Ceiling function

Pronunciation: /ˈsil ɪŋ ˈfʌŋk ʃən/ ?

Graph showing the ceiling function. A solid point at (-2,-1) is connected by a horizontal line to a hollow point at (-1,-1). A solid point at (-1,0) is connected by a horizontal line to a hollow point at (0,0). A solid point at (0,1) is connected by a horizontal line to a hollow point at (1,1). This pattern repeats infinitely in both directions.
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. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pg 57 (greatest integer function). International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n74/mode/1up/search/greatest.

More Information

  • McAdams, David. Floor 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=Floor Function.
  • 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 Function.

Cite this article as:


Ceiling function. 2009-11-19. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/ceilingfunction.html.

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2009-11-19: Added text about step function and ceil(). (McAdams, David.)
2009-10-25: Initial version (McAdams, David.)

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