[continued from previous message]   
      
   >>>>>>>> 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... !   
   >>   
   >>   
   >>   
   >>   
   >>   
   >   
   > Perhaps you should learn "Russian peasant arithmetic".   
   >   
   > I.e., perhaps he was using different arithmetic.   
   > One shifts, the other rolls, then either expecting   
   > algebraic cancellation to erase the difference.   
   >   
   >   
   > Or, perhaps you had no idea what you were/weren't doing.   
   > Or, that there are many _replete_ ways that things are,   
   > the continuous manifold.   
   >   
   >   
   > Please consult Kosmanson and request his latest dispatch   
   > and further ask if he might carry on for a good ten or fifteen   
   > paragraphs, or however much endurance so arrives.   
   >   
   >   
   > The linear curriculum, the standard linear curriculum,   
   > is a development and refinement of what results that   
   > there are many, yet only so few: ways and ways,   
   > then that greater reasoners naturally arrive at these.   
   >   
   > So, again, bring us more of Kosmanson's journals, that   
   > we might engage in a critique and admire their brilliance.   
   >   
   >   
   >   
   >   
      
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   --- SoupGate-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)