An uncountable countable set
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From: imaginatorium on 29 Sep 2006 23:04 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
From: Virgil on 29 Sep 2006 23:18 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 only question is whether the vase is empty after noon. 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. 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. 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.
From: Virgil on 29 Sep 2006 23:19 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.
From: Virgil on 29 Sep 2006 23:24 In article <451dd1f2(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > >> Are you saying that aleph_0 naturals only require ln(aleph_0+1)/ln(2) > >> bit positions? > > > > Not at all. I am talking about indvidual natural numbers as members of > > N, ,not N itself, which is not a member of N. > > > > > > And also for every set of contiguous naturals starting at 0 EXCEPT for > N. Why EXCEPT for N? > For the same reason that a paper sack holding oranges is not an orange. > >>>> ...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. > > > > Irrelevant. That does not tell me anything about which , if any, actual > > computers deal with infinitely long strings of binary digits. > > Like, none, man, unless you droppa lotta 'cid, dude. Then it is irrelevant to infinite strings. > > Go watch one, and don't come back till its finished. > > Alright.... Bye!
From: Virgil on 29 Sep 2006 23:26
In article <451dd293(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <451d83c4(a)news2.lightlink.com>, > > So what balls remain in the vase at noon, oh waffler extraordinary? > > For n balls inserted, balls n/10+1 through n remain at the end of any > iteration n. You specify the number of iterations, I'll give you the > sum. What was it? Aleph_0? All iterations executed before noon. |