Theorems – Flipping
The theorems of flipping are derived from the theorems in Axioms for Real Numbers as interpreted for Wave Numbers. Next: Distributive Previous: Zero
Theorems – Zero
The theorems of zero are derived from the theorems in Axioms for Real Numbers as interpreted for Wave Numbers. Next: Flipping Previous: Introduction
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
Axioms – Rotation Definition
Introduction The definition of rotation has no equivalent in the Axioms for Real Numbers. As a fundamental operation, it necessitates its own definition: A rotation moves a point, represented by Opposite Value(s), to a new location, also represented by Opposite Value(s), through a circular movement around an axis, which is similarly represented by Opposite Value(s). […]
Axioms – Equality
Axioms for Real Numbers states the following about equality: “In modern mathematics, the relation “equals” can be used between any two “mathematical objects” of the same type, such as numbers, matrices, sets, functions, etc. To say that a = b is simply to say that the symbols a and b represent the very same object. […]
Definition – Operations
Introduction This post defines the Wave Number math operations: Addition, rotation, rotication, multiplication and flipping. Addition a + b denotes the result of adding two Opposite Values a and b. This result is referred to as the sum of a and b. Rotation (↺?) The second operation is rotation. a ↺? b denotes the result […]
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 – Dimensions
The Wave Number system encompasses an unlimited number of dimensional subsets, each representing a different number of dimensions, starting with one dimension. Each dimensional subset is denoted as Rn. Next: Axes Previous: Opposite Values