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 the x-axis is a line running from left to right with the origin at the center. An Opposite Value to the left of the origin is a v Opposite Value, while to the right of the origin, it is a ^ Opposite Value.
Opposite Values in R1 include integers, fractions, and irrational numbers, denoted as 1^, 1v, √2^,√2v, π^, πv, e^ and ev etc.
R2
R2 consists of the x and y-axes. The standard configuration of the x-axis is a line running from left to right through the origin, while the y-axis runs from north to south through the origin. Opposite Values on the x-axis are the same as in R1. An Opposite Value south of the origin on the y-axis is an iv Opposite Value, and one north of the origin is an i^ Opposite Value.
Opposite Values in R2 include all R1 Opposite Values on the x-axis, as well as integers, fractions, and irrational numbers on the y-axis, denoted as i^, iv, √2i^,√2iv, πi^, πiv, ei^, eiv etc.
R3
R3 consists of the x, y, and z-axes. The standard configuration places the y-axis running from east to west (left to right) through the origin, the z-axis running from north to south through the origin, and the x-axis running from front to back through the origin.
Opposite Values in R3 include all R2 Opposite Values on the x and y axes, as well as j^ and jv integers, fractions, and irrational numbers on the z-axis, denoted as: j^, jv, √2j^,√2jv, πj^, πjv, ej^, ejv etc.
An Opposite Value on the x-axis behind the origin is a v Opposite Value, while in front of the origin, it is a ^ Opposite Value. On the y-axis, left of the origin, an Opposite Value is an iv Opposite Value, while right of the origin, it is an i^ Opposite Value. On the z-axis, south of the origin, an Opposite Value is a jv Opposite Value, while north of the origin, it is a j^ Opposite Value. The standard orientation in R3 places j^ on top and ^ facing the viewer.
Higher Dimensions
In higher dimensions (Rn > 3), there are no standard configurations for the axes. Opposite Values in Rn include all Opposite Values in Rn-1 and a new range of Opposite Values based on the new axis. For example, R4 includes all R3 Opposite Values on the x, y, and z-axes, and adds k^ and kv integers, fractions, and irrational numbers on the w-axis, denoted as: k^, kv, √2k^,√2kv, πk^, πkv, ek^, ekv etc.
In higher dimensions than R3, there are no standard configurations for the axes.
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