1 is 0.9999999999999............

Discussion in 'Alternative Theories' started by chinglu, Oct 27, 2013.

  1. Quantum Quack Life's a tease... Valued Senior Member

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    I tend to think it is better to consider the infinitesimal as a boundary condition and not a value , the end of reality before it hits zero or nothingness is of itself of no actual dimension or value. A mere imaginary line between zero and the material universe.
    So when they say 1/infinity = 0 they are not really wrong in doing so, but then again neither is saying 1/infinity =/= 0 when the answer is the boundary or vanishing point between nothing and something.
    Butting up against zero is a little different to being zero if you know what I mean.
     
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  3. Undefined Banned Banned

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    You haven't been reading the 'word salad' on offer, then? Obviously. If you had, you would have realized that
    MY point was that SOME (any) NUMBER was needed to make the string 'shift' across the decimal point, and not the decimal point doing the shifting. That was the point from ME to Pete originally.

    Any so-called REQUIREMENT for a particular number '0' is not my point at all in YOUR discussion with MD, Dinosaur etc.

    Get it? From my point of view it is that the NUMBER changes in the string are the more fundamental action/operation etc, and NOT merely 'shifting the decimal point' right or left, which is mere formatting after the event. That was what I was addressing, for that aspect/side-discussion with Pete etc. about "moving the decimal point" as if it was some sort of numerical action/operation (which it isn't, which is the thrust of all I have had to say about that aspect).

    There are TWO separate issues with '0'. One is what to do about it when faced with an infinite string. The other is that when multiplying with ten in particular, it is the effect of placing a zero in the string that is the more fundamental action (and NOT the mere 'moving the decimnal point, which is a NON-number non-action abstraction).

    That is all I have had to say on those TWO aspects.

    Please keep your specific "REQUIRED 0" issue contained to your whomever introduced such a 'requirement'. Thanks.

    Cheers.

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  5. Undefined Banned Banned

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    It was an example of some possible CATEGORY for the further characterizing of the infinitesimal, that's all. Anything else is your own imaginary strawman 'correction'.

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  7. Undefined Banned Banned

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    Hi QQ.

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    Yes, and that boundary condition is a real state/value of 'effectiveness' which separates the one 'domain' from the next.

    However, it logically and physically must have some NON-nothing value (albeit an 'unimaginably' infinitesimal one) in reality, since there is no such thing as NON-something in real energy-space phenomenological dynamics.

    In other words, there is NO 'hole' where a NOTHING-zero can 'hide'. Everything in energy-space ha a definite existence, to all scales/regions. Even in uncertainty/superposition states, there is SOMETHING THERE which is uncertain/superposed, isn't there?

    So, thinking that 'NOTHING ZERO' can 'exist' within some 'boundary condition' is a non-sequitur when looked at in the cold hard light of reality.

    To use your example, only an infinitesimal-zero-SOMETHING exists where a sphere is reduced to its central point.

    Hence that central point is NOT 'dimensionless' or without some extent. Its extent must be infinitesimally-zero SOMETHING, else there lay NON-EXISTENCE absolutely. Yes?

    That is, something-from-nothing-absolutely is not a real or acceptable 'take' in any context, is it? Or is it?

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    Hence the drive to re-define 'points' as having a 'something-zero' infinitesimal extent. That would make every point/number, including '0', an infinitesimal by nature of reality first and foremost. Thus replacing the currently primitive notion of a 'dimensionless point' which the current axioms are based on (and which currently lead to all the absurd undetermined/undefined etc incomplete/inconsistent 'outputs').
     
  8. Monimonika Registered Member

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    Stop replying to me if you're not going to address what my posts are actually talking about (which are definitely NOT about "shifting the decimal point right or left" as you keep obsessively bringing up for no reason in your replies to me). Why should I read your word salad when, as you've repeatedly clearly stated, that word salad has NOTHING WHATSOEVER TO DO WITH what I am posting about? Screw your insincere smiley face at the end.

    Oh, and you're on my ignore list now. Toodles :wave:
     
  9. Undefined Banned Banned

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    Sure, no problem, Monimonika. (sincere

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    )

    I only said anything at all to you because in your response to MD/Dinosaur you made much of "where is the zero?" etc in your examples.

    I politely provided the long-division exercise example to show "where the zero was" that's all; mainly for your benefit and the benefit of your ongoing discussion on that aspect with MD/Dinosaur (which discussion I hoped was going to go more politely and less 'angrily' in future). Good luck and see ya round, Monimonika.

    I will accede to your request of me to make no further reply to you in future (unless the situation seriously warrants it). No hard feelings this end (sincere

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    ). Cheers.
     
  10. Trippy ALEA IACTA EST Staff Member

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    I understand now why zero was so difficult for humanity to grasp and why it took so long to understand such a basic principle.

    What does non-action 'place-holder' even mean? It's a nonsense phrase. Numbers don't represent action, they represent quantity.

    The zeroes are always there, that's the point.

    No, it's an explanation as to why multplying a number by ten in a decimal counting system has the effects it does.

    See, this proves you haven't understood my argument. The 'introduced 0' is not an effective cause of anything. It's a consequence of the fact that 1 is really 1.00(0) which is really \(1\times 10^0 + 0\times 10^{-1} + 0\times 10^{-2} + 0\times 10^{-3} + ...\) and when we multiply by ten, we raise those powers by 1 to give: \(1\times 10^{(0+1)} + 0\times 10^{(-1+1)} + 0\times 10^{(-2+1)} + 0\times 10^{(-3+1)} + ...\) which is 10.00(0) which we agree to write as 10.

    The 'active part of the process' (I can at least imagine what you might mean by that) is the raising of the powers of ten by 1.

    This is (part of) where your thinking is flawed. Zero is a quantity, not a placeholder. But it's okay to struggle with that concept, it took humanity a long time to figure it out.

    Nothing is frozen, and I'm not even sure what you mean by infinity state.
    0.999(9) is just another way of writing \(0\times 10^{0} + 9\times 10^{-1} + 9\times 10^{-2} + 1\times 10^{-3} + ...\) when we multiply it by ten it becomes \(0 \times 10^{(0+1)} + 9 \times 10^{(-1+1)} + 9\times 10^{(-2+1)} + 1\times 10^{(-3+1)} + ...\) which we agree to write as 9.999(9).

    See, this is the thing I have repeatedly pointed out to you, and you have repeatedly failed to understand. Your hypothesis gives nonsense answers, and leads you to nonsense conclusion and talking of numbers being frozen in an infinity state. My hypothesis leads you to a liberating fundamental understanding.

    My hypothesis provides a correct answer to the problem \(\frac{1}{7} \times 10[/frac] it allows us to evaluate it as 1.(428751) which is the same answer we get when we compute [tex]\frac{10}{7}\). Your hypothesis requires us to treat \(\frac{1}{7}\) as being somehow fundamentally different from \(\frac{1}{8}\) and unable to have operations performed on it because it is 'frozen in an infinity state'. Your hypothesis would have us treat \(\frac{13}{7}\) as being somehow fundamentally different from \(\frac{14}{7}\).

    Your hypothesis is absurd in the extreme and totally useless.

    This leads me to wonder if you have actually read, or perhaps more importantly, understood anything I have actually said, or if you're just reacting to what you think I have said.

    Thankyou though for educating me on why zero was such a difficult concept for humanity to grasp.
     
  11. Tach Banned Banned

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    The zero action of the Lagrange coordinate-independent Hamiltonian of the dimensionless pseudo-sphere in the equi-particle cloud produces covariant derivatives that imply null geodesics over the Levi-Civitta manifold thus proving the undetermined/undefined etc incomplete/inconsistent set of axiomatic derivations. There, mate, have at it .

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  12. someguy1 Registered Senior Member

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    Ah you're a physicist. That explains why you don't know any math!!

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  13. Tach Banned Banned

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    Yes, an experimentalist physicist , more correct.

    Says you, who can't solve the 8-th grade geometry exercise of trisecting the circle. Seriously speaking, do you have a sense of humor? You understand that was a tongue-in-cheek paraphrase, no?
     
  14. Undefined Banned Banned

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    Lol.

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    In your joke allusions you have unwittingly alluded to a '0' state of real balanced state of all possible forces effecting a null line along which there is no net displacement normal to that line. Thanks for your unwitting example of '0' as a balance state of two or more real things acting in opposing directions to equalize/balance to '0' as the least possible 'infinitesimal effectiveness' AT the boundary (the null line) between those possible displacement forces 'domains'.....thus making that null geodesic line the 'boundary line' of all points along it that comprise '0' infinitesimal non-nothing points in real energy-space context/terms.

    So, now, even in your joke responses, you have made the case for me!....about re-working the axioms to re-define:

    - 'points' as NOT non-dimensional, and hence have an energy-space "infinitesimal of effectiveness" physical extent in THREE dimensioned energy-space;

    - 'lines' as NOT just UNI-dimensional (length only), but rather as having ALSO three-dimensional extent in energy-space (one point THICKNESS "infinitesimal of effectiveness" extent 'normal' to that line in three-d energy-space, as well as the applicable contiguous linear assembly of "infinitesimal of effectiveness extent" points which form the "length extent" of the line of non-nothing points constructing the non-nothing THICK line).

    Thanks, Tach. You have been (unwittingly) useful to the discussion/point for once! Kudos! (sincere

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  15. Undefined Banned Banned

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    Hi Trippy.

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    You sure put a lot of assumptions in my mouth when making your strawmen which you then go on to build your counter-arguments/assumptions on.

    The point was that it is the numbers/entities and the operations that affect the strings; be the strings finite of infinite. IE, that it is the numbers involved that make the string 'shift' across the decimal point, and NOT 'shifting the decimal point' which changes a 'frozen string'. That was the essential point I tried to make to Pete when he and others used the "shift the decimal point" as part of their 'explanation/proof' arguments. Ok?

    AS to the rest, sure, the current treatment under the current axioms give the 'results' you get above. BUT, it is the INCOMPLETENESS of those same axioms when we hit the 'domain of applicability/sense' WALL that the issues I and certain others are canvassing/exploring further....ie, from the stage where "undefined" and "undetermined" are the 'results'....and where 'infinity' is invoked (Limits treatment) in order to even get some sense out of the repeating fraction cases in general, in reality, and irrespective of the math/number system used.


    And further on that 'invoking infinity' in the Limits treatments:

    Did you read where I pointed out that the Limits formulation/concept approach essentially invokes the INFINITESIMAL 'last step of effectiveness' concept/point/value/number or whatever is involved in that particular 'infinity' used?

    Do you understand where the last step of any infinity as used in the Limits formulae is effectively INVOKING an FINAL INFINITESIMAL of that infinity as a REAL CONCEPT which allows us to REASONABLY conclude the LIMIT IS REACHABLE (and hence something like 0.999...=1 IS ok to conclude from such reasonable invocation of the infinity/infinitesimal as per the LIMITS formulae?

    That makes even more sense when you consider that 'infinitesimal of effectiveness' is NOT '0'-nothing, but '0'-SOMETHING which is the last effective (non-nothing 3-d energy-space extent....ie, 'points' are NOT really "non-dimensional, as per previous posts/explanations) REAL step between one boundary condition/domain and another adjacent....and hence repeating decimals like the ones whose 'limit' is reached ARE REAL POSSIBLE STATES where the last effectiveness step IS a-non-nothing '0'.

    Further consideration that in PHYSICAL energy-space terms reality there is NO such thing as NON-existence; only balanced states, or transitioning states between SOMETHING and SOMETHING ELSE etc.


    That is where my perspective is coming from. No more than that. All the usual tit-for-tats based on the old stock-standard arguments and cross-purpose exchanges don't really interest me enough to want to pursue down the old 'two sides that never communicate' emotionally charged and status quo 'frozen' attitudes to any new perspectives which are not being read closely enough to distinguish the novel/reasonable new points/subtleties from the usual old dead-end 'pre-conceived' stances/notions which do nothing to elucidate those new points/subtleties I am interested in.

    I have said all that I can/should say at this juncture, so I will read-only for a while; as I have much work to do off-line that will demand most of my time for the next few weeks. Naturally I shall be very interested to see where others take this and the other discussion/thread.

    Good luck, Trippy, everyone. Thanks for your contributions to the discussion to date, Trippy, everyone. Believe it or not, they have helped to focus where the final step/problem lay and what sort of new 'treatment' based on new 'axioms' may be necessary to advance us from the "undetermined" and "undefined" status quo situation with current maths/physics 'definitions' and 'notions' etc.
     
  16. arfa brane call me arf Valued Senior Member

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    Numbers don't "do" anything except in some abstract sense "act" on symbols to give them a value. But the real actors or actions are the operations, like addition, multiplication.
    There is absolutely (don't you just love that word?) no problem at all with defining multiplication by powers of 10 as acting on the decimal point. Just as there is no problem with representing a value like 1 as 0.999... or 0.9(9) = 0.(9)*. The two representations with an "=" between them have a decimal point, and the leading zero is just a redundant symbol that signifies the first digit to the left of the decimal point.

    So you can shift this point to the left or right, but only relative to the left digits or the point itself (which would mean that multiplying and dividing by powers of 10 is affine--you can have this point anywhere and still shift it left or right). It makes zero sense to refer to the "end" of the string, a nonexistent mathematical object. Furthermore, such a map from powers of 10 is a function that maps integers, the powers, to integers in the decimal system of numbers, as left/right "shifts" of the decimal point.

    yada yada.
     
  17. Undefined Banned Banned

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    1,695
    You say that (and I agree it is the operation involving the numbers etc)......but then you and others make statements such as : "Move the decimal point", as if that has any meaningful fundamentality attached to it at all! I think you got the original point now, arfa. I said that 'shifting the string' because of number operations is more fundamental action/concept and more meaningful description of what happens, than "shift the decimal point" is. That was my point. Glad you agree, mate.

    As to the existence of some infinitesimal entity/state/value etc, I ask you to read my posts where I point out that using the infinity concept in the Limits formulae/treatment is essentially invoking that 'last step' infinitesimal OF that infinity concept. Hence the 'last infinitesimal of effectiveness' step across domains/states IS already in the mathematics, only 'hidden subtly' and not recognized for what it is.

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    As to the actual 'real' value etc of the infinitesimal, I already pointed out that in reality energy-space terms there in NO such thing as 'non-existence. Hence the last effectiveness step/quantity/entity in phenomenological reality dynamics IS there as the POINT which has 'infinitesimal' dimensional extent in three-d). Hence there can be no such thing as a NULL '0' entity in energy-space context reality, as something is always there, whether changing across domains of states. Hence no such thing as a NULL '0' state exists excpt as a balanced state of SOME THINGS opposing to form transient/persistent equilibrium, but NOT 'nothing there'.

    Hence my drive for '0' (ie, the 'point' ) in reality/axioms should be treated as NOT 'non-dimensional' but as having infinitesimal 3-d extent (as I already explained why). Then perhaps we can deal properly and consistently with all the current "undefined" and "undetermined" cases without 'blowing an axiomatic fuse', as it were. Anyhow, I leave you and others to progress the discourse for now. I have run out of time for now. Will read-only for a while. Cheers and thanks for your participation and interesting contributions to the discourse so far, arfa brane, everyone.

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  18. arfa brane call me arf Valued Senior Member

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    But I don't agree with one being more fundamental than the other. If you want to look at the function "x 10[sup]n[/sup]" as acting on the string of digits, then as I said you can only consider the left hand ones, or equivalently those to the left or right of the decimal point (up to n for 10[sup]n[/sup]).

    Either view of the "action" is acceptable, so there is nothing wrong (my point) with saying the decimal shifts to the left or right, anywhere in the string. But what happens to the string is that the number of digits to the left of this point decreases or increases, and it makes no sense to talk about a "suffix action", or what happens to the rightmost digits.

    So a repeating decimal is like a list, which is a data structure that has two parts, a head and a tail (resp. prefix and suffix). Multiplication by powers of 10 acts on the head by adding/subtracting digits to it "from" the infinite tail, i.e. the size of the head of the list or the length of the prefix changes, but the tail does not change, it's an infinite source of digits so adding/subtracting makes no sense.
     
  19. Undefined Banned Banned

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    Great! Thanks for 'getting' it, arfa. It does not matter where along the 'string' its constituents 'occur', it is the function of the operation on numbers that determines what new locations are given to such numbers so as to generate/change a new string which transitions across that decimal point construct/notation. In no way has just 'moving a decimal point' notation actually performed any 'function' on the numbers except as a FORMATTING short-cut once the actual number string is determined BY the function/operation ON that string.

    Ie, it is not the decimal point that 'shifts', it is the string constituents that move across from decimal place/location to decimal place/location as the function determines FIRST, and then the decimal point notation merely confirms in conveying the results OF that operation involving numbers not decimal notation as the 'function' elements/entities.

    PS: If it hadn't been for Tach and his trolling, I would not have been here to respond, mate. So you can thank him for that.

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  20. arfa brane call me arf Valued Senior Member

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    It is the decimal point that shifts, or it's the digits that do. Once again, I said it doesn't matter which point of view you use.
    The point that makes more sense, at least to me, is that the number of digits to the right of the decimal point doesn't change, it remains infinite. So as I said, the action "times 10[sup]n[/sup]", can be said to shift the decimal by n, or increase/decrease the number of digits, but only in the prefix.

    I'm genuinely surprised that you seem to want to see what I've posted as agreeement with your choice of one view rather than the other, and that this is somehow an important choice to make.
     
  21. Trippy ALEA IACTA EST Staff Member

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    Undefined: Maybe you need to spend more time reading peoples posts instead of reacting to what you think they're saying, for example, you wasted bandwidth bemoaning my use of shifting decimal points and complaining about Strawman hypotheses, and yet the only time I mentioned shifting decimal places in my last post was to illustrate that, like the addition of zero at the end of a nom repeating decimal it was a consequence of the fact that multiplying by 10 in a base 10 system has the effect of performing operations on the n in 10[sup]n[/sup].
     
  22. Undefined Banned Banned

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    Oh, I see where you're coming from on that. Sure, for convenience it isn't important what you do to convey the results by formatting it any way you want. Sure. No argument about that aspect.

    However, when such convenience formatting-after-the-event (of the results of actual operations/functions involving the numbers/values/entity 'strings/constituents) aspect is then attempted to be used by some to purportedly construct a 'proofs' argument/basis, then it becomes important to distinguish which is the fundamental aspect and which is the trivial and non-relevant aspect when the string and actions upon same are being discussed in this context.

    That distinguishing focus, between the fundamental and non-fundamental aspects, was important to get straight; especially before any further 'proofs' and 'explanations' were attempted (in this discussion context) using such non-fundamental convenience/formatting aspect of 'shifting the decimal point' non-action which 'hides' the fundamental aspect of 'shifting string' transitioning along/across that decimal notation formatting system of results/strings values etc.

    In short, I agree that for convenience aspect, no problem using the non-fundamental non-action of 'shift the decimal point' to convey the result.

    It's only when discussing how the result comes about, and what entities/actions are the more fundamental 'functional aspects', then the distinction to be drawn between 'shifting decimal point' and 'shifting string' really does matter substantively if the discussion is not to confuse vague convenience aspects with specific fundamentality in reality.

    Thanks again for your patient engagement, arfa. Very useful to the discourse! Cheers.

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  23. Undefined Banned Banned

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    Yes. Thanks. I was only clarifying where I was coming from. Any cross-purpose misunderstandings are just that. I am fast running out of time for internet discussion/posting. I will soon have time to read-only (if I ever get out of here today!

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    ) Thanks again for your patient engagement, Trippy. Good luck in your future discourse. I will read with interest anything else you have to contribute to sciforums discussions here and elsewhere. Apologies for any misunderstandings on my part!

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