TITLE:
Shift, the Law of the Invention of Zero
AUTHORS:
Emmanuel Cadier Anaxhaoza
KEYWORDS:
Axiom, Axiom of Linear Algebra {ALA}, Any Base Calculation, ABC Theory, Number’s Origin, Number Theory, Newton’s Binomial Formula, Pascal’s Triangle, Base Z, Canonical Bases, Calculator Revolution, Infinite Sums of Inverse of Integer to the Successive Powers, Information Completion Theory, Cipher, Factorizations That Are Numbers, Infinite Numbers That Are Infinite Sums
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.5,
May
16,
2023
ABSTRACT: After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten; first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.