### Re: Numerus "Numerans Numeratus"

by **Philostotle** on February 14th, 2019, 2:57 am

I had hoped for more interest. Supposing this is because I chose to leave out negative integer examples I will post the following.

In keeping with the assertion that the entirety of Numerus Numerans Numeratus is Isomorphic except regarding multiplication and division by zero, we acquire the current definitions of subtraction and negative.

Subtraction is: add the opposite of.

http://www.softschools.com/math/topics/subtracting_integers/

Negative is: the opposite of.

https://www.khanacademy.org/math/arithmetic/arith-review-negative-numbers/arith-review-number-opposites/a/number-opposites

Therefore, subtraction is not an operation other than addition, which remains unchanged.

Therefore, the negative symbol represents a characteristic of the following given quantity.

Let the given characteristic of the negative symbol for the numerical quantity exist without change.

Let the numerical quantity of the number 0: exist without an opposite numerical quantity.

-1: the opposite of the numerical quantity 1.

Allow that the characteristic of the negative symbol for the dimensional unit quantity to exits as: “place the opposite of”

-(_): “place the opposite of” a given numerical quantity into the dimensional unit quantity of (_).

Classic

-2 * 3 = -6

Isomorphic

-(_,_) * 3 = -6

3: the numerical quantity of the number 3.

-(_,_): the dimensional unit quantity of the number 2, indicating that the opposite of the given numerical quantity is to be placed into it.

(-3,-3): the opposite of the given numerical quantity of the number 3, placed into the dimensional unit quantity of the number 2.

(-3 + -3 = -6): the opposite of the given numerical quantity of the number 3, placed into the dimensional unit quantity of the number 2, then all numerical quantities in all dimensional unit quantities are added.

Classic

-2 * -3 = 6

Isomorphic

-(_,_) * -3 = 6

Or relatively:

-(_,_,_) * -2 = 6

-(_,_): the dimensional unit quantity of the number 2, indicating that the opposite of the given numerical quantity is to be placed into it.

-3: the numerical quantity given.

3: the opposite of the numerical quantity given.

(3 + 3 = 6): the opposite of the opposite of the numerical quantity of the number 3 placed into the dimensional unit quantity of the number 2, then all numerical quantities in all dimensional unit quantities are added.

Or relatively:

-(_,_,_): the dimensional unit quantity of the number 3, indicating that the opposite of the given numerical quantity is to be placed into it.

-2: the numerical quantity given.

2: the opposite of the numerical quantity given.

(2 + 2 + 2 = 6): the opposite of the opposite of the numerical quantity of the number 2 placed into the dimensional unit quantity of the number 3, then all numerical quantities in all dimensional unit quantities are added.