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 – Advanced
This post looks at more advanced R1 multiplications using expressions. The examples show that R1 multiplication of expressions is commutative. Multiplication of Expressions that Contain Terms A term can be multiplied with an Opposite Value. Multiplication is commutative. For example: x*2v = 2v*x. Firstly, look at the equation (x + 1v )*(x + 3^) and […]
R1 – Multiplication – Simple
This post looks at some simple multiplication of Opposite Values together, using flip signs and with counters. The examples show the commutativity, associativity and distributivity of R1 math multiplication. R1 Unitary Multiplication Table * 1^ 1v 1^ 1^ 1v 1v 1v 1^ Simple Multiplication with R1 Opposite Values Multiplication using Flip Sign A flip sign […]
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 […]
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
Theorems – Quotients
The theorems of quotients are derived from the theorems in Axioms for Real Numbers as interpreted for Wave Numbers. Next: Squares Previous: Multiplicative Inverses