Does One equal infinity? 7 step argument.
Does One equal infinity? 7 step argument.
Presented Argument:
1) "1" exists as "unity" and "wholeness".
2) As unity and wholeness "1" must maintain a selfreflective symmetry in order to exist. We observe this in common life where a physical or abstract structure maintains its stability through the reflection of points, with these points in turn forming a symmetry between eachother which allows the structure to exist.
3) "1" reflects upon itself to maintain itself. In doing so it reflects "2" (as: 1 ≡ 1 ≅ 2), "3" (as: 1 ≡ 1 ≡ 1 ≅ 3), "4" (as: 1 ≡ 1 ≡ 1 ≡ 1 ≅ 4), etc. unto infinity. In this respect all numbers are strictly structural extensions of 1.
4) As structural extensions of "1" all numbers reflect both "1", themselves "1x", and eachother "1y" unto infinity. In this respect 1 reflects infinity.
5) All number, including "1", continually manifests through selfreflective symmetry unto infinity. Infinity, as "totality", is synonymous with both "unity" and "stability" for there is no deficiency in it. In this respect both 1 and infinity are equal.
6) The selfreflective nature of 1, 1xy, and infinity observes a circular reflective symmetry, and in this respect observes selfreflection as the "maintenance of structure through the maintenance of center(s)".
7) The nature of "1" as infinite through reflective symmetry, observes all number as structural extensions of "1" as mere approximates of "1". In this respect, all approximates observe a form of "deficiency in unity." This deficiency is unity is not a thing in and of itself, as all number is composed of "1" and exists as "1" reflecting upon itself, therefore it is equivalent to 0. 0 is strictly the limit of infinity, as an observation that only infinity exists as 1.
Agree, disagree, don't know? Explain why.
1) "1" exists as "unity" and "wholeness".
2) As unity and wholeness "1" must maintain a selfreflective symmetry in order to exist. We observe this in common life where a physical or abstract structure maintains its stability through the reflection of points, with these points in turn forming a symmetry between eachother which allows the structure to exist.
3) "1" reflects upon itself to maintain itself. In doing so it reflects "2" (as: 1 ≡ 1 ≅ 2), "3" (as: 1 ≡ 1 ≡ 1 ≅ 3), "4" (as: 1 ≡ 1 ≡ 1 ≡ 1 ≅ 4), etc. unto infinity. In this respect all numbers are strictly structural extensions of 1.
4) As structural extensions of "1" all numbers reflect both "1", themselves "1x", and eachother "1y" unto infinity. In this respect 1 reflects infinity.
5) All number, including "1", continually manifests through selfreflective symmetry unto infinity. Infinity, as "totality", is synonymous with both "unity" and "stability" for there is no deficiency in it. In this respect both 1 and infinity are equal.
6) The selfreflective nature of 1, 1xy, and infinity observes a circular reflective symmetry, and in this respect observes selfreflection as the "maintenance of structure through the maintenance of center(s)".
7) The nature of "1" as infinite through reflective symmetry, observes all number as structural extensions of "1" as mere approximates of "1". In this respect, all approximates observe a form of "deficiency in unity." This deficiency is unity is not a thing in and of itself, as all number is composed of "1" and exists as "1" reflecting upon itself, therefore it is equivalent to 0. 0 is strictly the limit of infinity, as an observation that only infinity exists as 1.
Agree, disagree, don't know? Explain why.

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Re: Does One equal infinity? 7 step argument.
How does one represent unity and wholeness if unity suggests parts, and each part is one?
If a part is one, yet separate from other parts, then when you include those parts, the sum of unity is more than one. Wholeness therefore is more than one.
If a part is one, yet separate from other parts, then when you include those parts, the sum of unity is more than one. Wholeness therefore is more than one.
Re: Does One equal infinity? 7 step argument.
Was that clear? If not I can continue, or just ask another question.EchoesOfTheHorizon wrote: ↑Fri Oct 27, 2017 1:18 amHow does one represent unity and wholeness if unity suggests parts, and each part is one?
Unity is an absence of "particulation". It is the summation of parts in 1.
I think you are talking about individuation where a "part" is considered a "whole". In this respect, if I understand you correctly, these parts exists if and only if they relate to other parts, so on and so forth, adinfinitum. So a unit is only a unit if there are infinite number of units it can relate to.
Take for example all number exists as being both composed of one and moving towards infinity as "a 1's".
If a part is one, yet separate from other parts, then when you include those parts, the sum of unity is more than one. Wholeness therefore is more than one.
One reflects itself through all numbers as "1 reflecting 1, etc." In this respect all number is structural extension of 1. Add x and y is still adding 1 upon itself.
Re: Does One equal infinity? 7 step argument.
Here is a sample argument about 1 being proportional to infinity:
1) The problem is "infinity" implies existence as number exists if and only if they manifest unto infinity. 1n cannot exist unless their are infinitely further numbers to quantify it as 1n.
2) "1" implies existence as number exists if and only if they are structural extensions of 1.
3) 1 and quantitative infinity seem to cycle between eachother as neither can exist without the other as all rational numbers are merely reflections of "1" unto infinity. 1 exists if and only if their is quantitative
infinity. Quantitative Infinity exists if and only if their is one. In this respect they can be observed as dualistic: ⟨1∞⟩.
4) Infinity must contain "1" as an element otherwise it would not exist. 1 must contain infinity as an element otherwise it would not exist.
5) All number contains as an element "1" and "1" exists through selfreflection if and only if there is infinity as it must reflect itself through infinite number to infinitely exist. If One does not contain as an
element "infinity" is is not "stable" as it is "finite". If Infinity does not contain 1 as an element neither is it stable as it does not contain "all".
6) Because 1 as a unit or "unity" must both contain as an element and be an element of infinity as: 1 ∋ ∞ and 1 ∈ ∞ which would be similiar but not equal to ∞/1 and 1/∞ as "fractions". This is considering if x contains
as an element y, the element y can be observed as a degree of x.
∞/1 and 1/∞ can be observed as "proportional to eachother" as fractions even though these fractions in themselves cannot equate to anything other than themselves.
so ∞/1 ∝ 1/∞
The problem occurs as "lack of definition" is proportional to "lack of definition" cannot exist as thier is no definition to be proportional too.
7) In this respect ∞/1 ∝ 1/∞ cannot exist except as 1nx/1ny and 1ny/1nx as both contains as elements and are elements of 1nx and 1ny. 1nx/1ny and 1ny/1nx are striclty observation of "division" in one respect and "ratios"
in another for a ratio exists if an only if their is division and vice versa.
In this respect 1 and ∞ contain as an element and are an element of "proportionality/ratios" and "division". In this respect, and possiblity this respect only, 1 is proportional to infinity as they both contain
as an element and are an element of 1nx and 1ny.
or (1 ∝ ∞) ↔ ∃(∞/1 ∝ 1/∞) ↔ {(1,∞) ∈∋ (1nx,1ny) ∧ (1nx/1ny ∝ 1ny/1nx)}
Assuming the equation is correct, and that is where I need an opinion, One is proportional to infinity maybe only in this respect.
1) The problem is "infinity" implies existence as number exists if and only if they manifest unto infinity. 1n cannot exist unless their are infinitely further numbers to quantify it as 1n.
2) "1" implies existence as number exists if and only if they are structural extensions of 1.
3) 1 and quantitative infinity seem to cycle between eachother as neither can exist without the other as all rational numbers are merely reflections of "1" unto infinity. 1 exists if and only if their is quantitative
infinity. Quantitative Infinity exists if and only if their is one. In this respect they can be observed as dualistic: ⟨1∞⟩.
4) Infinity must contain "1" as an element otherwise it would not exist. 1 must contain infinity as an element otherwise it would not exist.
5) All number contains as an element "1" and "1" exists through selfreflection if and only if there is infinity as it must reflect itself through infinite number to infinitely exist. If One does not contain as an
element "infinity" is is not "stable" as it is "finite". If Infinity does not contain 1 as an element neither is it stable as it does not contain "all".
6) Because 1 as a unit or "unity" must both contain as an element and be an element of infinity as: 1 ∋ ∞ and 1 ∈ ∞ which would be similiar but not equal to ∞/1 and 1/∞ as "fractions". This is considering if x contains
as an element y, the element y can be observed as a degree of x.
∞/1 and 1/∞ can be observed as "proportional to eachother" as fractions even though these fractions in themselves cannot equate to anything other than themselves.
so ∞/1 ∝ 1/∞
The problem occurs as "lack of definition" is proportional to "lack of definition" cannot exist as thier is no definition to be proportional too.
7) In this respect ∞/1 ∝ 1/∞ cannot exist except as 1nx/1ny and 1ny/1nx as both contains as elements and are elements of 1nx and 1ny. 1nx/1ny and 1ny/1nx are striclty observation of "division" in one respect and "ratios"
in another for a ratio exists if an only if their is division and vice versa.
In this respect 1 and ∞ contain as an element and are an element of "proportionality/ratios" and "division". In this respect, and possiblity this respect only, 1 is proportional to infinity as they both contain
as an element and are an element of 1nx and 1ny.
or (1 ∝ ∞) ↔ ∃(∞/1 ∝ 1/∞) ↔ {(1,∞) ∈∋ (1nx,1ny) ∧ (1nx/1ny ∝ 1ny/1nx)}
Assuming the equation is correct, and that is where I need an opinion, One is proportional to infinity maybe only in this respect.

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Re: Does One equal infinity? 7 step argument.
I'm at the logic/rationale point (irrational?) where it seems like any symbol can mean anything once it's applied with meaning. For instance, I could just as easily say "A" (or 0 for that matter) stands for infinity, and try to make some form of argument for it. The question is, I think, does it make sense to the one that is arguing it? And does it allow them to operate at the level they wish to operate in, and at the level of reality they wish to work in?
Instance: "A" stands for a unit, "B" stands for another unit in addition to the previous unit.... "Z" does the same in addition to all previous symbols used. Does this logic carry forth to the point that "Z+..." is just another way to build to "Infinity"? And that "Infinity" itself, may be an inductive inference upon this model of logic?
Instance: "A" stands for a unit, "B" stands for another unit in addition to the previous unit.... "Z" does the same in addition to all previous symbols used. Does this logic carry forth to the point that "Z+..." is just another way to build to "Infinity"? And that "Infinity" itself, may be an inductive inference upon this model of logic?
Re: Does One equal infinity? 7 step argument.
Plato's Rock wrote: ↑Sun Nov 19, 2017 5:40 amI'm at the logic/rationale point (irrational?) where it seems like any symbol can mean anything once it's applied with meaning.
Thanks for the response, this is a "tricky" subject to deal with as the dividing line between order and chaos when dealing with infinity is a very thin line to walk across..and to get on point:
Assuming the equation is correct (and I am looking for someone to prove it either wrong in form/function or the missuse of terms such as "proportionality") one possible biproduct in quantitative terms would be exactly what you are saying as all "symbol" shares the same root as medial point through "unity" or "1".
What differs from "any symbol" is the respect that "1" is a constant symbol when viewed as a spatial structure. In these respects there is constant "meaning" irrespective of the symbol as certain constants are inevitable and these constants are inherent within all symbols.
In these respects the symbols are strictly structural extensions of a constant.
Considering all number is rooted in "1", and all arithmetic functions are strictly extensions of 1 through the application of ratios (as multiplication and division are the median points between addition/subtraction and powers/roots) the nature of infinity can be observed within all mathematical structures as a form of "justification through consistency and nontemporality".
If one is equivalent to infinity, then by default all mathematical entities are eternal and true in nature as "1" is a medial point that "centers" all realities.
In a simultaneously respect we gain a deeper understanding about the foundations of number in both quantitative and qualitative degrees. This enables, potentially speaking, a further development of mathematics into the unknown.
For instance, I could just as easily say "A" (or 0 for that matter) stands for infinity, and try to make some form of argument for it. The question is, I think, does it make sense to the one that is arguing it?
The symbol may "stand" for infinity as strictly a structural "extension" of it, considering we cannot conceive infinity in its entirety without a median to it. In these respects, all mathematical entities are justified in there own right as "truth" that never changes.
And does it allow them to operate at the level they wish to operate in, and at the level of reality they wish to work in?
If memory serves correctly, it was Euler who helped develop the mathematical symbolism we see today. His work helped provide the foundations of "perspective" through a symbolism that "centered" meanings into compact entities. In these respects the synthesis of symbols is the synthesis through ratios.
The question occurs as to where does the difference between symbolism and perspective occur? Or are they both the same as both justify the other through the reality we call "order" or "evidence"?
Instance: "A" stands for a unit, "B" stands for another unit in addition to the previous unit.... "Z" does the same in addition to all previous symbols used. Does this logic carry forth to the point that "Z+..." is just another way to build to "Infinity"?
Does it have to build to infinity as A,B...Z exist as structural extensions of eachother? The study of number, in both quantitative and qualitative means, is the study of infinity as all exist through infinity as infinity curving upon itself as 1.
The best visual means to observe this would be 1 being equivalent to a point in the center of a circle, whose circumference exists as infinite points which mirror itself through the center point.
Considering this center point as 1 is positive in value (equating to addition) this perpetual mirroring of itself, through the circumferance, not only manifests all number as form but all arithematic functions (as all arithmetic functions are results of addition mirroring itself)
Each numerical "space" is equivalent to the pythagorean conception of the "point through circle" mirroring itself to not only form all number (which it inherently contains as "infinity") but simultaneously all spatial structures as extensions of geometry.
And that "Infinity" itself, may be an inductive inference upon this model of logic?
Abductive and deductive also. In these respects, what we understand of logic is fundamentally trifold nature resulting in infinite extensions much in a similar form and function that we observe in Pi.

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Re: Does One equal infinity? 7 step argument.
This is where I think we talked a little bit past each other. I'm having a hard time seeing where "1" is a constant symbol, so you may need to explain that more. In particular what is meant by "Constant". Along with what you mean by spatial structure.Eodnhoj7 wrote: ↑Sun Nov 19, 2017 5:54 pm
What differs from "any symbol" is the respect that "1" is a constant symbol when viewed as a spatial structure. In these respects there is constant "meaning" irrespective of the symbol as certain constants are inevitable and these constants are inherent within all symbols.
This makes a little more sense, it'd be like me saying (building upon my example usage of "A") "AA" is "2", and if i were to divide "AA" by "A", I'd have "AA", or "2".Eodnhoj7 wrote: ↑Sun Nov 19, 2017 5:54 pmConsidering all number is rooted in "1", and all arithmetic functions are strictly extensions of 1 through the application of ratios (as multiplication and division are the median points between addition/subtraction and powers/roots) the nature of infinity can be observed within all mathematical structures as a form of "justification through consistency and nontemporality".
I think I did something similar to this chain of logic in my mind with "Zero"/ "0". In my point of view, zero may be interpreted as an "infinity" because it feeds back upon itself. Both as a symbol (it's an unbroken loop...theoretically), and one can feed as much as they want into it without changing it. Say one had something like this; 1, 0, ()1. The one "1" would be something like your "extension" (I don't know that much math "language", so bear with me). "1", or "Antione" would be like an "antiextension", and that it redacts the previous "1". Although it's still an "extension" in it's own right. Just in a different direction. I hadn't run with the thoughts as far as you seemed to have done so, so I can't explain further. Mainly because I'm not certain of what I'm saying myself.
Symbolism, probably is, the meaning applied to any given character at any given time. Whereas perspective, is likely, the interpretation of any given symbol at any given time (both for the self that made it, and for others).
Re: Does One equal infinity? 7 step argument.
Plato's Rock wrote: ↑Sun Nov 19, 2017 6:56 pmThis is where I think we talked a little bit past each other. I'm having a hard time seeing where "1" is a constant symbol, so you may need to explain that more. In particular what is meant by "Constant". Along with what you mean by spatial structure.Eodnhoj7 wrote: ↑Sun Nov 19, 2017 5:54 pm
What differs from "any symbol" is the respect that "1" is a constant symbol when viewed as a spatial structure. In these respects there is constant "meaning" irrespective of the symbol as certain constants are inevitable and these constants are inherent within all symbols.
The post is too long but this thread covers it: viewtopic.php?f=26&t=14835&start=15
This makes a little more sense, it'd be like me saying (building upon my example usage of "A") "AA" is "2", and if i were to divide "AA" by "A", I'd have "AA", or "2".Eodnhoj7 wrote: ↑Sun Nov 19, 2017 5:54 pmConsidering all number is rooted in "1", and all arithmetic functions are strictly extensions of 1 through the application of ratios (as multiplication and division are the median points between addition/subtraction and powers/roots) the nature of infinity can be observed within all mathematical structures as a form of "justification through consistency and nontemporality".
I think I did something similar to this chain of logic in my mind with "Zero"/ "0". In my point of view, zero may be interpreted as an "infinity" because it feeds back upon itself.
It would be the "limit" of infinity in these respects as "absence" and not a thing in itself. "Limit" of Infinity, is infinite however.
Both as a symbol (it's an unbroken loop...theoretically), and one can feed as much as they want into it without changing it. Say one had something like this; 1, 0, ()1. The one "1" would be something like your "extension" (I don't know that much math "language", so bear with me). "1", or "Antione" would be like an "antiextension", and that it redacts the previous "1". Although it's still an "extension" in it's own right.
Through 1, as  exists if and only +, yes...the thread I posted above should cover alot of these questions, so I am hesistant in repeating myself.
Just in a different direction. I hadn't run with the thoughts as far as you seemed to have done so, so I can't explain further. Mainly because I'm not certain of what I'm saying myself.
Symbolism, probably is, the meaning applied to any given character at any given time. Whereas perspective, is likely, the interpretation of any given symbol at any given time (both for the self that made it, and for others).
All symbolism originates in geometry, with the foundations of geometry being the "point" and "line". The thread I linked you should answer further questions.
Re: Does One equal infinity? 7 step argument.
1) is nonsensical. The number 1 may represent the first element in a series. Or the class of all sets containing one element. Now the idea of an 'element' may seem to 'exist as unity'. But your talk of numbers 'maintaining' themselves or doing this or that is also nonsensical.Eodnhoj7 wrote: ↑Thu Oct 19, 2017 5:22 pmPresented Argument:
1) "1" exists as "unity" and "wholeness".
2) As unity and wholeness "1" must maintain a selfreflective symmetry in order to exist. We observe this in common life where a physical or abstract structure maintains its stability through the reflection of points, with these points in turn forming a symmetry between eachother which allows the structure to exist.
3) "1" reflects upon itself to maintain itself. In doing so it reflects "2" (as: 1 ≡ 1 ≅ 2), "3" (as: 1 ≡ 1 ≡ 1 ≅ 3), "4" (as: 1 ≡ 1 ≡ 1 ≡ 1 ≅ 4), etc. unto infinity. In this respect all numbers are strictly structural extensions of 1.
4) As structural extensions of "1" all numbers reflect both "1", themselves "1x", and eachother "1y" unto infinity. In this respect 1 reflects infinity.
5) All number, including "1", continually manifests through selfreflective symmetry unto infinity. Infinity, as "totality", is synonymous with both "unity" and "stability" for there is no deficiency in it. In this respect both 1 and infinity are equal.
6) The selfreflective nature of 1, 1xy, and infinity observes a circular reflective symmetry, and in this respect observes selfreflection as the "maintenance of structure through the maintenance of center(s)".
7) The nature of "1" as infinite through reflective symmetry, observes all number as structural extensions of "1" as mere approximates of "1". In this respect, all approximates observe a form of "deficiency in unity." This deficiency is unity is not a thing in and of itself, as all number is composed of "1" and exists as "1" reflecting upon itself, therefore it is equivalent to 0. 0 is strictly the limit of infinity, as an observation that only infinity exists as 1.
Agree, disagree, don't know? Explain why.
Infinity is not 'totality.' Totality is a finite concept, as it implies all  a whole with nothing missing. Infinity implies the impossibility of there being 'all' or a totality of elements.
Re: Does One equal infinity? 7 step argument.
Wyman wrote: ↑Tue Nov 21, 2017 8:36 pm1) is nonsensical. The number 1 may represent the first element in a series. Or the class of all sets containing one element. Now the idea of an 'element' may seem to 'exist as unity'. But your talk of numbers 'maintaining' themselves or doing this or that is also nonsensical.Eodnhoj7 wrote: ↑Thu Oct 19, 2017 5:22 pmPresented Argument:
1) "1" exists as "unity" and "wholeness".
2) As unity and wholeness "1" must maintain a selfreflective symmetry in order to exist. We observe this in common life where a physical or abstract structure maintains its stability through the reflection of points, with these points in turn forming a symmetry between eachother which allows the structure to exist.
3) "1" reflects upon itself to maintain itself. In doing so it reflects "2" (as: 1 ≡ 1 ≅ 2), "3" (as: 1 ≡ 1 ≡ 1 ≅ 3), "4" (as: 1 ≡ 1 ≡ 1 ≡ 1 ≅ 4), etc. unto infinity. In this respect all numbers are strictly structural extensions of 1.
4) As structural extensions of "1" all numbers reflect both "1", themselves "1x", and eachother "1y" unto infinity. In this respect 1 reflects infinity.
5) All number, including "1", continually manifests through selfreflective symmetry unto infinity. Infinity, as "totality", is synonymous with both "unity" and "stability" for there is no deficiency in it. In this respect both 1 and infinity are equal.
6) The selfreflective nature of 1, 1xy, and infinity observes a circular reflective symmetry, and in this respect observes selfreflection as the "maintenance of structure through the maintenance of center(s)".
7) The nature of "1" as infinite through reflective symmetry, observes all number as structural extensions of "1" as mere approximates of "1". In this respect, all approximates observe a form of "deficiency in unity." This deficiency is unity is not a thing in and of itself, as all number is composed of "1" and exists as "1" reflecting upon itself, therefore it is equivalent to 0. 0 is strictly the limit of infinity, as an observation that only infinity exists as 1.
Agree, disagree, don't know? Explain why.
Considering all rational number is both composed of one and "constant" in nature, a mirror effect of perpetual symmtry through 1 as reflecting itself does not contradict anything in current mathematics. There is no foundation explaining what number is other than "blind belief". The foundations for modern mathematics, in regards to what number is, do not work.
Infinity is not 'totality.' Totality is a finite concept, as it implies all  a whole with nothing missing.
Seriously....and infinity does not qualify by that standard?
Infinity implies the impossibility of there being 'all' or a totality of elements.
Infinity is "all" at bare minimum as it is all and beyond all. You will have to explain your "logic" further.
Re: Does One equal infinity? 7 step argument.
"Considering all rational number is both composed of one and "constant" in nature, a mirror effect of perpetual symmtry through 1 as reflecting itself does not contradict anything in current mathematics."
This makes no sense. What does it mean for a number to be composed of something? Or to be 'in nature', constant or otherwise?
You interpret numbers as things in nature that possess nonmathematical properties. This is mysticism.
Is the number 3 'composed' of 1,1,1? Is this property of being 'composed of' what others would call being 'defined as?'
This makes no sense. What does it mean for a number to be composed of something? Or to be 'in nature', constant or otherwise?
You interpret numbers as things in nature that possess nonmathematical properties. This is mysticism.
Is the number 3 'composed' of 1,1,1? Is this property of being 'composed of' what others would call being 'defined as?'
Re: Does One equal infinity? 7 step argument.
Wyman wrote: ↑Tue Nov 21, 2017 8:52 pm"Considering all rational number is both composed of one and "constant" in nature, a mirror effect of perpetual symmtry through 1 as reflecting itself does not contradict anything in current mathematics."
This makes no sense. What does it mean for a number to be composed of something?
All abstract and physical realities at bare minimum are composed of space, in these respects number manifests itself as a spatial entity.
Or to be 'in nature', constant or otherwise?
1 must always equal 1, otherwise it is not constant.
You interpret numbers as things in nature that possess nonmathematical properties.
Considering you understand so much about number, please give a definition. At minimum, through the nature of abstract thought, number is "rooted" in space. If it is rooted in space as "thought" then by default it has spatial properties, the question occurs "what are these properties"?
This is mysticism.
Take it up with Srinivasa Ramanujan. https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
Is the number 3 'composed' of 1,1,1?
1 + 1 + 1 cannot be viewed as a foundation of 3?
Is this property of being 'composed of' what others would call being 'defined as?'
Observing foundational structures is one aspect of definition, is it not?

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Re: Does One equal infinity? 7 step argument.
You defining one as unity and wholeness, and equating it to infinity, does not make it so, mathematically. However, you can use one in programming as true, and create an infinite loop, if the value remains unchanged. But then, any nonzero value can fill in for one as true. So it's not special.Eodnhoj7 wrote: ↑Thu Oct 19, 2017 5:22 pmPresented Argument:
1) "1" exists as "unity" and "wholeness".
2) As unity and wholeness "1" must maintain a selfreflective symmetry in order to exist. We observe this in common life where a physical or abstract structure maintains its stability through the reflection of points, with these points in turn forming a symmetry between eachother which allows the structure to exist.
3) "1" reflects upon itself to maintain itself. In doing so it reflects "2" (as: 1 ≡ 1 ≅ 2), "3" (as: 1 ≡ 1 ≡ 1 ≅ 3), "4" (as: 1 ≡ 1 ≡ 1 ≡ 1 ≅ 4), etc. unto infinity. In this respect all numbers are strictly structural extensions of 1.
4) As structural extensions of "1" all numbers reflect both "1", themselves "1x", and eachother "1y" unto infinity. In this respect 1 reflects infinity.
5) All number, including "1", continually manifests through selfreflective symmetry unto infinity. Infinity, as "totality", is synonymous with both "unity" and "stability" for there is no deficiency in it. In this respect both 1 and infinity are equal.
6) The selfreflective nature of 1, 1xy, and infinity observes a circular reflective symmetry, and in this respect observes selfreflection as the "maintenance of structure through the maintenance of center(s)".
7) The nature of "1" as infinite through reflective symmetry, observes all number as structural extensions of "1" as mere approximates of "1". In this respect, all approximates observe a form of "deficiency in unity." This deficiency is unity is not a thing in and of itself, as all number is composed of "1" and exists as "1" reflecting upon itself, therefore it is equivalent to 0. 0 is strictly the limit of infinity, as an observation that only infinity exists as 1.
Agree, disagree, don't know? Explain why.
Re: Does One equal infinity? 7 step argument.
Dalek Prime wrote: ↑Thu Nov 23, 2017 3:01 amYou defining one as unity and wholeness, and equating it to infinity, does not make it so, mathematically.Eodnhoj7 wrote: ↑Thu Oct 19, 2017 5:22 pmPresented Argument:
1) "1" exists as "unity" and "wholeness".
2) As unity and wholeness "1" must maintain a selfreflective symmetry in order to exist. We observe this in common life where a physical or abstract structure maintains its stability through the reflection of points, with these points in turn forming a symmetry between eachother which allows the structure to exist.
3) "1" reflects upon itself to maintain itself. In doing so it reflects "2" (as: 1 ≡ 1 ≅ 2), "3" (as: 1 ≡ 1 ≡ 1 ≅ 3), "4" (as: 1 ≡ 1 ≡ 1 ≡ 1 ≅ 4), etc. unto infinity. In this respect all numbers are strictly structural extensions of 1.
4) As structural extensions of "1" all numbers reflect both "1", themselves "1x", and eachother "1y" unto infinity. In this respect 1 reflects infinity.
5) All number, including "1", continually manifests through selfreflective symmetry unto infinity. Infinity, as "totality", is synonymous with both "unity" and "stability" for there is no deficiency in it. In this respect both 1 and infinity are equal.
6) The selfreflective nature of 1, 1xy, and infinity observes a circular reflective symmetry, and in this respect observes selfreflection as the "maintenance of structure through the maintenance of center(s)".
7) The nature of "1" as infinite through reflective symmetry, observes all number as structural extensions of "1" as mere approximates of "1". In this respect, all approximates observe a form of "deficiency in unity." This deficiency is unity is not a thing in and of itself, as all number is composed of "1" and exists as "1" reflecting upon itself, therefore it is equivalent to 0. 0 is strictly the limit of infinity, as an observation that only infinity exists as 1.
Agree, disagree, don't know? Explain why.
You are absolutely correct in that statement. The problem occurs in that is not the argument. 1 as unity (with unity being "wholeness", mirroring itself adinfinitum through all rational number (thereby manifesting all rational number) cycles back to itself as infinity as all rational number simultaneously justifies 1 as 1 (rational number exists if and only if they continually mirror eachother through 1).
All rational number is infinite if and only if 1 is infinite. 1 is infinite if and only if it is mirrored adinfinitum. Considering 1 is mirrored adinfinitum it maintains that dual definition of "definitionless definition" that equates it to infinity or "numberless number".
https://www.bing.com/search?q=infinite+ ... F595F0551A
While these rational numbers may simultaneously be infinite in numbers, they do so strictly as structural extensions of 1 mirror itself
1, in these respects manifests itself is an infinite selffeflecting/mirroring point that forms itself as 1.[/
However, you can use one in programming as true, and create an infinite loop, if the value remains unchanged. But then, any nonzero value can fill in for one as true. So it's not special.
Any nonzero value can fill in for one as true strictly because it is a structural extension of 1, in these respects 1 must be justified as both unity and infinity.
1 equaling infinity, through an inherent mirror effect which constitutes it, allows for 1 not only to be observed as a foundation for all number but simultaneously a foundation for all arithmetic functions as seen in the cyclic numbers thread:
viewtopic.php?f=26&t=14835
None of this contradicts any current axioms within mathematics but rather extends our understanding.
Re: Does One equal infinity? 7 step argument.
How are abstract entities composed of space?Eodnhoj7 wrote: ↑Wed Nov 22, 2017 1:02 amWyman wrote: ↑Tue Nov 21, 2017 8:52 pm"Considering all rational number is both composed of one and "constant" in nature, a mirror effect of perpetual symmtry through 1 as reflecting itself does not contradict anything in current mathematics."
This makes no sense. What does it mean for a number to be composed of something?
All abstract and physical realities at bare minimum are composed of space, in these respects number manifests itself as a spatial entity.
Or to be 'in nature', constant or otherwise?
1 must always equal 1, otherwise it is not constant.
You interpret numbers as things in nature that possess nonmathematical properties.
Considering you understand so much about number, please give a definition. At minimum, through the nature of abstract thought, number is "rooted" in space. If it is rooted in space as "thought" then by default it has spatial properties, the question occurs "what are these properties"?
This is mysticism.
Take it up with Srinivasa Ramanujan. https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
Is the number 3 'composed' of 1,1,1?
1 + 1 + 1 cannot be viewed as a foundation of 3?
Is this property of being 'composed of' what others would call being 'defined as?'
Observing foundational structures is one aspect of definition, is it not?
If I had to give a definition of number, it would be a settheoretical definition. Or, it would take the number 1 and 0 and a couple other terms as undefined terms. 2 would be defined as the successor of 1, three as the successor of 2, etc.. The term 'number' itself would then be the set of 0, 1 and all successors of 1.
The symbols are physical. If you believe there is something more here than symbols  abstract entities  then they do not exist in space and time. For instance, can you point to one or see it with ha microscope?
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