[continued from previous message]   
      
   >>>>>>>>>>>> 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   
   >>>>>>>>> with regards to the objects of analysis meeting the objects of   
   >>>>>>>>> geometry,   
   >>>>>>>>> where for example Hilbert says "there must be a postulate   
   >>>>>>>>> of continuity" as with regards to Leibniz' "there _is_ a principle   
   >>>>>>>>> of perfection".   
   >>>>>>>>>   
   >>>>>>>>> Then, Dedekind is considered a sort of mere hanger-on and it's so   
   >>>>>>>>> that models of reals as Dedekind cuts are considered shallow and   
   >>>>>>>>> as after an assignment that presumes what it intends to   
   >>>>>>>>> demonstrate.   
   >>>>>>>>>   
   >>>>>>>>> Two wrongs is two wrongs.   
   >>>>>>>>>   
   >>>>>>>>>   
   >>>>>>>>   
   >>>>>>>>   
   >>>>>>>> But I (and my past audience in that linux newsgroup) am not that   
   >>>>>>>> concerned to go that much down into the nitty gritty of this   
   >>>>>>>> thing. The   
   >>>>>>>> point in my blog there was to test the audience whether they were   
      
   [continued in next message]   
      
   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)