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