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 other Opposite Values.
Counter One
The symbol 1 represents the Counter one.
Unitaries – A New Primitive
Unitaries are a new type of primitive in Wave Numbers. Each Opposite Type has 2 unitaries, one for each Opposite Sign. A unitary Opposite Value has a magnitude of 1 and in R1 they are 1^ and 1v. In R2 they are 1^, 1v, i^ and iv and so on.
Absolute Value
The absolute value of a, denoted by |a|, is the magnitude of a such that |n??| = n. This is a Counter and is not an Opposite Value but a magnitude. As such the use of it as a standalone term is incorrect. An Opposite Type and Sign can be assigned to an absolute value as follows:
- |n?^|?^ = |n?v|?^ = n?^
- |n?^|?v = |n?v|?v = n?v
Less Than – A New Interpretation of this Primitive
The last of the various primitives in this post is the new interpretation of the comparison operation, <, less than. The less than concept only applies to the absolute values of Opposite Values. i.e. only the magnitudes of Opposite Values can be compared.
Opposite Values differ in three ways, the magnitude, the Opposite Sign and the axis. If comparison was based on locations on the axis you would not be able to say that b is between a and c where a = 2^, b = 3v and c = 4^. Clearly 3v is not between 2^ and 4^ on the x-axis.
The magnitude of Opposite Values of different signs or types can be compared using <, = or >. For example:
- |6^| < |7v|, |6^| < |7i^|.
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