌋ = 0
0.5⌊0.5⌋ = 0
1.375⌊1.375⌋ = 1
22.2⌊22.2⌋ = 22
1394.75⌊1394.75⌋ = 1394
Table 1

References

  1. Richard Crandall and Carl Pomerance . Prime Numbers: A Computational Perspective, 2nd ed., Ch. 3.1. Springer, August 4, 2005.
  2. Refaat El Attar. Special Functions and Orthogonal Polynomials, pg 102. Lulu.com, February 2, 2006.
  3. Mike Faust. SQL Built-In Functions and Stored Procedures: The i5/iSeries Programmer's Guide, pg 27. Mc Press, June 15, 2005.

More Information

  • McAdams, David. Ceiling Function. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-10-25. http://www.allmathwords.org/article.aspx?lang=en&id=Ceiling%20Function.
  • McAdams, David. Step Function. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-11-20. http://www.allmathwords.org/article.aspx?lang=en&id=Step%20Function.

Cite this article as:


Floor Function. 2010-02-04. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/floorfunction.html.

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2010-02-04: Added "References" (McAdams, David.)
2009-01-13: Initial version (McAdams, David.)

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