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. (shrink)

The MgAl2O4 spinel doped with Eu2+ ions powder phosphor was prepared at temperature as low as 500 oC using the combustion route. A structural property of the powder was characterized by X-ray diffraction (XRD). This XRD pattern shows the well crystallized cubic phase, Fd-3m space group of MgAl2O4. The estimated average crystalline size is about 36 and 30 nm for MgAl2O4 and Eu doped MgAl2O4 particles respectively. The photoluminescent property of prepared powder was investigated using excitation and emission spectroscopy (...) at room temperatures. Energy levels scheme is proposed for emission from MgAl2O4: Eu2+. (shrink)