Mirror Theory-Multidimensional Reflective Arithmetic / Logic

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Mirror Theory-Multidimensional Reflective Arithmetic / Logic

Postby Eodnhoj7 on March 5th, 2018, 1:34 pm 

Presented Argument:

Mirror Theory

Below is a "part", emphasis on "part" as it is unfinished with the exception of the mathematics section, of a paper I am working on called Mirror Theory.

ll number exists as reflective space, with 1 being an intradimensional point that exist ad-infinitum through a mirroring process that constitutes space itself as space, while simultaneously providing the foundations for "space as dimension through direction". Considering the point exists as unified and everchanging, we observe it locally in space/time through approximation in which the points (as extension of the point) exist through the connection of -1 dimensional lines that are: imaginary, negative in dimension (deficient in dimension but existing the the 1d point) and provide the foundation for what we understand of as deficiency in structure, aka randomness, as the limit of unity. This points mirrors itself ad-finitum at such a high rate, that it does not move while simultneously relflecting the dualistic understanding of infinity as spatial "limit" and "no-limit" with the third dimension being...well dimension itself as "direction".

Because the 1d point is the foundation for all reality, including consciousness (in which we intuitively "number" the 0d point contradictory) it is the foundation for what we understand of as number. 1 as positive cannot be seperated from the point, as it is the point. In its positive nature, as equal to addition as summation, if reflects upon itself to maintain +1. Simultaneously, addition as + which is inherent and inseperable from the number, reflects to form multiplication as the addition of addition or *1. +1 also reflects to form +2 and *2.

So where standard addition observes 1+1=2, reflective arithmetic observes both this and an inherent "set" with which the equation is composed:
+1 ≡ +1 ≅ {+1,*1,+2,*2}

****This post is old and the symbols used have been changed to avoid confusion. I have to update the post when I am finished with the calculations, several of the equations in the above text are void.

This set in turn existing as points, or lines if negative numbers, approximates. This approximation function observes that each point must find the corresponding connection between them. This approximation as connection, in turn results as the negative number (equivalent to negative dimensions as the line), wich both connects the points and exists as subtraction and division. Subtraction merely being the approximation of addition, division the approximation of multiplication, and subtraction mirroring subtraction to form division.

All positive arithmetic functions are inseperable from the point, as 1d space (not 0d space). All negative arithmetic functions are inseperable from the line as -1d space.


I will cut this out for brevity, assuming questions for the first part, however the equation about converting geometric solids gives a glimpse of the calculations. I will cover approximation later, as the negative dual to the reflective portion, if you wish.


This does not argue against the standard foundations of mathematics and geometry (founded in the 0d point and 1d line) but observes them as foundations for "relativism" or "relation" in which the symbols exist if and only if they "relate". In these respects standard mathematics is founded, and at its peak, from relativistism as the relation of parts that exist as 1d linear spaces individuating through 0d point.

In simple terms, from the perspective of an ethereal binding space, all numbers exist as positive points and negative lines which are inseperable from sets rooted in 1 as 1, while providing a foundation for both number and arithmetic as an inherent mirroring space that acts as binding median through the promulgation of symmetry.

Agree/Disagree Why?
Attachments
Mirror Theory.docx
Part of Paper 6 pages out of 34 out of 105+ pages.
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Eodnhoj7
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Re: Mirror Theory-Multidimensional Reflective Arithmetic / L

Postby Eodnhoj7 on June 11th, 2018, 2:42 pm 

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Re: Mirror Theory-Multidimensional Reflective Arithmetic / L

Postby Eodnhoj7 on June 12th, 2018, 12:25 pm 

Few issues need worked out, but here is a general update on Mirror Theory with some basic examples:

Axioms:

A) All numbers are inseparable from there arithmetic functions, with these arithmetic functions inherent within the number itself.



B) All mirroring numbers maintain themselves as part of the inherent set. These mirroring numbers as extensions of 1 by default maintain 1 as an inherent element of the set.
b1)This can be seen in Step A.



C) All arithmetic functions inherent within the numbers composed both the number an eachother.
c1) All additive functions, marked by (∙), mirror into a multiplicative function, marked by (:). Multiplication is the addition of addition, with multiplication having an inherent element of addition in it.
c2) All multiplicative functions, marked by (:), mirror into a power function, marked by (⁞). Powers are the multiplication of multiplication, with powers having an inherent element of addition in it through multiplication.
c3) All mirrored functions have an inherent element of 1 corresponding to that function which is mirrored into the numbers.
c4) This can be seen in Step B.



D) All numbers mirror each other in accordance with their inherent function. If the function is a mirror of base addition or subtraction, such as multiple or powers, this mirroring process contains as an element the basic functions which compose it.
d1) Considering the arithmetic function is inherent within the answer, where the arithmetic will be the same, the corresponding number as the answer will mirror in structure the arithmetic function in which it is composed.
d2) This corresponding answer will contain as an element 1 and its corresponding arithmetic properties
d3) This can be seen in Step C and D along with their corresponding sub-steps



E) All positive numbers are called point numbers, in reference to positive 1 (as additive), being the point of origin. The resulting numbers from steps A, B, C/D and their corresponding substeps resulted in a set. All repeated numbers are observed once. In these respects mirror theory observes the mirroring of numbers resulting in sets of numbers whose inherent elements provide the foundation for arithmetic functions. All numerical form and function is premised as an extension of 1.



Example Set 1:

⨀ (∙1,∙1) ⧂ (∙1, :1, ∙2, :2)


a) (∙1, ∙1) → ∙1

b) (1, 1) → :1 ∋ ∙1

c) (∙1, ∙1) → (:2 ∋ (:1 ∋ ∙1)) ∋ (∙2 ∋ ∙1)



⨀ (∙2,∙3) ⧂ (∙1, :1, ∙2, :2, ∙3, :3, ∙5, :5)


a) (∙2, ∙3) → ∙2 ∋ ∙1 , ∙3 ∋ ∙1

b) (2, 3) → :2 ∋ (:1 ∋ ∙1), :3 ∋ (:1 ∋ ∙1)

c) (∙2, ∙3) → (:5 ∋ (:1 ∋ ∙1)) ∋ (∙5 ∋ ∙1)



⨀ (∙2,:3) ⧂ (∙1, :1, ∙2, :2, ∙3, :3, ∙5, :5, ∙6, :6)

a) (∙2, :3) → ∙2 ∋ ∙1, (:3 ∋ (:1 ∋ ∙1)) ∋ (∙3 ∋ ∙1)

b) (2, :3) → :2 ∋ (:1 ∋ ∙1), :3 ∋ (:1 ∋ ∙1)

c) (∙2, :3 ∋ ∙3) → (:5 ∋ (:1 ∋ ∙1)) ∋ (∙5 ∋ ∙1)

c) (∙2, :3) → (:6 ∋ (:1 ∋ (:1 ∋ ∙1)) ∋ (∙6 ∋ ∙1)



⨀ (:2,:3) ⧂ (∙1, :1, ⁞1, ∙2, :2, ⁞2, ∙3, :3, ⁞3, ∙5, :5, ∙6, :6, ⁞6)


a) (:2, :3) → (:2 ∋ (:1 ∋ ∙1)) ∋ (∙2 ∋ ∙1), (:3 ∋ (:1 ∋ :1)) ∋ (∙3 ∋ ∙1)

b) (:2, :3) → ((⁞2 ∋ (⁞1 ∋ (:1 ∋ ∙1)) ∋ (:2 ∋ (:1 ∋ ∙1))) ∋ (∙2 ∋ ∙1)
b1) ((⁞3 ∋ (⁞1 ∋ (:1 ∋ ∙1)) ∋ (:3 ∋ (:1 ∋ ∙1))) ∋ (∙3 ∋ ∙1)

c) (:2, :3) → ((⁞6 ∋ (⁞1 ∋ (:1 ∋ ∙1)) ∋ (:6 ∋ (:1 ∋ ∙1))) ∋ (∙6 ∋ ∙1)
C1) (:2 ∋ ∙2, :3 ∋ ∙3) → (:5 ∋ (:1 ∋ ∙1)) ∋ (∙5 ∋ ∙1)
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