R1 – Logs
This post covers the definition of R1 logs with details of the logarithmic formulae and some examples. Definition Wikipedia defines logs as follows: ‘In mathematics, logarithm (log) is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.’ Logs are […]
R1- Exponentiation – Definition
This post covers the definition of exponentiation in R1. It also includes reciprocals and examples. Introduction In Wikipedia, exponentiation is defined as follows: ‘Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as “b raised to the power of n“. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that […]
R1 – Roots – Definition
This post on R1 roots covers the definition of roots and how roots are derived from the multiplication table. It includes examples of square, cube and higher roots. Definition Wikipedia defines a root as: ‘an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: ‘ Wave […]
R1 – Division – Definition
What is R1 Division? R1 Division is the inverse of R1 multiplication. The result of division of an operand by an operator is described by a math expression. Multiplying the operator with the result gives the operand. For example: It is a scalar type operation that takes into account the Opposite Signs. As the inverse […]
R1 – Multiplication – Definition
What is R1 Multiplication? Multiplication in R1 is similar to multiplication in classical maths. It is a scalar type operation that takes into account the Opposite Signs. It can be considered a ‘times-add’ operation with the Opposite Sign of the result dependent on the R1 multiplication table. By ‘times-add’ operation is meant to add the […]
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
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
Definition – Opposite Values
^ 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 […]