[continued from previous message]   
      
   >> refrigerator. There was nothing there but the cat food he had cooked on   
   >> 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.   
   >   
   >   
   >   
   >   
      
   https://www.youtube.com/watch?v=HsGOZp7jrEY&list=PLb7rLSBiE7F4_E   
   POURNmVLwp-dyzjYr-&index=4   
      
   "Non-standard analysis: continuum infinitesimal analysis, and sweep"   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)