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