The floor function maps a real number to the largest previous integer. More precisely, floor(x)=[x] is the largest integer not greater than x. The square bracket notation [x] for the floor function was introduced by Gauss in his third proof of quadratic reciprocity in 1808. The floor function is also called the greatest integer or entier (French for "integer") function, and its value at x the integral part or integer part of x. The floor function has many applications in all areas of mathematics, especially in number theory, algebra or analysis and in consequence it was studied by a wide number of authors. The aim of this article is to establish and discuss some properties of the floor function. It demonstrates how mathematical analysis can be used to prove some results about the floor function.