[continued from previous message]   
      
   >>> the day he first saw the magic mountain. He got on the computer to order   
   >>> something zesty from HelloFresh. After choosing the closest to a healthy   
   >>> nice pre-agricultural food kit, he clicked, "Go to checkout" button,   
   >>> after which the computer waited for a few seconds but instead of getting   
   >>> to the check out screen, a screen came up to make sure Physfit was not a   
   >>> robot. It had a simple question that he had to give it the correct   
   >>> answer, otherwise food nommo.   
   >>>   
   >>> The question went like this:   
   >>>   
   >>>      "In math, is there a difference between the two numbers   
   0.999999...   
   >>> and 1 ?"   
   >>>   
   >>> The digits of "9" continued forever to the right of the radix point. So   
   >>> of course, Physfit clicked on the "yes" button. If there was not a   
   >>> difference, then one wouldn't even bother to write 1 in that funky form,   
   >>> using an infinite series of digit 9.   
   >>>   
   >>> But the screen disappeared, and a message said, "You're a robot. Bye!"   
   >>>   
   >>> Physfit said, "Fuck!" (first of the fix number of curses Jesus had   
   >>> allowed him for that day). So he took a pen and paper and started   
   >>> jotting down:   
   >>>   
   >>>      x = 0.99999....   
   >>>   
   >>> Therefore:   
   >>>   
   >>>      10x = 9.99999....   
   >>>   
   >>> Now he subtracted the former from the latter:   
   >>>   
   >>>      10x - x = 9.99999... - 0.99999...   
   >>>   
   >>> Which simplifies to:   
   >>>   
   >>>      9x = 9   
   >>>   
   >>> And therefore:   
   >>>   
   >>>      x = 1   
   >>>   
   >>> "What the fuck??", said Physfit (his 2nd curse of the day).   
   >>>   
   >>> Why x which was 0.99999... and not 1, turned out to be 1? ... "   
   >>>   
   >>>   
   >>> (end of quote)   
   >>>   
   >>>   
   >>> So, is this problem pointing to what Kosmanson has been so keen   
   >>> about? :)   
   >>>   
   >>>   
   >>>   
   >>>   
   >>>   
   >>   
   >> Once I was reading a book or article,   
   >> and was introduced the introduction of .999 (...),   
   >> vis-a-vis, 1. A cohort of subjects was surveyed   
   >> their opinion and belief whether .999, dot dot dot,   
   >> was equal to, or less than, one. About half said   
   >> same and about half said different.   
   >>   
   >>   
   >> It's two different natural notations that happen   
   >> to collide and thus result being ambiguous.   
   >>   
   >> So, then these days we have the laws of arithmetic   
   >> introduced in primary school, usually kindergarten,   
   >> about the operations on numbers, and also inequalities,   
   >> and the order in numbers.   
   >>   
   >> Yet, even the usual account of addition and its   
   >> inverse and its recursion and that's inverse,   
   >> as operators, of whole numbers, has a different   
   >> account, of increment on the one side, and, division   
   >> on the other, sort of like the Egyptians only had   
   >> division or fractions and Egyptian fractions,   
   >> and tally marks are only increment, that though   
   >> it was the Egyptian fractions that gave them a   
   >> mathematics, beyond the simplest sort of conflation   
   >> of "numbering" and "counting".   
   >>   
   >> So, where ".999 vis-a-vis 1" has a deconstructive account,   
   >> to eliminate its ambiguities with respect to what it's   
   >> to model, or the clock-arithmetic and field-arithmetic,   
   >> even arithmetic has a deconstructive account, then,   
   >> even numbering versus counting has a deconstructive account,   
   >> to help eliminate what are the usually ignored ambiguities.   
   >>   
   >>   
   >> So, pre-calculus, the course, goes to eliminate or talk   
   >> away the case .999, dot dot dot, different 1. Yet,   
   >> it can be reconstrued and reconstructed, on its own   
   >> constructive account. So, it's a convention.   
   >>   
   >>   
   >> It's "multiplicity theory", see, that any, "singularity   
   >> theory", which results as of admitting only the principal   
   >> branch of otherwise a "bifurcation" or "opening" or "catastrophe"   
   >> or "perestroika (opening)", as they are called in mathematics,   
   >> branches, that singularity theory is a multiplicity theory,   
   >> yet the usual account has that it's just nothing,   
   >> or that it's apeiron and asymptotic.   
   >>   
   >>   
   >> So, there's a clock arithmetic where there's a reason why   
   >> that there's a .999, dot dot dot, _before_ 1.0, in the   
   >> course of passage of values from 0, to 1, and, it's also   
   >> rather particularly only between 0 and 1, as what results   
   >> thusly a whole, with regards to relating it to the modularity   
   >> of integers, the integral moduli.   
   >>   
   >> Thusly, real infinity has itself correctly and constructively   
   >> back in numbers for "standard infinitesimals" here called   
   >> "iota-values".   
   >>   
   >> Then, this is totally simple and looks like f(n) = n/d,   
   >> for n goes from zero to d and d goes to infinity, this   
   >> is a limit of functions for this function which is not-   
   >> a- real- function yet is a nonstandard function and that   
   >> has real analytical character, it's a discrete function   
   >> that's integrable and whose integral equals 1, it illustrates   
   >> a doubling-space according to measure theory in the measure problem,   
   >> it's its own anti-derivative so all the tricks about the exponential   
   >> function in functional analysis have their usual methods about it,   
   >> it's also a pdf and CDF of the natural integers at uniform random,   
   >> of which there are others, because there are at least three laws   
   >> of large numbers, at least three Cantor spaces, at least three   
   >> models of continuous domains, and, at least three probability   
   >> distributions of the naturals at uniform random.   
   >>   
   >> So, "iota-values" are not the same thing as the raw differential,   
   >> which differential analysts will be very familiar with as usually   
   >> not- the- raw- differential yet only as under the integral bar   
   >> in the formalism, yet representing about the solidus or divisor bar   
   >> the relation of two quantities algebraically, then indeed there's   
   >> that "iota-values" are as of some "standard infinitesimals", yet   
   >> only under the limit of function the "natural/unit equivalency function"   
   >> the N/U EF, about [0,1]. This thus results a model of   
   >> a continuous domain "line reals" to go along with the usual standard   
   >> linear curriculum's "field reals" then furthermore later there's   
   >> a "signal reals" of at least these three models of continuous domains.   
   >>   
   >>   
   >> The usual demonstration after introducing the repeating terminus   
   >> and using algebra to demonstrate a fact about arithmetic,   
   >> is good for itself, and is one of the primary simplifications   
   >> of the linear curriculum, yet as a notation, it's natural that   
   >> two different systems of notation can see it variously, then   
   >> that it merely demands a sort of book-keeping, to disambiguate it.   
   >>   
   >> If you ever wonder why mathematics didn't have one of these,   
   >> or, two of these as it were together, it does, and it's only   
   >> a particular field of mathematics sort of absent the super-classical   
   >> and infinitary reasoning, that doesn't.   
   >>   
   >> Then at least we got particle/wave duality as super-classical,   
   >> then Zeno's classical expositions of the super-classical were   
   >> just given as that the infinite limit as introduced in pre-calculus   
   >> said we could ignore the deductive result that it really must complete,   
   >> the geometric series.   
   >   
   > Then again, one can define the reals as the convergences of uncountably   
   > infinitely many infinite series. There is no differece between 0.999...   
   > and 1, they are simply two different representations of the same   
   > mathematical object.   
      
      
   Bullshit. The point in question is exactly whether what you say is   
   bullshit :)   
      
   The answer to the baby problem shows, quite simply, that X is indeed   
   0.9999... and _certainly_ not 1.   
      
   Physics, only in its most useful form for humans, can speak for   
      
   [continued in next message]   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)