# 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
xx
-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

• 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.

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.

### 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.)