In this video we will learn about the Greatest Integer Function (Floor function) and also its limit.
The greatest integer function is a function that gives the largest integer which is less than or equal to the number x. This function is denoted by [x] or ⌊x⌋ or ⟦x⟧. We will round off the given number to the nearest integer that is less than or equal to the number itself. 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.
Carl Friedrich Gauss introduced the square bracket notation [x] in his third proof of quadratic reciprocity (1808). This remained the standard in mathematics until Kenneth E. Iverson introduced, in his 1962 book A Programming Language, the names "floor" and "ceiling" and the corresponding notations ⌊x⌋ and ⌈x⌉. Both notations are now used in mathematics, although Iverson's notation will be followed in this article.
