Unary operations | Mathematical notation | Special functions
Floor and ceiling functions
In mathematics and computer science, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted floor(x) or ⌊x⌋. Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ceil(x) or ⌈x⌉. For example, ⌊2.4⌋ = 2, ⌊−2.4⌋ = −3, ⌈2.4⌉ = 3, and ⌈−2.4⌉ = −2. The integral part or integer part of x, often denoted [x] is usually defined as the ⌊x⌋ if x is nonnegative, and ⌈x⌉ otherwise. For example, [2.4] = 2 and [−2.4] = −2. The operation of truncation generalizes this to a specified number of digits: truncation to zero significant digits is the same as the integer part. Some authors define the integer part as the floor regardless of the sign of x, using a variety of notations for this. For n an integer, ⌊n⌋ = ⌈n⌉ = [n] = n. (Wikipedia).
