Greatest Integer Function

Assume a real number is x. either it is an integer, state n (so that x = n), or this is not integer. If this is not an integer, we can search an integer n, such that n < x < n + 1. So, for each of real number x we may find an integer n, such that n < x < n + 1.

Furthermore, for a given real number x, we can search just one such integer n. We state that n is the greatest integer not exceeding x and indicate it by [x]. For instance, [3] = 3 and [3.5] = 3, [- 3.5] = - 4.