• apokrisis
    No. It's not. That's the point. i is a number but it's not a quantity.fishfry

    Perhaps this is pedantic, but even in terms of rotations in the complex plane i does have a couple of associated quantities with its notion of multiplication. It represents an anti-clockwise rotation of 90 degrees and a magnitude of 1 in terms of the size of complex numbersfdrake

    Fdrake is right. If we want to ask what i quantifies, it quantifies the number of dimensions that a number is constrained by. So i is a widget to rotate a real number into an orthogonal direction that turns the number line into a number plane.

    The number line stands for the most constrained notion of continuity. Complex numbers relaxes that strong constraint and allow numbers to wander in two dimensions. And the numbers still behave like numbers - objects that meet the functional criteria of associative division algebras.

    We can continue to relax the number of dimensions in play. We could consider a three dimensional number. But now it doesn’t behave arithmetically. It is not a suitable object of algebraic structure - a fact of undoubted physical significance when it comes to why space winds up being three dimensional.

    Then with quarternions, we have four dimensions and a bounce back to a large amount of algebraic structure. Five, six and seven dimension again see that structure disappear. Then the octonions provide a last echo.

    So i is a good example of structualism at work. We can define some basic relational properties that numbers are meant to have. The associative division algebras do that. And then we can see how the “hard structure” emerges as constraints are added.

    As we constrain the dimensionality that defines the continuous space in which discrete mathematical objects are meant to move, we can see the role those constraints play in actually defining the mathematical properties those objects are understood to have.

    The limits maketh the objects and not the other way round.
  • tim wood
    I pointed out that it's very difficult to define in general what a number is. You suggested that a number is something that can be quantified or that represents or is a quantity. I gave as a counterexample the number i, which is a number but is not and does not represent a quantity.

    You said a quantity is something that can be quantified. I don't find that helpful because it doesn't tell me what a quantity is. If you tell me a cat is a furry domesticated mammal with retractile claws, that's a lot more helpful than saying that a cat is anything that's cat-like.

    Read the English, fishfry!! What is your native language, please? If you cannot understand what you read, how are the rest of us to credit anything you write?!

    like 2 apples is a quantity.fishfry
    Two apples is not a quantity! Try to wrap your mind around that. As to i being a quantity, you say it isn't. I suspect you're mistaken, but I'll raise the question elsewhere. As to a definition of number, there's no shortage of them. The problem you're having is that you're confused about what definitions are, what they're used for, and how they work. Research it! I will offer this: I think you're making a category error in being confused about what, exactly, is being defined. If your reading truly reflects your thinking, then you have your work cut out for on this. Good luck! .I'd go for it, but you have so clearly exhibited an odd (and annoying) problem with reading that I am stopped from writing further.
  • fdrake

    I do of course agree with you point that 2i is a quantity of two i's, like 2 apples is a quantity. So the question reduces to asking exactly what is a quantity. @tim wood brought up the idea of quantity a while back so I asked him what is a quantity, and so far I have not gotten an answer.

    By saying that the magnitude of i is 1, what I meant wasn't that there was a single i, an answer to how many 'i's are there - but that a vector that starts at the origin in the complex plane and points to i has length 1. This allows for there to be real numbers of 'i' as the 'number of i's in a complex number, so to speak.

    More generally, speaking about complex numbers like z=4+pi*i. Pi isn't exactly an answer to 'how many' i's are there in z since its interpretation is severed from counting numbers in a few ways. The first way it's severed is that z is not a multiple of i in anything like the counting number sense (there are pi-4i i's in z), so we cannot chunk z into i sized bits through division. an 'i sized bit' doesn't even make sense as imaginary numbers don't enter into the notion of size for complex or imaginary numbers.**

    The second way the interpretation of the magnitude of z is severed from the interpretation of a real number or fraction is that z has two senses of magnitude inherent in it. There's the real part and the imaginary part (which individually work exactly the same as real numbers and usual counting in terms of 'how many' questions, to the extent that irrational numbers can be said to be answers to 'how many' questions) or there's the polar form of the radius and angle - requiring two descriptors of magnitude to specify the quantity ('number') rather than the single one for scalars. Polar form and Cartesian form for complex numbers also have differences in interpretation since the polar form contains an unbounded quantity (radius) and a bounded one (the angle), and Cartesian form is done in terms of two unbounded quantities (the magnitudes of real and imaginary parts). They also mean different things (polar form and Cartesian form) even though they are just different ways of talking about the same thing (naming complex numbers).

    There's also the wrinkle which you already mentioned about the tension between irrational numbers (which are implicated in the magnitude of complex numbers in both directional and radial senses) as magnitudes and fractions as answers to 'how many x go into y' questions. Even the Gaussian integers have this problem (such as 1+i having magnitude 2^(1/2)).

    Actually looking at 'numbers', even in relatively simple cases like these, shows that there's no single sense of magnitude or quantity implicated within them - even if there are formally equivalent representations.

    **the closest approximation to this in the complex plane being dividing a complex number z=x+iy by r=sqrt(x^2+y^2) yielding u=z/r, u has magnitude 1, which is the same magnitude as i - all this says is that z lies on the unit circle and u can be obtained again by scaling by r.
  • MindForged
    Kind of a horribly vague question. For one thing, "number" is going to be quite different depending on A) What kind of "number" you're referring to B) What sort of mathematics you're working in (numbers in ZFC + classical logic look quite different than numbers in Paraconsistent Mathematics), etc.

    This topic is simply too vast for me and I personally try not to think about it too much, lol.
  • Dzung
    And now you don't need some purposeful and transcendent creator.apokrisis
    There are too many things going on here but I would like to start with an inquiry on the above statement: specifically is it Peircean or not? I haven't found anywhere Peirce expressed atheism or the like. Or maybe I didn't follow you correctly.
    The next maybe another inquiry about your support of "symmetry" concept, but let's set it aside for a moment.
  • Harry Hindu
    Numbers exist because they can establish causal relationships. Numbers can cause us to do different things.
  • apokrisis
    I would like to start with an inquiry on the above statement: specifically is it Peircean or not? I haven't found anywhere Peirce expressed atheism or the like. Or maybe I didn't follow you correctly.Dzung

    It is notoriously difficult to agree what Peirce actually believed about god or divinity. But he himself stressed he certainly did not follow any kind of orthodox view.

    And my point there was that he definitely did not argue for an external creator with some mission in mind for mankind. Instead, he identified the divine with the vague ground of being - the Firstness of pure unformed potential. And so the Comos is a state of logical regularity that evolved into being in a purely self-creating fashion with no purpose in mind except to be "increasingly reasonable" in its lawfulness and organisation.

    He did say he was more Buddhist on this score. :)
  • Dzung
    he was more Buddhist on this scoreapokrisis
    wow, if you happen to have a public link, kindly share. I found only this content http://www.gnusystems.ca/CSPgod.htm#aq1 ("I think we must regard Creative Activity as an inseparable attribute of God." C.S Peirce.)... there maybe more pieces but let another time to connect them together.

    Just to play fair with the thread, numbers are in mathematics which is in turn sub-semiotics. I am not sure the last has been maturely explored but math is thought by Platonists as another world. Even the "semeiotic" sounds much to do back with Plato's Ideas, now with a better weapon of Synechism.
    If the multiverse-like metaphysics is accepted then we can perceive such a Cosmos that circumscribes it in. Old story while I find your posts more interesting and will switch to enquire about Peircean buddism or non-Peircean symmetry, where possible.

    For symmetry, I am not sure you have come across talks similar to these https://www.closertotruth.com/series/why-do-we-search-symmetry
    I drew a note that fundamentally deep down, symmetry is quite empirical and approximate. It's useful in many talks but we have to recognize its limitations and avoid it at extremes.
    Being aware of no symmetry from Peirce, I think if we still need to linger on it, we may want to analyze Synechism, not only Tychism.
  • apokrisis
    if you happen to have a public link, kindly share.Dzung

    Actually the quote I was thinking of was misleading as it wasn't connected to his evolutionary cosmology but to the more mundane thing of how his Christian contemporaries view his "scandalous affair". Buddhism wouldn't be so judgemental.

    I can't help thinking that the mother of Christianity, Buddhism, is superior to our own religion. (NEM III/2 p. 872)

    So it was more that Eastern metaphysics was in the air in his time as something exotic, but not really studied.

    Here is a more direct reference in terms of his evolutionary cosmology where he talks about its roots...

    ... tychism must give birth to an evolutionary cosmology in which all the regularities of nature and of mind are regarded as products of growth, and to a Schelling-fashioned idealism which holds matter to be mere specialized and partially deadened mind. I may mention, for the benefit of those who are curious in studying mental biographies, that I was born and reared in the neighborhood of Concord - I mean in Cambridge - at the time when Emerson, Hedge, and their friends were disseminating the ideas that they had caught from Schelling, and Schelling from Plotinus, from Boehm, or from God knows what minds stricken with the monstrous mysticism of the East. [6.102]

    Being aware of no symmetry from Peirce, I think if we still need to linger on it, we may want to analyze Synechism, not only Tychism.Dzung

    Yeah, I don't think Peirce said much about symmetry and symmetry-breaking principles. It was implicit rather than explicit at best.

    Peirce had a Victorian level understanding of phase transitions and other physical manifestations of symmetry breaking. Group theory and its fundamentality in physics was a 20th century thing, after all.
  • Janus
    I can identify the types of numbers I already know about: integers, reals, etc. But I can't determine in general what is a number.fishfry

    How can you identify types of numbers if you don't know what a number is?
  • apokrisis
    Checking further, there is this attempt at a pantheistic reading of Peirce....


    Peirce, as a pantheist, thought God and the cosmos constituted one substance. To introduce his views we will trace the philosophic theme that runs through all four stages of his thought: the cosmos is an infinite semiotic goal-directed evolutionary process that converges on the good and the real....

    ...Peirce's evolutionary pragmatic idealism was a radically new form of pantheism. He replaced the theist's idea of a "one-shot" creation of the world by the gradual creation of the world through the evolutionary process of Tychism-Synechism-Agapism. He thought of cosmic evolution as a divine learning process. Chance, continuity, and cosmic purposes are all aspects of God, and we humans are parts of this infinite evolutionary divine system. ...

    ...When asked "Do you believe this Supreme Being to have been the creator of the universe?" he answered "Not so much to have been as to be now creating the universe",...

    ...Peirce's evolutionary pragmatic idealism is an evolutionary form of pantheism that operates in the opposite direction from emanationism and Spinozism. Whereas the latter theologies proceed from the highest level (God) on down through successively lower levels, Peirce's cosmic evolutionism begins at the simplest level of a random chaos of feelings and gradually improves under the guidance of final causality toward an infinite limit of perfection. Thus Peirce's pantheism is emanationism "turned upside down"...
  • Dzung
    it wasn't connected to his evolutionary cosmologyapokrisis
    in deed your above quote is from a letter of him to Williams James. The majority of his quotes are scattered over different kinds of media but I do think all are connected, much like his philosophy about the continuum - Synechism. He also said "I do not agree with you that my papers about the evolution of the Laws of Nature are the best things I have done."[/i] (C.S.Peirce) and "I think unquestionably my best work has been my Logic.". This really helped me to grab a knot from his web.
    The information conveyed in any of his works is massive and cannot be plainly elaborated in a small article or even book. It seems his doctrines such as triadic reduction, synechism, infinitestimal and even his flatly established religion (in the same letter he also mentioned people had scoffed at his religion so he would refrain from expressing it)...have yet to be duly understood.
  • Tim3003
    The question 'Do numbers exist?' needs to be made more precise. I take it that by 'exist' we mean exist in the natural world, outside of man's imagination. So does the number '2' exist outside of my mind(and the minds of other people)? No.

    If I have an orange, and beside it I have another orange. What I have is an orange and an orange. The concept of '2' oranges is one I apply. The '2' does not exist outside my mind in the real world. If you say it does, where is it? Show me it. There is no '2' in the objective world, only matter and energy. It's easier to see that '0' does not exist, but '2' is no different. Thus Maths is invented. It is a spectacularly accurate tool for describing the laws of nature, but it is created by us just as any other language is.
  • Relativist
    "2" is a property of certain states of affairs (such as your state of affairs "orange and orange"). It has no independent existence. We can think abstractly about it the same as we think abstractly of colors.
  • EnPassant
    Kummer said that God created the integers and all else is the work of man. He did not believe that real numbers are real. If we consider, for example, the square root of 2 as an infinite expansion, we can argue that the digits of the expansion are only a 'map' of a (geometric) quantity. What is real is the proportional relationship between the unit and the square roof of 2. In geometry the unit is often taken to be the radius of a circle (or side of a square) and square root 2 is such in proportion to the unit line. When this proportion is translated into a real number the digits map the ratio.

    This poses a number of questions-
    1. Is the algorithm that generates the digits real? If so, are not the digits also real?
    2. Does number precede geometry or vise versa? Some extraordinary infinite series have been discovered that map, with infinite precision, real numbers like Pi, e, etc.

    If infinite series can map Pi exactly does that mean that number precedes geometry (space)? Do numbers exist in God's Mind before space or do numbers arise out of (Euclidean) space?

    It seems to me that number is more primitive than space and as such they precede space.
  • eodnhoj7
    The quantification of all empirical phenomena, where the nature of number is dependent upon empirical sense, necessitates the number existing as directed movement through the object as being a movement in time as 1 directional.

    All numbers are directed movements.
  • macrosoft
    But do numbers exist?Purple Pond

    To me the way to frame this question from the very beginning is how numbers exist, because if they don't exist in some way then what are we talking about in the first place?
  • LD Saunders
    eodnhoj7: How are numbers "directed movements"? Vectors have direction as part of their characteristics, but not scalars. And even a vector is not necessarily linked to any movement, like a velocity vector.
  • eodnhoj7
    If a number exists, due to empirical sense (where I see an orange and apply "1" or "2" as a quantity to it), what I am observing is the phenomena being directed through time in 1 direction where the number existing because of the empirical phenomena (and the empirical phenomena existing because of the number as I may make 1 division in an empirical object resulting in 2 objects) because an observation of time and has a directional quality because of it.

    Numbers are directed movements in the finite sense, where the absolute nature of number occurring through "infinite directed movement" as a constant limit.

    Infinite movement, as perceivable no movement, can be equated to a wheel spinning at the rate of infinity where while it is moving is observed as "still" and "constant"; hence number has a dual state of absolute truth and relative finite truth (with finiteness being multiple infinities).
  • LD Saunders
    eodnhoj7: You never see a number anywhere you look in the universe. If you did, then the existence of numbers would not be a philosophical question. You are describing how one applies numbers to a physical situation, which is irrelevant to the issue of whether numbers actually exist. One can't point to the number five anywhere in the universe, or hold it in one's hand, it's simply not there. Even the symbols we use in math to describe numbers --- the numerals -- are not the actual numbers.
  • eodnhoj7

    I apologize for the long post ahead of time, however in this case it may be a necessary "evil".

    We see "number" in the universe relative to the symbolic context in which we apply it, for the symbol acts as a medial point between the observer and what is being measured.

    The problem occurs in the respect of the symbol itself and not just interpretation, but how it reflects "our" perception of reality and in these respects takes on a subjective context, that while objective in many circumstances, does not necessarily mirror the objective nature of reality we observe it through.

    The question of "perceiving" a number, as an empirical entity (with empiricism being founded in directed movement), is a question of observing not just directed movement but universal symbols that reflect that directed movement.

    Considering the linear nature of time necessitates a 1 dimensional nature, where this 1 dimensional nature effectively observes "1 as directed movement" through the line, it may be logically argued that the 1 dimensional line and "1" are both the same literally and symbolically.

    We can observe this in the quantification of any temporal object is fundamentally an observation of time and numerical with number having a relativistic nature of part through part.

    So if I see 1 orange, I see one direction in time.

    If I see two oranges I see 2 times zones, or two directions in time, where these 2 directions in time still exist as 1 direction considering this is "one" 2 (if you understand what I am saying here).

    So while time may be linear, but the line exists relative to other lines with these multiple lines observing multiple directions which may be off by just a quantum of a degree, time as linear results in time as multdirection effectively leading to a circle or sphere as "all directions" as 1. In these respects 1 takes on a dual role of constant and absolute truth through the "Monad" while observing a relativistic nature of "Monads"(atoms) that again exist through linear directions in themselves.

    The nature of number alternates between a relativistic notion and one of absolute truth, where each finite reality is but an extension (or approximation) of an infinite one.

    So if we quantify all of reality as "one" we are left with instead of a line, a 1d point existing as pure movement. The point exists through a point as a point and in turn can only be observed approximately as a boundless field in one respect while the connection of the points existing through eachother through lines without direction (negative dimensional).

    Then you have the question of frequencies as literal numbers being alternating lines as a 1 dimensional line inverts to another.

    So an angle observes 2 directions as 1 direction in the respect the angle is still directed and exists as a line in itself when viewed from far enough away. The concept of the "degree" which all angles are composed of becomes relativistic as a degree is strictly the number of geometric shapes which fit in a circle.

    The foundation of the "degree" as a relation of geometric forms.

    1) The circle is the universal form through which all forms exist.

    x) The triangle, as three points, exists 120 times within a circle of 360 degrees with each point acting as a degree in itself. Hence as 120 times the angles which form the interior of the triangle (from the center point) form the interior of the triangle as 120 degrees.

    2) The square, as four points, exists 90 times within a circle of 360 degrees with each point acting as a degree in itself. Hence as 90 times the angles which form the interior of the square exist as internal 90 degrees.

    3) The pentagon, as five points, exists 72 times within a circle of 360 degrees with each point acting as a degree in itself. Hence as 72 times the angles which form the interior of the pentagon exist as internal 72 degrees.

    4) The hexagon exists 60 times with an internal degree of 60.

    5) The septagon exists 51.4287 times with an internal degree of the same.

    6) The octagon exists 45 times with an internal degree of the same.

    7) The nonagon exists 40 times with an internal degree of the same.

    8) The Decagon exists 36 times with an internal degree of the same.

    9) The 1 directional line exists 360 times as 1 degree with the 2 directional line existing 180 times as an observation of 180 degrees.

    All degree, through angulature, exists as relation and is subject to the number of relations measured, hence the degree changes with the number of "x" shapes applied to the circle. Measurement itself is relativistic.

    Yet the degree is still a line and is 1 dimensional, so what we understand of the number as a line is strictly 1 as relative units.

    The frequency, in the respect it is composed of multiple alternating lines within a give framework is still projection in one direction as well, with the frequency appearing as a 1 dimensional line from a different framework. The 1 dimensional line can be observed as a quantum frequency necessitating all "1's" are composed of a finite set of numbers in themselves where "relatively speaking" a "1" may not be the same to another "1" as the first 1 may be composed of 1/1, 2/2, 3/3 to infinity and the second one may be equal to (1±x)/(1±x), (2±x)/(2±x), (3±x)/(3±x) to infinity.

    Curvature equates strictly a series of approximate angles, which appear as angles relative to some limit of a different size.

    So while reality observes number in a literal sense, because an localization results in a simultaneous clarity and ambiguity number takes on a possibilistic, potential and random (approximate) sense as well.

    Number exists as

    1) a causal (with cause being structure) and random duality.
    2) actualized locality (part or atom) and potential locality.
    3) limit (directed movement) and possible limit (no-limit as no directed movement).

    This argument may seem a little ambiguous because of the large amount of information in one section, and may be elaborated on.

    In simpler terms, "number" is perpetually moving and hence because it is perpetually moving it is constant, but relatively ambiguous at the same time when we localize any phenomenon. While we may be able to continual quantify number not all number is quantifiable relative to time.
  • Hallucinogen
    Any ontology has to be based on what you know for certain. It's known unquestionably that "this" feels like "that", and inferences and concepts have no influence on that fact. Whatever ontology you have it has to be based on something you cannot question away, which are qualities, or qualia. And when you think about it, they're not static things. Pain repels, pleasure attracts. Redness is red "outwardly". They're fundamentally moving, or becoming. So when we're talking about continuous quantities, they're really just assignments we make onto those moving feelings. It's mostly visual of course, and what is logic and counting? They're both extensions of visual reasoning. They're consequences of our ability to resolve two things in space, to tell one thing apart from another. What does it mean for there to be 5 things without a perception of 5 things? It's just an abstraction. Numbers are assignments consciousness makes when it's perceiving something.
  • eodnhoj7
    directed movement is the only rational ontology I can observe, unless you see something different. I am trying to be proven wrong.
  • LD Saunders
    eodnhoj7: You gave a lengthy response, but you committed the same error you did previously: you are assuming an application of a number proves a number exists, while it most definitely doesn't. The use of any abstraction does not mean the abstraction exists.
  • eodnhoj7
    The application of a number, which in turn forms reality, observes the number shaping reality, hence having a degree of existence in the empirical respect.

    For example the abstraction of 1/2 applied to an empirical object results in the object being divided in half. The reverse is true as well, the object divided at center point, results in 1 object moving to two objects. The 1 objective represents a prior unity in time, a potential one in the respect it contains some degree of formlessness, with the 2 objects stemming from it as actual (directed and moving in time).

    Now stepping back and looking at the time line in itself as a framework, and observing the 1 object moving to two objects, it can be observed three objects exist as 1 time line (1 object, 2 objects each 1/2 of the prior object).

    The nature of time takes on a quantitative role in these regards where the 1 object is a timeline, the 2 objects as 1/2 each of the original, as time lines as well.

    The division in the timeline observes a point of one object inverting to many.

    Time is its own measuring system, and strictly is directed movement...nothing more or less. The application of time creates new time zones, where each object acts as a time zone in itself as itself.

    However, the difference between abstract and empirical phenomenon leads to some problems when both are observed as both directed and moving.
  • DiegoT
    you need to try to define numbers a little more so that people can take a stand. The current notions of what numbers are, derive from accounting, book-keeping, measuring and calculating, so their meaning is reduced to their use in economics, engineering and science. However, bear in mind that ancient philosophers both in the West and the East consider numbers in a more qualitative, comprehensive way. I think Numbers in philosophy are closer to the meaning we give to "Laws of Nature", if we consider, not the manifest laws we know such as gravity or thermodynamics, but the underlying restrictions that give shape all of Reality.
  • LD Saunders
    eodnhoj7: You again keep relying on the same argument, and it gets you no where. You even made the mistake of equating an operation of addition with number itself. The mere application of an abstract concept, like a number, does not in any way demonstrate a number actually exists. Numbers are pure abstractions. The number one can refer to one electron, one planet, one galaxy, or one universe. Does that ability to use an abstract concept like a number make it more or less likely that it exists in reality? It does neither. It simply shows the value of abstract reasoning, and every mathematical object, from numbers to sets to fields are all made-up abstract objects. Whether they are in some sense real, cannot be answered merely by showing that abstract objects have wide applications.
  • DiegoT
    maybe you are all in the right, and numbers are the way we construct our experiences dealing with a real underlying reality.
  • eodnhoj7
    Actually, all arguments are variations of the same argument, they are determined by definition which is a progressively expanding circle. No argument is different in these respects, as all argument stems from one comment set of axioms of function and form which determine it.

    All arguments are variations of the same thing, but differ due to the entropy of language.

    Numbers as pure abstractions cannot exist without an empirical base from which the abstraction arises from, hence the number takes on a directional quality due to the temporal nature of all empirical phenomenon.

    In turn all empirical phenomenon formed by number, take for example one using abstract mathematical concepts to form a building, shows that abstraction exists through physicality.

    Now 1 as a continuous function can be observed in the respect 1 is defined through the function of addition/subtraction/multiplication/division as well considering:

    1 = 3-2,4-3,5-4 to infinity or -2+3, -3+4, -4+5 to infinity
    1= (1/2)/(1/2), (1/3)/(1/3), (1/4)/(1/4) to infinity or 2*1/2, 3*1/3, 4*1/4 to infinity

    and so on and so forth. 1 is equivalent to continuous addition, subtraction, multiplication and division where 1 is equivalent to an operation in itself as the operation is a constant. 1 takes on a role of function as well as form in these respects as well as being composed of an infinite series of numbers through which it exists.

    Here is a response I put on the material as a medial thread but it applies as well here, where 1 is equivalent to a continuous function.

    1 is a function through the line, hence 1 is a equivalent to a process of directed movement where the line and 1 are the same through Pi.

    All fractals are composed of further fractals as evidence by Pi.

    1) Pi is: the symbol π denoting the ratio of the circumference of a circle to its diameter

    b : the ratio itself : a transcendental number having a value rounded to eight decimal places of 3.14159265

    http://www.bing.com/search?q=Pi+definit ... 1B982EA403

    2) Pi is a line between two points that exists from the center point of the circle to the circumference. All lines in turn exists as center points of a circle towards is circumference where all lines exist as the ratio of Pi as 3.14159...

    3) The line as composed of infinite points is composed of infinite lines, hence the line is composed of infinite circles as all lines exist as Pi.

    4) The line is composed as infinite circles projecting, hence the line is equivalent not just to infinite points but infinite quantum circles as well.

    5) Each line, as composed of infinite further lines, is composed of infinite "pi's" where the line as Pi is composed of further Pi's. Hence Pi is divided by an infinite number of Pi being divided by Pi. All functions exists through further functions as 1 function, hence 1 is equivalent to a function that is a continuum. 1 is a continuous function.

    Hence Pi dividing itself observes Pi as its own function of self-division conducive to 1 through the line where 1 is Pi as a function of perpetual self division.

    f(x)= 3.14159→(x→∞)
    ............f(x)= (3.14159→(x→∞) =1
    ................f(x)= (3.14159→(x→∞)


    f(x)= (3.14159→(x→∞))/( f(x)= (3.14159→(x→∞))/(f(x)= (3.14159→(x→∞))/…)) = 1

    X= a continuous series to infinity where the counting of Pi has stop. X= the limit of Pi as a finite rounded number.

    Hence “x = all number with all number equivalent to 1.”
  • eodnhoj7
    That means number is an experience in itself?
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