Principles
The Wave Numbers system comprises of the ^ Opposite Values (called ‘Hat’ Opposites) and the v Opposite Values (called ‘Vee’ Opposites). All the Opposite Values in the Wave Numbers system start from 0.
Axioms – Property of Order
Definition of the Property of Order In Cecilia Hamm’s ‘Making Sense of Negative Numbers’ she states: A: “For natural numbers, if and then and there exists a number such that and . Hence for any N if then . Including zero in the domain and taking will lead to a contradiction: if then “ However, […]
Axioms – Ratios
In Cecilia Hamm’s “Making Sense of Negative Numbers,” she states, “Arnauld (1612-1694) claimed that the basic principle of multiplication is that the ratio of unity to one factor is equal to the ratio of the second factor. i.e., given the product x , then x or x .” This is known as the axiom of […]
Theorems – Order Properties of Integers
The theorems of order properties of integers are derived from the theorems in Axioms for Real Numbers as interpreted for Wave Numbers. Next: Ratios Previous: Inequalities
Theorems – Squares
The theorems of squares are derived from the theorems in Axioms for Real Numbers as interpreted for Wave Numbers. Next: Inequalities Previous: Quotients
Theorems – Inequalities
The theorems of inequalities are derived from the theorems in Axioms for Real Numbers as interpreted for Wave Numbers. Transitivity Other Properties Next: Order Properties of Integers Previous: Squares
General Axioms
The following axioms are adapted from the 15 axiom statements in Axioms for Real Numbers , specifically interpreted for Wave Numbers. Wave Numbers assumes that the following statements are true. Here a, b, c and d represent arbitrary Opposite Values. Next: Theorems Previous: Properties of Rotation
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
Primitives – Various – Old
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 […]