^ 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 number in classical mathematics.
The foundational equation of the Wave Number system reflects the opposing nature of Opposite Values and is expressed as follows:
1^+ 1v = 0
Counters
An Opposite Value is composed of three parts. The first part is the Counter, which determines the magnitude of the Opposite Value. The absolute value of an Opposite Value is its Counter, denoted as |a| where a is the Opposite Value.
Opposite Types
The second component of an Opposite Value is the Opposite Type, which indicates the axis on which the Opposite Value is situated. If no Opposite Type is specified, the Opposite Value resides on the x-axis. For example, 2^ is on the x-axis. Different letters denote other axes, such as 2i^ on the y-axis and 2j^ on the z-axis.
Opposite Signs
The third component of an Opposite Value is the Opposite Sign, which indicates whether the Opposite Value is a ^ or v . Opposite Values with the same Counter but different Opposite Signs cancel each other out when added. Hereafter, the symbol ? will represent any Opposite Type, and the superscript ? will denote any Opposite Sign.
An alphabetic character or term can represent an unknown Opposite Value or Counter.
Unitaries
Each Opposite Type has two unitaries, corresponding to each Opposite Sign. A unitary Opposite Value has a Counter of 1, and thus a magnitude of 1. The unitaries in R1 are 1^ and 1v. In R2, they are 1^, 1v, i^ and iv. In R3, they are 1^, 1v, i^, iv, j^ and jv.
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