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Floor function

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In mathematics and computer science, the floor function is the function that takes as input a real number [math]\displaystyle{ x }[/math] and gives as output the greatest integer less than or equal to [math]\displaystyle{ x }[/math], denoted [math]\displaystyle{ \operatorname{floor}(x) = \lfloor x\rfloor }[/math].

Similarly, the ceiling function maps [math]\displaystyle{ x }[/math] to the least integer greater than or equal to [math]\displaystyle{ x }[/math], denoted [math]\displaystyle{ \operatorname{ceil}(x) = \lceil x \rceil }[/math].


x Floor [math]\displaystyle{ \lfloor x\rfloor }[/math] Ceiling [math]\displaystyle{ \lceil x\rceil }[/math]
2 2 2
2.4 2 3
2.9 2 3
−2.7 −3 −2
−2 −2 −2

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