[continued from previous message]   
      
   >>>>>>>>>>>>> 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,   
   >>>>>>>>>>> to help eliminate what are the usually ignored ambiguities.   
   >>>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> So, pre-calculus, the course, goes to eliminate or talk   
   >>>>>>>>>>> away the case .999, dot dot dot, different 1. Yet,   
   >>>>>>>>>>> it can be reconstrued and reconstructed, on its own   
   >>>>>>>>>>> constructive account. So, it's a convention.   
   >>>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> It's "multiplicity theory", see, that any, "singularity   
   >>>>>>>>>>> theory", which results as of admitting only the principal   
      
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