Cantor Confusion
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From: Virgil on 28 Oct 2006 18:31 In article <1162068028.638690.242480(a)b28g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Can you calculate sqrt(2) to > 10^100 digits? No. But we can both get as close as necessary to obtain > correct results. Results which are not exact are not mathematically "correct", they are merely approximate. "WMueckenheim" assumes that what is good enough for physics is good enough for everyone, but he is again wrong.
From: Virgil on 28 Oct 2006 18:38 In article <1162068521.341383.99300(a)k70g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > > And once again WM deliberately confuses, "all positions are > > finite", with "there are a finite number of positions". > > There is no confusing! Every finite position belongs to a finite > segment of positions (indexes). If you don't believe that and assert > the contrary, then try to find a finite position which dos not belong > to a finite segment (of indexes). It is equally true that for every finite segment of indexes there are positions beyond that segment. > > It is simply purest nonsense, to believe that "all positions are > finite" if "there are an infinite number of positions". There are certainly more than any finite number of positions. And it is even purer nonsense to believe that in such a situation there are only finitely many of them.
From: Virgil on 28 Oct 2006 18:51 In article <1162068618.817730.147560(a)f16g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > You are so much caught inside your theory that you are unable to look > > > at it from outside. > > > > No, I'm not. I think about philosophical problems with set theory > > frequently. And I keep in mind my agenda to learn about other > > foundational proposals as I try to get at least some of the outline or > > even just the flavor (if that's all I'm capable of) of such alternative > > proposals while I study to put myself in a position to rigorously > > understand them. > > If you think objectively then you cannot avoid the conclusion that > fractions of edges can be summed and you cannot avoid the conclusion > that lim {n-->oo} (1 - 1/2^n)/(1 - 1/2) = 2 is the number of edges per > path. A path passing through only two edges is finite. Every edge is shared by infinitely many paths, so that by "WMueckenheim"'s analysis the number of edges per path is a sum of zeros, equalling zero. But in fact it takes infinitely many complete edges to make one path. And each edge is incorporated in uncountably many paths.
From: Virgil on 28 Oct 2006 18:55 In article <1162068904.623260.163670(a)f16g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > What is the set N? It is the unique set which is a subset of every inductive set containing {}.
From: Virgil on 28 Oct 2006 18:59
In article <1162069034.872037.22830(a)e3g2000cwe.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > > 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? > > One condition of the problem is that the contents of the vase grows. It > has nothing to do with the "infinitely many integer jump > discontinuities which cluster around noon". If those would prohibit the > continuous growth of the contents then they would prohibit also the > calculation of the removed set. The growth of contents of the vase is a mere deduction, not an explicit statement in the gedankenexperiment, so does not override the explicit statements. And it is explicitly stated that every ball, n, has a time before noon at which it is removed from the vase before noon. So which ball, n, does "WMueckenheim" claim remains at noon? > > Regards, WM |