[PMO Tutorial #8] The Greatest Integer Function, Part 1 - Algebra

Hello PMO Contestants!

The Greatest Integer Function (GIF), aka the Floor Function, is one of those functions that regularly appears in the PMO and other math contests. In this video, Kerish Villegas, MOSC Trainer and former PMO National Finalist, introduces the GIF as he solves a PMO problem.

Since we can't type math symbols here, let's use Floor(x). Thus, for example, Floor(pi) = 3, Floor(-4.2) = -5, and Floor(5) = 5. Some properties of the GIF appear technical but an example should help clear things out. For instance, it is a fact that pi is between 3 and 4. In general, if x is not an integer, then x is between Floor(x) and Floor(x) + 1.

Philippine Mathematical Olympiad

Mathematical Society of the Philippines