Floor Function

Pronunciation: /flɔr ˈfʌŋk.ʃən/ Explain

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. McAdams, David E.. All Math Words Dictionary, floor function. 2nd Classroom edition 20150108-4799968. pg 80-81. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Richard Crandall, Carl Pomerance . Prime Numbers: A Computational Perspective. 2nd edition. Ch. 3.1. Springer. August 4, 2005. Last Accessed 7/11/2018. Buy the book
3. Refaat El Attar. Special Functions and Orthogonal Polynomials. 2nd edition. pg 102. Lulu.com. February 2, 2006. Last Accessed 7/11/2018. Buy the book
4. Mike Faust. SQL Built-In Functions and Stored Procedures: The i5/iSeries Programmer's Guide. pg 27. Mc Press. June 15, 2005. Last Accessed 7/11/2018. Buy the book

More Information

• McAdams, David E.. Ceiling Function. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 10/25/2009. https://www.allmathwords.org/en/c/ceilingfunction.html.

Cite this article as:

McAdams, David E. Floor Function. 4/21/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/f/floorfunction.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/21/2019: Modified equations and expression to match the new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/9/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/4/2010: Added "References". (McAdams, David E.)
1/13/2009: Initial version. (McAdams, David E.)