<P> In mathematics and computer science, the floor function is the function that takes as input a real number x (\ displaystyle x) and gives as output the greatest integer less than or equal to x (\ displaystyle x), denoted floor ⁡ (x) = ⌊ x ⌋ (\ displaystyle \ operatorname (floor) (x) = \ lfloor x \ rfloor). Similarly, the ceiling function maps x (\ displaystyle x) to the least integer greater than or equal to x (\ displaystyle x), denoted ceil ⁡ (x) = ⌈ x ⌉ (\ displaystyle \ operatorname (ceil) (x) = \ lceil x \ rceil). </P> <P> For example, floor ⁡ (2.4) = ⌊ 2.4 ⌋ = 2 (\ displaystyle \ operatorname (floor) (2.4) = \ lfloor 2.4 \ rfloor = 2) and ceil ⁡ (2.4) = ⌈ 2.4 ⌉ = 3 (\ displaystyle \ operatorname (ceil) (2.4) = \ lceil 2.4 \ rceil = 3). </P>

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