[continued from previous message]   
      
   >>>>>>>   
   >>>>>>> Here I quote the part of the blog that contained that problem:   
   >>>>>>>   
   >>>>>>> (beginning of the quote)   
   >>>>>>>   
   >>>>>>>   
   >>>>>>>    "Then, swoooooooshhshsh!.... and Jesus and all that intense light   
   >>>>>>> went   
   >>>>>>> back up and out of there. Physfit looked up and there wasn't even an   
   >>>>>>> opening in the ceiling anymore. But now for some reason he was   
   >>>>>>> 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   
      
   [continued in next message]   
      
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