July 22, 2024
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Definition – Opposite Values

^ and v Opposite Values

Opposite Values are math primitives in the Wave Numbers System. The system uses two types of numbers known as  ^, called ‘Hat’ and v, called ‘Vee’, Opposite Values.  These form fundamental math primitives 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 basic rule of the Wave Number system reflects the opposite nature of Opposite Values and is that:

1^+ 1v = 0

Counters

Three parts make up an Opposite Value primitive. The first is the Counter which gives the magnitude of the Opposite Value. The absolute value of an Opposite Value is its Counter. i.e. |a| is the Counter of a.

Opposite Types

The second part of the primitive Opposite Value is the Opposite Type which represents the axis where the Opposite Value is located. If no Opposite Type is present, then the Opposite Value is on the x-axis. For example: 2^ is on the x-axis. Different letters are used for the other axes. For example: 2i^ is on the y-axis and 2j^ is on the z-axis.

Opposite Signs

The third part of the primitive Opposite Value is the Opposite Sign which distinguishes whether the Opposite Value is a ^ or v . Opposite Values with the same Counter but different Opposite Signs cancel each other out when added. From here onwards the ? represents any Opposite Type and the superscript ? represents any Opposite Sign. 

An alphabetic character or term can represent an unknown Opposite Value or Counter.

Unitaries

Each Opposite Type has 2 unitaries, one for each Opposite Sign. A unitary Opposite Value has a Counter of 1 and therefore 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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