R1 – Division – Flipping
Flipping in division can be applied to the individual Opposite Values or to the result to reverse their signs.
R1 – Division – Simple
Division by Opposite Values is guided by the Rotation Division table for R1.
R1 – Division – Advanced
This post covers more advanced math division in R1 such as with expressions, long division and multiplicative inverses. Division of Expressions using Long Division The element of the result above the line is multiplied with the divisor. As the subtraction operation does not exist, the result is flipped and added to the numerator. In the […]
R1 – Exponentiation – Fractions, Flip Sign and Rules
This post covers the use of exponents with fractions and flip signs as well as the rules of exponentiation in R1. Exponent Fractions as Roots Exponents in fractions represent roots. As described in an earlier post, the root of an expression can be expressed as the root of the counter multiplied by the root of the […]
R1 – Addition
R1 Addition in Wave Numbers math is straightforward. Opposite Values with Opposite Signs cancel each other out through interference. It is commutative and associative. See examples below: Examples of R1 Addition Conclusion Try these examples of addition with our online calculator. Next: Rotation Previous: Property of Order
R1 – Rotation – Multiplication Table
Orthogonal Rule The Orthogonal rule, states that multiplication by a unitary is the equivalent of rotation around the unitary’s single point axis by 90o. This allows the derivation of the R1 multiplication table that follows. Multiplication Table The unitary multiplication table of R1 shows the result of multiplying by 1^ or 1v. Multiplying by 1^ equates […]
R1 – Rotation – Definition, Flipping and Prop
What is Rotation in R1? The Wave Number principles describe rotation as a fundamental operation. The rotation axioms support this. Rotation moves a point represented by an Opposite Value to a location represented by another Opposite Value. Rotation performs a circular movement around a single point axis represented by an Opposite Value. The single point […]
Theorems – Introduction
The theorems in this section are derived from the theorems selected in Axioms for Real Numbers as interpreted for Wave Numbers. These theorems can be proved from the axioms in the order listed. In all of these statements, a, b, c, d represent arbitrary Opposite Values. Theorems Next: Theorems – Zero Previous: General Axioms
Axioms and Primitives
Approach to Developing Axioms and Primitives The Axioms for Real Numbers from the Department of Mathematics at the University of Washington are presented in a meticulously structured format for defining axioms and primitives Similarly, the development of the Wave Number system’s axioms and primitives employs this well-considered methodology. Starting with Primitives The Axioms begin with […]
Quantum – Circuits – Bellagio – Definition
Introduction This post provides a definition of the Bellagio scheduling problem that will be solved in the following posts using a Wave Number quantum circuit. The Wave Numbers Bellagio circuit has been adapted from the solution in Quantum Computing Program Next-Gen Computers for Hard, Real-World Applications. Problem Definition Logic Definition for Day 1 at the […]