Cantor Confusion
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From: Virgil on 26 Oct 2006 16:15 In article <1161884266.746124.280550(a)k70g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Even Virgil has understood, although > he does not try to find any error but plainly refuses the result > because there is a contrary proof by Cantor. I am not at all sure what "WMueckenheim" claims I "understand". What I do understand is that "WMueckenhiem" works from some secret set of axioms which are in conflict with ZF, and ZFC, and NBG, but will not acknowledge that he bases his arguments on unproven and unprovable assumptions, just as all axiom followers do.
From: Virgil on 26 Oct 2006 16:18 In article <1161884380.178413.126960(a)i3g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > David Marcus schrieb: > > > > > > > All the balls have been removed before noon. > > > > OK. > > > > > But more balls are in the vase. > > > > Reason? Proof? Example? Anything? > > Consider a strictly increasing sequence with non-negative > terms.--------- If you can. Consider that the number of balls as a function of time has infinitely many integer jump discontinuities which cluster around noon, so that there is no way that the function can be continuous at noon.
From: Virgil on 26 Oct 2006 16:20 In article <1161884564.586304.139720(a)i3g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > In article <1161806870.567125.312870(a)e3g2000cwe.googlegroups.com>, > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > There are many books on binary trees and many others on geometric > > > series. I put these topics together. That is new and not everybody can > > > understand it immediately. You must not be sad on that behalf. Follow > > > just my discussion with those guys who have understood this > > > comparatively simple matter. At the end, you may get it too. > > > > May God protect me from such evil. > > You know, praying is the last promising action you can do? But not even > that will help. You mean that that evil will overtake me despite anything that God can do to forstall it? > > > > > > > > Or, he could continue to do as Humpty Dumpty did and use his own > > > > > meanings for words without telling people what they are. > > > > > > You must not think that everything you cannot understand is > > > ununderstandable. It is just some new idea. Otherwise it would not be > > > so interesting. You prefer to learn old knowledge from your old books > > > with their old trodden paths? My paths are new! > > > > And go nowhere. > > They do not end anywhere. Correct. They split and split and split. But > at every split another pair of edges is created. And that does not end > too. Like the growth of the input of the vase. Why do you only look at > one side, not at the other? The only relevant question is "According to the rules set up in the problem, is each ball inserted before noon also removed before noon?" An affirmative answer confirms that the vase is empty at noon. A negative answer directly violates the conditions of the problem. How does "WMueckenheim"answer?
From: MoeBlee on 26 Oct 2006 16:25 Lester Zick wrote: > So symbolizing various phrases gives us a mathematically exhaustive > definition of the phrases? We don't define the English phrases. We define symbols. > "Exact venue of syntax"? What the hell is that when it's at home? In the context, or setting, of pure syntax. That is, with regard to syntax alone. > >The cardinality of x = the least ordinal equinumerous with x. > > Then the accurate definition for "cardinality" would appear to be: > cardinality=least ordinal equinumerosity. No, because that is neither a predicate symbol nor operation symbol that is being defined there. Whatever "cardinality=least ordinal equinumerosity" is meant by you, the phrase is not something that renders a formula of set theory. > The problem here is that you > were discussing "cardinality" in general terms and the best you can do > is define the "cardinality of x" instead. Please quote what I said about 'cardinality' in general terms that is not handled by my definition. > Or do you just run around > spouting "nicknames" and "single one place operations" instead of > defining what your talking about? Like I said, I'm giving you explanations and defintions that are from page 100 which requires that you have read 1-99. Please regard any possible future silence of mine in response to ceratain of your posts just to be a reflection of my weariness in talking to someone who can only respond to my own answers by abysmally misconstruing them due to his own will not to even read page 1 of a textbook on the subject. MoeBlee
From: Virgil on 26 Oct 2006 16:26
In article <1161884901.561123.314310(a)h48g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > > All the balls have been removed before noon. > > > But more balls are in the vase. > > > > Where do those ephemeral balls materialize from? > > >From the same matter which the others materialize from: pure thought! The original balls are all provided by the gedankenexperiment itself, but it does not provide any balls which are not removed before noon. So that IN THAT EXPERIMENT, the vase is empty at noon, regardless what may happen in other experiments. > > > > Nowhere nearly as bad as WM's claiming > > " All the balls have been removed before noon. > > But more balls are in the vase." > > That is a fine contradiction. And is entirely due to WM's counterfactual assumptions. > > > > > > Correct. And therefore no such thing can exist unless it exists in the > > > mind. But we know that there is no well order of the reals. in any > > > mind, because it is proven non-definable. > > > > It is perfectly definable, and perfecty defined, it is merely incapable > > of being instanciated. > > Then let me know one of the perfect definitions, please. A set is well ordered when every nonempty subset has a first member. |