[continued from previous message]   
      
   >>>>>>>>>>>>>> have for wider reason and itself rationality, that the   
   >>>>>>>>>>>>>> repleteness   
   >>>>>>>>>>>>>> of their completeness, has a pre-Cartesian "only-diagonal"   
   >>>>>>>>>>>>>> and   
   >>>>>>>>>>>>>> then for that the rationals are HUGE, keeping it then   
   >>>>>>>>>>>>>> altogether   
   >>>>>>>>>>>>>> that in extra-ordinary foundations of mathematics, a MODERN   
   >>>>>>>>>>>>>> mathematics,   
   >>>>>>>>>>>>>> that it rescues modern mathematics from blindness (in its   
   >>>>>>>>>>>>>> dumbness).   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> If you didn't play Zork in the 80's then I suppose you   
   >>>>>>>>>>>>>> weren't around or didn't have a computer or didn't have   
   >>>>>>>>>>>>>> a copy of Zork. It's a text-based adventure.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> So, I suppose there may be other reasons, though here there's   
   >>>>>>>>>>>>>> that all the reasons and none sort of result at least one.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>> Yeah, I imagine if you let Kosmanson go on then there'd   
   >>>>>>>>>>>>>> be quite more to it.   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> A note about Kosmanson's emphasis on what's often truncated   
   >>>>>>>>>>>>> in an   
   >>>>>>>>>>>>> infinite series. A year or so back I was forming baby   
   >>>>>>>>>>>>> problems in a   
   >>>>>>>>>>>>> blog   
   >>>>>>>>>>>>> for a Linux newsgroup frequenters to solve, and in one of   
   >>>>>>>>>>>>> them one   
   >>>>>>>>>>>>> would   
   >>>>>>>>>>>>> begin with a correct equation, would make correct changes   
   >>>>>>>>>>>>> in it,   
   >>>>>>>>>>>>> but   
   >>>>>>>>>>>>> would end up in an obviously wrong equation :) Nobody   
   >>>>>>>>>>>>> solved it of   
   >>>>>>>>>>>>> course (audience were mostly morons). But I now wonder if that   
   >>>>>>>>>>>>> problem   
   >>>>>>>>>>>>> had something about Kosmanson's concerns about handling   
   >>>>>>>>>>>>> infinities.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Here I quote the part of the blog that contained that problem:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> (beginning of the quote)   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>    "Then, swoooooooshhshsh!.... and Jesus and all that intense   
   >>>>>>>>>>>>> light   
   >>>>>>>>>>>>> went   
   >>>>>>>>>>>>> back up and out of there. Physfit looked up and there wasn't   
   >>>>>>>>>>>>> even an   
   >>>>>>>>>>>>> opening in the ceiling anymore. But now for some reason he was   
   >>>>>>>>>>>>> horizontally on the floor, in his bed. Right in the living   
   >>>>>>>>>>>>> room!   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> He thought a bit about what was happening, when he found   
   >>>>>>>>>>>>> himself   
   >>>>>>>>>>>>> quite   
   >>>>>>>>>>>>> hungry. Last time he had eaten anything was the night   
   >>>>>>>>>>>>> before he had   
   >>>>>>>>>>>>> waken up on the summit of the magic mountain in an urban   
   >>>>>>>>>>>>> Dallas   
   >>>>>>>>>>>>> area.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> He thought to himself, "I'm going to assume that more than 48   
   >>>>>>>>>>>>> hours has   
   >>>>>>>>>>>>> passed since. So got up and walked to the kitchen and took   
   >>>>>>>>>>>>> a look   
   >>>>>>>>>>>>> inside   
   >>>>>>>>>>>>> refrigerator. There was nothing there but the cat food he had   
   >>>>>>>>>>>>> cooked on   
   >>>>>>>>>>>>> the day he first saw the magic mountain. He got on the   
   >>>>>>>>>>>>> computer to   
   >>>>>>>>>>>>> order   
   >>>>>>>>>>>>> something zesty from HelloFresh. After choosing the closest   
   >>>>>>>>>>>>> to a   
   >>>>>>>>>>>>> healthy   
   >>>>>>>>>>>>> nice pre-agricultural food kit, he clicked, "Go to checkout"   
   >>>>>>>>>>>>> button,   
   >>>>>>>>>>>>> after which the computer waited for a few seconds but   
   >>>>>>>>>>>>> instead of   
   >>>>>>>>>>>>> getting   
   >>>>>>>>>>>>> to the check out screen, a screen came up to make sure   
   >>>>>>>>>>>>> Physfit was   
   >>>>>>>>>>>>> not a   
   >>>>>>>>>>>>> robot. It had a simple question that he had to give it the   
   >>>>>>>>>>>>> correct   
   >>>>>>>>>>>>> answer, otherwise food nommo.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> The question went like this:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>      "In math, is there a difference between the two numbers   
   >>>>>>>>>>>>> 0.999999...   
   >>>>>>>>>>>>> and 1 ?"   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> The digits of "9" continued forever to the right of the radix   
   >>>>>>>>>>>>> point. So   
   >>>>>>>>>>>>> of course, Physfit clicked on the "yes" button. If there   
   >>>>>>>>>>>>> was not a   
   >>>>>>>>>>>>> difference, then one wouldn't even bother to write 1 in   
   >>>>>>>>>>>>> that funky   
   >>>>>>>>>>>>> form,   
   >>>>>>>>>>>>> using an infinite series of digit 9.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> But the screen disappeared, and a message said, "You're a   
   >>>>>>>>>>>>> robot.   
   >>>>>>>>>>>>> Bye!"   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Physfit said, "Fuck!" (first of the fix number of curses   
   >>>>>>>>>>>>> Jesus had   
   >>>>>>>>>>>>> allowed him for that day). So he took a pen and paper and   
   >>>>>>>>>>>>> started   
   >>>>>>>>>>>>> jotting down:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>      x = 0.99999....   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Therefore:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>      10x = 9.99999....   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Now he subtracted the former from the latter:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>      10x - x = 9.99999... - 0.99999...   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Which simplifies to:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>      9x = 9   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> And therefore:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>      x = 1   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> "What the fuck??", said Physfit (his 2nd curse of the day).   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> Why x which was 0.99999... and not 1, turned out to be 1?   
   >>>>>>>>>>>>> ... "   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> (end of quote)   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> So, is this problem pointing to what Kosmanson has been so   
   >>>>>>>>>>>>> keen   
   >>>>>>>>>>>>> about? :)   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Once I was reading a book or article,   
   >>>>>>>>>>>> and was introduced the introduction of .999 (...),   
   >>>>>>>>>>>> vis-a-vis, 1. A cohort of subjects was surveyed   
   >>>>>>>>>>>> their opinion and belief whether .999, dot dot dot,   
   >>>>>>>>>>>> was equal to, or less than, one. About half said   
   >>>>>>>>>>>> same and about half said different.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> It's two different natural notations that happen   
   >>>>>>>>>>>> to collide and thus result being ambiguous.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> So, then these days we have the laws of arithmetic   
   >>>>>>>>>>>> introduced in primary school, usually kindergarten,   
   >>>>>>>>>>>> about the operations on numbers, and also inequalities,   
   >>>>>>>>>>>> and the order in numbers.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Yet, even the usual account of addition and its   
   >>>>>>>>>>>> inverse and its recursion and that's inverse,   
   >>>>>>>>>>>> as operators, of whole numbers, has a different   
   >>>>>>>>>>>> account, of increment on the one side, and, division   
   >>>>>>>>>>>> on the other, sort of like the Egyptians only had   
   >>>>>>>>>>>> division or fractions and Egyptian fractions,   
   >>>>>>>>>>>> and tally marks are only increment, that though   
   >>>>>>>>>>>> it was the Egyptian fractions that gave them a   
   >>>>>>>>>>>> mathematics, beyond the simplest sort of conflation   
   >>>>>>>>>>>> of "numbering" and "counting".   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> So, where ".999 vis-a-vis 1" has a deconstructive account,   
   >>>>>>>>>>>> to eliminate its ambiguities with respect to what it's   
   >>>>>>>>>>>> to model, or the clock-arithmetic and field-arithmetic,   
   >>>>>>>>>>>> even arithmetic has a deconstructive account, then,   
   >>>>>>>>>>>> even numbering versus counting has a deconstructive account,   
      
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