[continued from previous message]   
      
   >>>>>>>>>>>>> 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.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Then again, one can define the reals as the convergences of   
   >>>>>>>>>>>> uncountably infinitely many infinite series. There is no   
   >>>>>>>>>>>> differece   
   >>>>>>>>>>>> between 0.999... and 1, they are simply two different   
   >>>>>>>>>>>> representations   
   >>>>>>>>>>>> of the same mathematical object.   
   >>>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> Bullshit. The point in question is exactly whether what you   
   >>>>>>>>>>> say is   
   >>>>>>>>>>> bullshit :)   
   >>>>>>>>>>>   
   >>>>>>>>>>> The answer to the baby problem shows, quite simply, that X is   
   >>>>>>>>>>> indeed   
   >>>>>>>>>>> 0.9999... and _certainly_ not 1.   
   >>>>>>>>>>>   
   >>>>>>>>>>> Physics, only in its most useful form for humans, can speak for   
   >>>>>>>>>>> mathematics (that's where 1 + 1 equals 2 comes from - from   
   >>>>>>>>>>> direct   
   >>>>>>>>>>> observation by humans); and mathematics in general does not   
   >>>>>>>>>>> speak for   
   >>>>>>>>>>> physics at any level, for human or for future superhumans and AI   
   >>>>>>>>>>> all. It   
   >>>>>>>>>>> is only rarely used when techniques developed in math would help   
   >>>>>>>>>>> physics   
   >>>>>>>>>>> in its use for humans to eventually solve problems, again for   
   >>>>>>>>>>> humans.   
   >>>>>>>>>>>   
   >>>>>>>>>>> If you need help seeing the above baby problem's answer, then   
   >>>>>>>>>>> beg for   
   >>>>>>>>>>> it :)   
   >>>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> No, don't be making problems when there's a mis-understanding.   
   >>>>>>>>>>   
   >>>>>>>>>> It is so that the modern model of real numbers is as of   
   >>>>>>>>>> "equivalence classes of sequences with the property of being   
   >>>>>>>>>> Cauchy",   
   >>>>>>>>>> then as with regards to whether both least-upper-bound   
   >>>>>>>>>> property and   
   >>>>>>>>>> measure 1.0 are stipulated rather than derived, has that here   
   >>>>>>>>>> it's   
   >>>>>>>>>> acknolwedged that LUB is stipulated and measure 1.0 is stipulated   
      
   [continued in next message]   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)