An uncountable countable set
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From: Tony Orlow on 25 Oct 2006 15:10 David Marcus wrote: > Virgil wrote: >> In article <453e824b(a)news2.lightlink.com>, >> Tony Orlow <tony(a)lightlink.com> wrote: >>> Virgil wrote: >>>> In article <453e4a85(a)news2.lightlink.com>, >>>> Tony Orlow <tony(a)lightlink.com> wrote: >>>>> If the vase exists at noon, then it has an uncountable number of balls >>>>> labeled with infinite values. But, no infinite values are allowed i the >>>>> experiment, so this cannot happen, and noon is excluded. >>>> So did the North Koreans nuke the vase before noon? >>>> >>>> The only relevant issue is whether according to the rules set up in the >>>> problem, is each ball inserted before noon also removed before noon?" >>>> >>>> An affirmative confirms that the vase is empty at noon. >>>> A negative directly violates the conditions of the problem. >>>> >>>> How does TO answer? >>> You can repeat the same inane nonsense 25 more times, if you want. I >>> already answered the question. It's not my problem that you can't >>> understand it. >> It is a good deal less inane and less nonsensical than trying to >> maintain, as TO and his ilk do, that a vase from which every ball has >> been removed before noon contains any balls at noon that have not been >> removed. > > Ah, you are forgetting the balls labeled with "infinite values". Those > balls haven't been removed before noon. Although, I must say I'm not too > clear on when they were added. > At noon, and 9/10 are removed at noon as well.
From: Tony Orlow on 25 Oct 2006 15:14 imaginatorium(a)despammed.com wrote: > David Marcus wrote: >> Tony Orlow wrote: >>> David Marcus wrote: >>>> Tony Orlow wrote: >>>>> As each ball n is removed, how many remain? >>>> 9n. >>>> >>>>> Can any be removed and leave an empty vase? >>>> Not sure what you are asking. >>> If, for all n e N, n>0, the number of balls remaining after n's removal >>> is 9n, does there exist any n e N which, after its removal, leaves 0? >> I don't know what you mean by "after its removal"? > > Oh, I think this is clear, actually. Tony means: is there a ball (call > it ball P) such that after the removal of ball P, zero balls remain. > > The answer is "No", obviously. If there were, it would be a > contradiction (following the stated rules of the experiment for the > moment) with the fact that ball P must have a pofnat p written on it, > and the pofnat 10p (or similar) must be inserted at the moment ball P > is removed. > > Now to you and me, this is all obvious, and no "problem" whatsoever, > because if ball P existed it would have to be the "last natural > number", and there is no last natural number. So, there is no problem in deriving a contradiction from your set of assumptions? I thought that's all you cared about. > > Tony has a strange problem with this, causing him to write mangled > versions of Om mani padme hum, and protest that this is a "Greatest > natural objection". For some reason he seems to accept that there is no > greatest natural number, yet feels that appealing to this fact in an > argument is somehow unfair. > > I goes like this: "No Largest Finite!!!! (GONG!!!) Huyah huyah huyah.....Ommmmmmmmega!" Then you sprinkle your chicken blood or herbs or whatever on whatever you seem to be spooked by. >>> Sure. But it's easily explainable and resolvable once a proper measure >>> is applied to the situation. Omega doesn't lend itself to proper >>> measure. Infinite series do. Bijection loses measure for infinite sets. >>> N=S^L and IFR preserve measure. > > Oh, right, well Tony has a number of "explanations" for things, most of > them equally mysterious. > > Brian Chandler > http://imaginatorium.org > Uh, yeah, they're hiding behind omega in the closet.
From: Tony Orlow on 25 Oct 2006 15:14 Virgil wrote: > In article <1161754218.785144.91070(a)e3g2000cwe.googlegroups.com>, > imaginatorium(a)despammed.com wrote: > >> David Marcus wrote: >>> Tony Orlow wrote: >>>> David Marcus wrote: >>>>> Tony Orlow wrote: >>>>>> As each ball n is removed, how many remain? >>>>> 9n. >>>>> >>>>>> Can any be removed and leave an empty vase? >>>>> Not sure what you are asking. >>>> If, for all n e N, n>0, the number of balls remaining after n's removal >>>> is 9n, does there exist any n e N which, after its removal, leaves 0? >>> I don't know what you mean by "after its removal"? >> Oh, I think this is clear, actually. Tony means: is there a ball (call >> it ball P) such that after the removal of ball P, zero balls remain. >> >> The answer is "No", obviously. If there were, it would be a >> contradiction (following the stated rules of the experiment for the >> moment) with the fact that ball P must have a pofnat p written on it, >> and the pofnat 10p (or similar) must be inserted at the moment ball P >> is removed. >> >> Now to you and me, this is all obvious, and no "problem" whatsoever, >> because if ball P existed it would have to be the "last natural >> number", and there is no last natural number. >> >> Tony has a strange problem with this, causing him to write mangled >> versions of Om mani padme hum, and protest that this is a "Greatest >> natural objection". For some reason he seems to accept that there is no >> greatest natural number, yet feels that appealing to this fact in an >> argument is somehow unfair. >> >> >>>> Sure. But it's easily explainable and resolvable once a proper measure >>>> is applied to the situation. Omega doesn't lend itself to proper >>>> measure. Infinite series do. Bijection loses measure for infinite sets. >>>> N=S^L and IFR preserve measure. >> Oh, right, well Tony has a number of "explanations" for things, most of >> them equally mysterious. >> >> Brian Chandler >> http://imaginatorium.org > > And many of them downright wrong! WRONG!!!! :)
From: Virgil on 25 Oct 2006 15:18 In article <453faeb8(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > David R Tribble wrote: > > Tony Orlow wrote: > >> Does anything occur in the vase at noon? If not, then it should have the > >> same state as before noon. > > > > As which state before noon? > > > > The state of non-emptiness that persists continually from t>=-1 until t<0. What does TO mean by "from t >= -1"? Does TO mean the same as "from t = -1"? If so why not simply say so, and if not what does TO mean by it? And even more puzzling, what does TO mean by "until t < 0"? Since "t < 0" is true before the experiment starts, TO must mean from the beginning of time.
From: Virgil on 25 Oct 2006 15:23
In article <453fb038(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > David R Tribble wrote: > > David R Tribble wrote: > >>> I know you don't get this, but go back and read your own definition. > >>> Every H-riffic corresponds to a node in an infinite, but countable, > >>> binary tree. > > > > Tony Orlow wrote: > >>> No, like the reals, it corresponds to a path in the tree. > > > > David R Tribble wrote: > >>> No, read your own definition again. Each H-riffic is a finite node > >>> along a path in a binary tree. > > > > Tony Orlow wrote: > >> Where does it say anything about a node in my definition, or whether > >> strings can be infinite? Your baseless declarations about my definitions > >> don't fly. > > > > When you stated that > > 1 in H > > x in H -> 2^x in H > > x in H -> 2^-x in H > > > > The set H is a countable set. Each x in H corresponds to a node in the > > binary tree listing all the x's in H (where each left fork is 2^x and > > each right fork is 2^-x from the node of any x). > > > > In different terms, each x in H is a finite recursion > > x = 2^y or 2^-y for some other y in H > > where each recursion ends at > > y = 1 > > > > Your definition above does not allow for any infinite-length recursions > > or infinite-length paths in the binary tree. > > > > As I posted previously, if you want to extend your definition to > > include infinite-length paths in the tree (which I dubbed the > > H2-riffics), you need to define additional numbers using additional > > rules. Something akin to the way the irrationals are defined on > > top of the rationals (as infinite sequences of rationals) in order to > > define the complete set of reals. > > > > > > Is that true also of the digital reals? I disagree with the notion that > any sequence is countable. Then TO must have a very convoluted definition of sequence in mind. > In order to prove that the H-riffics really > cover the reals I have to use a Cauchy- or Dedekind-like method to prove > that any element in the continuum can be specified, even if it requires > an infinite specification. But, there is nothing explicit or inherent in > my rules that limits such specifications to finite lengths. You are > carrying that over from the standard notion of sequences as always > countable. I don't adhere to that concept. As far as anyone can see, TO does not adhere to anything except his own intuition. > > > Tony Orlow wrote: > >>> What makes you think infinite-length strings are excluded? They're not, > >>> in either of my riffic number systems. > > > > David R Tribble wrote: > >>> You're confused. Infinite-length fractions are not excluded, > >>> obviously. But we're not talking about fractions, we're talking about > >>> each H-riffic being a node in the binary tree that lists all of them. > >>> Each H-riffic is a node on a finite-length path in the tree. > > > > Tony Orlow wrote: > >> Who the hell said that? Is this your number system now, that you get to > >> declare that my H-riffics are nodes in your tree? Get real. It is TO's unreal notions of numbers that would be much improved by "getting real". > > > > It's what you did _not_ say that excludes them. There is no way to > > produce infinitely recursively-defined H-riffics from your existing > > definitions, so you must add another rule or two that allows such > > numbers to exist. Which gives you a different set, of course. > > > > Which rules would you recommend that counteract rules that I didn't > state? You are applying a rule that says that any sequence is finite. > That's not true. Countably infinite sequences exist, as in 1/3 in > decimal. They exist here too. |