An uncountable countable set
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From: Virgil on 29 Sep 2006 18:16 In article <451d8c58(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <451d6037(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> In article <451bac34(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>> > >>>>>> If the vase is empty at noon, but not before, how can that not be the > >>>>>> moment that it becomes empty? > >>>>> Saying that it is empty is quite different from saying anything about a > >>>>> "last ball". andy does not deny that the vase becomes empty, he just > >>>>> does not say anything about any "last ball out". > >>>> Does that answer the question of **when** this occurs? Of course not. > >>> It does answer the question of "whether" it occurs. "When" is of lesser > >>> importance. > >> So, you have no answer. And so it's not important. I see. > > > > When have all the balls, whether removed or not, all been inserted? > > Not until noon. > > > That is the time at which all have also been removed, as no ball can be > > removed before its insertion nor after all have been inserted. > > Repeat that to yourself 10 times, and you will see God. Whose notion of god? TO's? Thank you, no. I prefer a god who works within logic. > > > > > Except for the first 10 balls, each insertion follow a removal and with > > no exceptions each removal follows an insertion. > > Which is why you have to have -9 balls at some point, so you can add 10, > remove 1, and have an empty vase. Can you have -9 balls in your vase? Is > it like a ball bank account that can be overdrawn? Are you sure it's not > Cantor's ashes in there? TO deludes himself with the notion that what does not contain an ending must contain an ending. For him all intervals are closed intervals.
From: Virgil on 29 Sep 2006 18:17 In article <451d8e56(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > There is no equivalence between oo and 0 (though I have heard people > claim otherwise). Between oo and -oo there can sometimes be. > > > > > The fact that this bothers you does not constitute my "getting > > into trouble". > > > > - Randy > > > > Oh, you're in trouble, Buster. Not nearly as deep as the s*** TO is burying himself further and further into.
From: Virgil on 29 Sep 2006 18:25 In article <451d8f8d(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Randy Poe wrote: > > Tony Orlow wrote: > >> Randy Poe wrote: > >>> Tony Orlow wrote: > >>>> Virgil wrote: > >>>>> In article <451bac34(a)news2.lightlink.com>, > >>>>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>>> > >>>>>>>> If the vase is empty at noon, but not before, how can that not be > >>>>>>>> the > >>>>>>>> moment that it becomes empty? > >>>>>>> Saying that it is empty is quite different from saying anything about > >>>>>>> a > >>>>>>> "last ball". andy does not deny that the vase becomes empty, he just > >>>>>>> does not say anything about any "last ball out". > >>>>>> Does that answer the question of **when** this occurs? Of course not. > >>>>> It does answer the question of "whether" it occurs. "When" is of lesser > >>>>> importance. > >>>> So, you have no answer. > >>> If something doesn't occur, the question "when does it occur" > >>> does not have an answer. > >> "[R]andy does not deny that the vase becomes empty". That sounds like it > >> occurs. > >> > >>> If I ask you what date you took a trip to Mars last year, > >>> would you have an answer? > >> Does the vase become empty? > > > > Virgil and I differ on terminology here. As I have already said, > > you are trying to pin down an identifiable pair of contiguous > > moments where the vase is non-empty in one, and empty > > in the next. As I have already said, a verb like "emptying" > > conveys to me the existence of a PAIR of moments with > > that property, of an identifiable "change moment". I would > > not use the word "become" for the same reason. > > > > So I will continue to say what I have said. The vase is empty > > at noon, because before noon every ball put in was taken > > out. > > > > There is no moment when the vase "becomes empty". The > > first time when the vase IS empty is noon. > > > > - Randy > > > > Sorry, Randy, that's just daft. It's not, then it is, but it didn't > become, because that would mean you'd have to think about that moment of > becoming, and face the fact that you would need to have -9 balls two > iterations beforehand to get an empty vase. Can you say "avoidance"? What Randy is avoiding is TO's fallacious insistence that there must be a last ball removed if one is ever to achieve a state where the balls are all removed. In a physical world that might be the case, but in an ideological one it need not be. When one plays out a thought experiment. one must play it out by the rules given in that experiment. To tries to change, or break, those rules, which is a form of cheating.
From: Tony Orlow on 29 Sep 2006 18:52 Virgil wrote: > In article <451d6602(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > > >> I wouldn't put it that way. ...1111 can be interpreted as the largest >> binary natural, if you claim all bit positions are finite. > > Calling all bit positions finite does not require that there only be a > finitely many bit positions, and the binary string representation of > every finite natural n requires <= ln(n+1)/ln(2) bit positions. > If all bit positions are finite, and the string up to any finite bit position can only have a finite value, then there is no position in the string where it achieves anything but a finite value. Are you saying that aleph_0 naturals only require ln(aleph_0+1)/ln(2) bit positions? You're not allowed to use aleph_0 like that, now, are you? > >>> and that >>> ..11111111 + 1 = 0 >> ...11111 can be interpreted indeed as -1, as is done every millions of >> times per microsecond all over the world in computers. > > Which of the worlds computers can work with an infinitely long string of > binary digits? The fact works for an arbitrary number of bits, including in the 2-adics. Besides, any Turing machine can process an infinite string given infinite time.
From: Tony Orlow on 29 Sep 2006 18:55
Virgil wrote: > In article <451d66c0(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> stephen(a)nomail.com wrote: >>> Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >>>> Virgil wrote: >>>>> In article <d12a9$451b74ad$82a1e228$6053(a)news1.tudelft.nl>, >>>>> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >>>>> >>>>>> Randy Poe wrote, about the Balls in a Vase problem: >>>>>> >>>>>>> It definitely empties, since every ball you put in is >>>>>>> later taken out. >>>>>> And _that_ individual calls himself a physicist? >>>>> Does Han claim that there is any ball put in that is not taken out? >>>> Nonsense question. Noon doesn't exist in this problem. >>> Yes it is a nonsense question, in the sense >>> that it is non-physical. You cannot actually perform >>> the "experiment". Just as choosing a number uniformly >>> from the set of all naturals is a non-physical nonsense >>> question. You cannot perform that experiment either. >>> >>> Stephen >> Yes, they both sound equally invalid, and it all goes back to omega, but >> Han has a point about the density of the set in the naturals throughout >> its range, and the overall statistical probability of selecting one of >> that subset from the naturals, even if having probabilities of 1/omega >> for each natural presents problems. >> >> Tony > > Do statistical probabilities have to satisfy the condition that their > sum over all indivisible outcomes must equal 1? Yes, and that requires, for a uniform distribution, that we have a precise count. If aleph_0 is some kind of precise number, then we can say that a uniform probability distribution over a set of this size yields a probability of 1/aleph_0, and if aleph_0 is infinite, this individual probability is infinitesimal. Then you can add them all up and get the unit of universal inevitability. :) |