## Mirror Theory-Multidimensional Reflective Arithmetic / Logic

Philosophical, mathematical and computational logic, linguistics, formal argument, game theory, fallacies, paradoxes, puzzles and other related issues.  ### Mirror Theory-Multidimensional Reflective Arithmetic / Logic

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.
Eodnhoj7
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Posts: 102
Joined: 02 Mar 2018    ### Re: Mirror Theory-Multidimensional Reflective Arithmetic / L

Eodnhoj7
Banned User

Posts: 102
Joined: 02 Mar 2018    ### Re: Mirror Theory-Multidimensional Reflective Arithmetic / L

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)
Eodnhoj7
Banned User

Posts: 102
Joined: 02 Mar 2018    ### Re: Mirror Theory-Multidimensional Reflective Arithmetic / L

What are the undefined symbols ⨀ and ⧂? What does :1 mean?
⨀ = Mirror (number tending towards number resulting in a repetition of the original number through further number)
⧂ = Mirror in Structure (what all mirroring numbers equivocate to. Considering the mirroring function observe the repitition of the original number through further numbers, this repitition results in a set of numbers as resulting structures extending from the original set of numbers being mirrored)

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.

We cannot seperate a number from the basic arithmetic functions of addition or subtraction, with addition and subtraction being the foundations for the rest of arithmetic (and by default mathematics). The reason for this is inherent within the numbers themselves as they derive there identities as either being positive or negative, with the number itself (we will use 1 in this case) being a neutral third element from which "positive" and "negative" extend. In these respects all numbers main a triadic nature of positive, negative, and neutral.

1) This positive nature of number gives an inherent nature of summation as convergence.

2) This negative nature of number gives an inherent nature of seperation as divergence.

3) The neutral nature of number observes number in itself as the neutral boundary from which unity and seperation occur and in these respects can be viewed under the terms of "both/and" and "neither/nor" through the number as "either/or". I may have to extend upon this point further.

"Mirroring" acts as a verb, ie the numbers "mirror" with "mirroring" being a from of replication through direction in which one number tending towards another number (as observed in the above formulas) results in both the original numbers and new ones.

Considering the "+" or "-" nature inherent within the number exists as part of the number, and the numbers exist through other numbers, the observation of "+" and "-" results with "+" and "-" being directed into "+" and "-" considering the numbers are directed to further numbers.

In simpler terms, all numbers tend towards further numbers, resulting in the further numbers and "+" and "-" are inherent within the numbers, hence "+" and "-" tend toward eachother resulting in multiplication/division and powers/roots.

Where +1 would be observed as "additive one" (considering the premise of addition being inherent within the number itself), and *1 would be observed as "multiplicative one", the "+" and "*" have been replace with the dot system to observe intuitively, that all functions form through eachother with addition (as one dot) tending into multiplication (as the addition of addition as two dots) which in turn tends into powers (as the multiplication of multiplication as the addition of addition of addition of addition).

You claim 3 cannot tend to 4. 3 can tend to 4 in the respect of an infinite fractal.

1) (3 → 4)

2) (3 → 3.1 → 3.2 → 3.3 → 3.4 → 3.5 → 3.6 → 3.7 → 3.8 → 3.9 → 4.0)

3) (3.01 → 3.011 → 3.0111 → 3.01111 → ∞) → (3.02 → 3.021 → 3.0211 → 3.02111 → ∞) → .... → 4

4) (3.1 → 3.11 → 3.111 → 3.1111 → ∞) → (3.2 → 3.21 → 3.211 → 3.2111 → ∞) → .... → 4

This tendency, or movement towards, because of the nature of fractals observes an infinite change as progression. So 3 tending towards 4 observes a change in 3 as it becomes and infinite fractal. This constant change in 3 moving towards 4 observes 3 existing in relation to 4 because of this inherent movement as a boundary.

Now we can observe point three starting with the number 3.01 and in point four it progresses to 3.1. However these infinite series may start with 3.001 or 3.0001, etc. This itself is an infinite progression away from 4 as a starting point of movement towards 4.

In these respects the point of measurement is in constant change by the choice applied.

Because there is not just a series of infinite fractals moving towards 4, but also and infinite number of infinite fractals moving towards 4, what we observe in "→" is a boundary of continual change that observes the relationship of 3 and 4 respective of the direction the fractals move toward infinity.

3 tends to 4, or maybe in better terms is directed towards 4, and this nature of direction in turn forms the number line.

Now one can say that 3 is going towards 4 and 4 is going to 5, ad-infinitum with a simultaneous observation of the line going in a seperate direction as 4 directed towards 3 which is directed towards 2, etc.

In these respects the line exists as 2 directions, however the line as 2 directions in itself is:

1) 1 line as a localized set of 2 directions.
2) These 2 directions exist in relation to eachother. For example if a line is going in 1 direction it can only do so relative to another direction. This direction must be seperate from the original 1 direction and in doing so must be different direction.

Less than or greater than necessitates a direction in relation. So while 3 may be greater than 2, or 2 is less than three we observe:

1) Direction as expansion and contraction in relativistic size.

2) 2 being less than three observes 3 contracting quantitatively to 2 or 2 expanding quantitatively to 3.

Size, in these respects as quantitative, is direction through expansion and contraction with this expansion and contraction necessitating movement which we observing in the infinite progression of fractals.

Observing "→" is strictly observing a unified infinite movement as a constant boundary in itself. Observing 1 → 2 → 3 → 4 → ∞ in itself is another series of observed relations through direction as movement which in turn exists as 1(1 → 2 → 3 → 4 → ∞) which as 1 can be further observed as

_________1_________ In these respects each number is an observation of direction as change.
(1 → 2 → 3 → 4 → ∞)

with this in itself being 1 unit...and the number line progresses. In these respects the number line exists through a "folding function" conducive to simple alternation resulting in frequency. This folding observes that the number line must direct itself to further number lines, through itself (under a form of repitition as alternation) in order to exist.

We can see this inherent nature of "frequency" through repitition as alternation inherent with the flux of the city examples themselves.

In simpler terms each number is a localization of changing relations, as the boundary of the change itself which composed further change. Localization is an observation of change

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Eodnhoj7
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Joined: 02 Mar 2018  