[continued from previous message]   
      
   >>>>>>>>>> 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   
   >>>>>> actually "programmers" like a programmer really is, or they were mere   
   >>>>>> "code monkeys" hired by real programmers, to receive the menial   
   >>>>>> parts of   
   >>>>>> work, yet coming in the scene here in usenet pretending to be   
   >>>>>> programmers. This was the whole point of that blog.   
   >>>>>>   
   >>>>>> And only one among them, Farley Flud, proved to be a real   
   >>>>>> programmer. I   
   >>>>>> understood that by watching how he _tackles_ these baby problems.   
   >>>>>> Nobody   
   >>>>>> else there, including many "engineers" and "computer scientists"   
   >>>>>> there   
   >>>>>> were actually programmers.   
   >>>>>>   
   >>>>>> That's the level at which my baby problem was posed. I have not   
   >>>>>> delved   
   >>>>>> (or dived) into deeper areas as you do, and can not understand what   
   >>>>>> you're saying without spending a whole day with my books to review   
   >>>>>> stuff   
   >>>>>> so I could take a good look at it at least. And I won't. Solution to   
   >>>>>> that baby problem doesn't require that level of scrutiny.   
   >>>>>>   
   >>>>>> Would you like to see the solution?   
   >>>>>   
   >>>>>   
   >>>>> You mean what's its model of atomicity?   
   >>>>>   
   >>>>> Yeah, go ahead and uniquify that.   
   >>>>>   
   >>>>>   
   >>>>   
   >>>>   
   >>>> Hahhahhahhahh :-) I like that :) But remember, you should not mistake   
   >>>> Physfit's dick with Physfit! .. Physfit himself never posts to usenet.   
   >>>>   
   >>>>   
   >>>> X = 0.9999...   
   >>>> 10X = (9 +1)0.9999...   
   >>>> 10X = 9(0.9999...) + 0.9999...   
   >>>> after subtraction of first equation from the last one:   
      
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