Principles
The Wave Numbers system comprises of the ^ Opposite Values (called ‘Hat’ Opposites) and the v Opposite Values (called ‘Vee’ Opposites). All the Opposite Values in the Wave Numbers system start from 0.
Theorems – Order Properties of Integers
The theorems of order properties of integers are derived from the theorems in Axioms for Real Numbers as interpreted for Wave Numbers. Next: Ratios Previous: Inequalities
General Axioms
The following axioms are adapted from the 15 axiom statements in Axioms for Real Numbers , specifically interpreted for Wave Numbers. Wave Numbers assumes that the following statements are true. Here a, b, c and d represent arbitrary Opposite Values. Next: Theorems Previous: Properties of Rotation
Definitions – General
The axiom definitions that follow derive from the 19 axiom definitions in Axioms for Real Numbers as interpreted for Wave Numbers. Next: Equality Previous: Operations
Primitives – Various – Old
This post describes various other math primitives in the Wave Numbers System. Integer An integer is a whole number on any axis (?^, ?v or zero). Zero The symbol 0 represents the number zero. It is a special Opposite Value as it does not have an Opposite Type or Sign. It is less than all […]
Definition – Axes
All axes in an n-dimensional subset are orthogonal. Opposite Values on Axes An Opposite Value represents a point on a Wave Number axis or any value with a finite or infinite decimal representation. Unlike classical mathematics, which uses real and imaginary numbers, the Wave Number system exclusively uses Opposite Values. R1 The standard configuration of […]