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