[continued from previous message]   
      
   > 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.   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)