Abstract—The paper collects 42 frequently-used properties of the floor function, including 35 ones from other literatures and 7 newly added-and-proved ones. The collected properties cover basic inequalities, basic identities, conditional inequalities, conditional equalities and practical formulas. The paper is helpful for scholars of mathematics and computer science and technology in reading and writing scientific works, reasoning and designing algorithms.

Index Terms—Computational science, floor function, formula, mathematical reasoning.

Xingbo Wang is with Department of Mechatronic Engineering, Foshan University, Foshan, China and State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China.

Cite:Xingbo Wang, "Frequently-Used Properties of the Floor Function," International Journal of Applied Physics and Mathematics vol. 10, no. 4, pp. 135-142, 2020.

Copyright © 2020 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).