[continued from previous message]   
      
   >>>>>>>>> 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:   
   >>> 10X - X = 9(0.9999...) + 0.9999... - 0.9999...   
   >>> 9X = 9(0.9999...)   
   >>> X = 0.9999...   
   >>>   
   >>> Therefore the so called "programmer" of HelloFresh company creating that   
   >>> test to check whether a robot was ordering or a human, was just a "code   
   >>> monkey" mistakenly hired as a real programmer.   
   >>>   
   >>> But back to what Kosmanson was saying. My question was whether   
   >>> Kosmanson's concern applied to the fact that 10 times 0.9999... is   
   >>> really not 9.9999... Cause it's really not 9.999... !   
   >>>   
   >>>   
   >>>   
   >>>   
   >>>   
   >>   
      
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