An uncountable countable set
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From: Virgil on 29 Sep 2006 23:30 In article <451dd4b7(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > > TO deludes himself with the notion that what does not contain an ending > > must contain an ending. For him all intervals are closed intervals. > > You certainly seem to me to have very well defined bounds, but I'm not > sure you should project that on all my opinions about reality. It's more > of a personal observation. TO sets his own lack of bounds. Mathematicians are less loose, at least as mathematicians. They are governed by the rules of logic, among other things, which rules TO violates regularly.
From: Virgil on 29 Sep 2006 23:37 In article <451dd5cf(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > 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. > > > When the gedanken specifically states that only one ball is removed at a > time, what is fallacious about that statement? It omits that it is not just any ball which is removed. If one changes which one is to be removed, one changes the game and the result. \ > > > > In a physical world that might be the case, but in an ideological one it > > need not be. > > It is stated as a condition. Insert 10, remove 1, repeat. It is much more precise and detailed than that. > > > > > TO tries to change, or break, those rules, which is a form of cheating. > > Oh, by rearranging a sequence and violating a specified order? No, that > was your trick. I followed exactly the sequencing defined by the problem. It is TO who tries to change or ignore those rules.
From: Tony Orlow on 30 Sep 2006 00:16 imaginatorium(a)despammed.com 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. > > No, but I think the problem is elsewhere, slightly. Is there a formal > definition of what "transition" means? (Not in a nearby pocket "Dict. > of maths." for example) > > Seems to me that if you had the graph y = (1 if x<0; 2 if x>=0), and > and associated state transition diagram, then there would be a > "transition" from 1 to 2 "at" x=0. But such terminology does not > capture what the state is "at the point of" the transition, which may > be why it isn't used much. But if a vase has balls in it for values (-1 > <= t < 0), I can't see anything actually wrong with saying there is a > transition from empty to non-empty "at" t=-1 and a transition from > non-empty to empty "at" t=0. You need to be careful not to deduce > anything about the _state_ at the two transition values. > > After all, consider the graph of y = -x. This is positive for x<0, and > negative for x>0. It's undefined for x=0, but is there not a transition > from positive to negative at x=0? > > Brian Chandler > http://imaginatorium.org > That all makes very good sense, Brian. I can't see that there isn't a point of transition, especially when that point is very explicitly defined to be noon, and that it is at least then, and not until then, that the vase goes from being non-empty to empty. Is y=-x really "undefined" at x=0? I don't think so. It's 0, which equals -0.
From: Tony Orlow on 30 Sep 2006 00:25 Virgil wrote: > In article <451dcf42(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Virgil wrote: > >>> It is TO who is having problems with it because he won't play by the >>> rules. Those of us who follow the rules have no troubles. >> Hah! While you try to justify the contradiction between your nonsense >> and the formulation in terms of infinite series ((+10,-1)... diverges), >> by saying you can rearrange all the terms and postpone 9/10 of the >> +10's, making it all "balance out" to zero, that's specifically >> violating the sequence set forth in the premise. You changed horses and >> fell into the stream, on a rock. You add 10, then remove 1. Start with >> 0, an empty case, and try rolling the tape backwards. In two steps you >> have a negative set. Is that allowed? > > TO seems to have delusions of sanity. The operative word being "seems", indicating the subjectivity of the statement. > The only question is whether the vase is empty after noon. At noon and possibly thereafter. > Since there is a specific time prior to noon at which any given numbered > ball is removed, one must conclude that they have all been removed by > noon. Numbers aside, putting in more than you remove, you always end up with more. Unless 9+9+9+9...=0, you got yourself a contradiction here. > > Suppose the instead of being put in in batches of 10, they are all put > in when the first one is put in, but removed according to the original > scheduled. In this case it is clear that every ball is removed. In that case addition is all performed first, then all subtraction. Sure, that can work. But the measure of the addition is divorced from that of the subtraction. If one measures the whole process in some kind of common time frame, given the numbers for the additions and subtractions, one can get a "rate of filling", which isn't going to change in this case and cause the thing to suddenly empty. > > So that TO is claiming that putting the balls in earlier, but taking > them out the same way, leaves fewer balls than the original way. At least I have an explanation. You still haven't explained why I can't relabel the balls afterwards and make them disappear from the vase. :) Tony
From: Tony Orlow on 30 Sep 2006 00:26
Virgil wrote: > In article <451dcf88(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Virgil wrote: > >>> Except that this does not happen within the standard reals of >>> probability theory.\ >> God! No Duh! Like, as IF! In your dreams... ;) > > In TO's dreams, but not in any mathematical reality. Like, so NOT!!! Maybe in yours.... :) |