[continued from previous message]   
      
   >>>>> 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   
      
   [continued in next message]   
      
   --- SoupGate-DOS v1.05   
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