# Ceiling Function

Pronunciation: /ˈsil.ɪŋ ˈfʌŋk.ʃən/ Explain

 Figure 1: Graph of the ceiling function

The ceiling function returns the smallest integer greater than or equal to the argument. The ceiling function of x is denoted ⌈x⌉. In some computer languages the ceiling function is represented by 'ceil(x)'. The ceiling function is a type of step function.

Examples
x⌈x⌉
-4⌈-4⌉ = -4
-3.5⌈-3.5⌉ = -3
-0.5⌈-0.5⌉ = 0
0⌈0⌉ = 0
0.5⌈0.5⌉ = 1
1.375⌈1.375⌉ = 2
22.2⌈22.2⌉ = 23
1394.75⌈1394.75⌉ = 1395
Table 1

### References

1. McAdams, David E.. All Math Words Dictionary, ceiling function. 2nd Classroom edition 20150108-4799968. pg 30. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 57. www.archive.org. Last Accessed 6/25/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n74/mode/1up/search/greatest. Buy the book

• McAdams, David E.. Floor Function. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/f/floorfunction.html.

McAdams, David E. Ceiling Function. 3/1/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/ceilingfunction.html.

### Revision History

3/1/2019: Corrected formatting. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)