[continued from previous message]   
      
   >>>> horizontally on the floor, in his bed. Right in the living room!   
   >>>>   
   >>>> He thought a bit about what was happening, when he found himself quite   
   >>>> hungry. Last time he had eaten anything was the night before he had   
   >>>> waken up on the summit of the magic mountain in an urban Dallas area.   
   >>>>   
   >>>> He thought to himself, "I'm going to assume that more than 48 hours has   
   >>>> passed since. So got up and walked to the kitchen and took a look   
   >>>> inside   
   >>>> 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,   
      
   [continued in next message]   
      
   --- SoupGate-DOS v1.05   
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