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The floor of a real number is the greatest integer less than or equal to the number. The floor of  is usually denoted by
 .
Some examples:
Note that this function is not the integer part (![$ [x]$](http://images.planetmath.org:8080/cache/objects/343/l2h/img9.png "$ [x]$") ), since
 and
![$ [ -3.5]=-3$](http://images.planetmath.org:8080/cache/objects/343/l2h/img11.png "$ [ -3.5]=-3$") . However, both functions agree for non-negative numbers.
The notation for floor and ceiling was introduced by Iverson in 1962[1]. In some texts however, the bracket notation is used to denote the floor function (although they actually work with integer part) so it is sometimes also called the bracket function.
- 1
- N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998.
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"floor" is owned by yark. [ full author list (2) | owner history (2) ]
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(view preamble)
See Also: Beatty's theorem, ceiling
| Other names: |
floor function, bracket function, greatest integer function, greatest integer less than or equal to |
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Cross-references: ceiling, integer part, function, number, real number
There are 25 references to this entry.
This is version 16 of floor, born on 2001-10-18, modified 2008-03-16.
Object id is 343, canonical name is Floor.
Accessed 7878 times total.
Classification:
| AMS MSC: | 26A09 (Real functions :: Functions of one variable :: Elementary functions) | | | 11-00 (Number theory :: General reference works ) |
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Pending Errata and Addenda
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