TITLE:
The Njiki’s Fundamental Theorem-Definition on Fractions in the Mathematical Set ℚ and by Extension in ℝ and ℂ, for the Purpose of Leading to the Construction of Some Algebraic Structures as Its Theoretical Applications and for the Practical Ones
AUTHORS:
Jean Claude Njiki
KEYWORDS:
Operations of Addition, Additive Operations in ℚ, Laws in ℚ, THEOREM-DEFINITION, External Multiplication
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.14 No.3,
September
30,
2024
ABSTRACT: The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set
ℚ
and by extension in
ℝ
and
ℂ
and in order to construct some algebraic structures is about the proved EXISTENCE and the DEFINITION by NJIKI of two INNOVATIVE, IMPORTANT and TEACHABLE operations of addition or additive operations, in
ℚ
, marked
⊕
and
+
α,β
, and taken as VECTORIAL, TRIANGULAR, of THREE or PROPORTIONAL operations and in order to make THEM not be different from the RATIONAL ONE, +, but to bring much more and new information on fractions, and, by extension in
ℝ
and
ℂ
. And the very NJIKI’s fundamental THEOREM-DEFINITION having many APPLICATIONS in the everyday life of the HUMAN BEINGS and without talking about computer sciences, henceforth being supplied with very interesting new ALGORITHMS. And as for the work done in the research, it will be waiting for its extension to be done after publication and along with the research results concerned.