November 2, 2024
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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.

Wave Number Calculator – Guide

Introduction This is the online Wave Number calculator guide. The calculator supports the R1, R2, and R3 dimensions. Chose from these using the top menu bar of the calculator. Wave Numbers use Opposite Values. Each Opposite Value consists of 3 parts. The first is the Counter. This gives the magnitude.   The second part is […]

Axioms – Ratios

In Cecilia Hamm’s “Making Sense of Negative Numbers,” she states, “Arnauld (1612-1694) claimed that the basic principle of multiplication is that the ratio of unity to one factor is equal to the ratio of the second factor. i.e., given the product x , then x or x .” This is known as the axiom of […]

Theorems – Inequalities

The theorems of inequalities are derived from the theorems in Axioms for Real Numbers as interpreted for Wave Numbers. Transitivity Other Properties Next: Order Properties of Integers Previous: Squares

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 […]

Definition – Opposite Values

^ and v Opposite Values The Wave Number system utilizes two types of Opposite Values:  ^ (called “Hat”) and v (called “Vee”).  These are constructed using Counters, Opposite Types and Opposite Signs. The Wave Number system uses the term “Opposite Values” instead of “Opposite number” because an Opposite Value contains more information than a pure […]