Abstract

In this paper, we question the structure of number sets, particularly the real numbers R. By analyzing the construction of the integers Z and rationals Q, we show that certain fundamental properties of classical mathematics, such as the multiplication of negative numbers and the addition of fractions, could be reinterpreted under a different logical framework. We also discuss the idea that there is no "universal base" allowing all rational numbers to be expressed in a single form. Our work follows the reflections initiated by Fibonacci in the Liber Abaci, Peano in his axioms, and other research in set theory and the philosophy of mathematics.