Cantor Confusion
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From: mueckenh on 26 Oct 2006 13:39 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. Regards, WM
From: mueckenh on 26 Oct 2006 13:42 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. > > > > > > 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? Regards, WM
From: mueckenh on 26 Oct 2006 13:48 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! > > 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. > > > 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. Zermelo published his paper in 1904: The headline, translated by me, reads: "Proof that any set can be well ordered." If it can be well ordered, then do it please. Otherwise I do not believe that it "can be done" > > Nevertheless some cranks > > insist, it would exist somewhere. Do you know where? > > In minds less handicapped than WM's, If you know such a mind, please ask her to tell me how the well-order of uncountably many numbers fits in approximately 10^11 neurons or bits. If a defining fortmula is not available, then there must be one neuron per element. Or can you store more than one idea by one neuron? Regards, WM
From: mueckenh on 26 Oct 2006 13:54 jpalecek(a)web.de schrieb: > > The model is that simple that any student in the first semester could > > understand it. Every paths which branches into two paths necessarily > > needs two additional edges for this sake. It is only your formalistic > > attitude that blocks your understanding. But you must not think that > > anybody is blocked like you. > > This looks like a proof by induction. Indeed, you can prove your > formula > by induction for FINITE paths. Thanks for admitting your understanding so far. > But for infinite ones, you must do one > more transfinite step. No. Any real number has only finite digit positions, according to Dik, who rigorously denies that 0.111... cannot be indexed completely by natural indexes. Now you see that this opinion leads to induction and to a contradiction. So you hurry to switch to transfinity. > This is no unnecessary formalism, but something > you need to understand to get your proof working. And it is not > intuitive, > and it is not simple. Indeed, i is not simple. Do we need transfinite induction for all the reals? Then, in fact, the natural numbers are not sufficient. Then some digits of 0.111... are undefined. Or do we need transfinity only in special cases, namely then when otherwise set theory would be smashed? Regards, WM
From: mueckenh on 26 Oct 2006 14:02
Tony Orlow schrieb: > mueckenh(a)rz.fh-augsburg.de wrote: > > Tony Orlow schrieb: > > > > > >>> How would you construct an actually infinite set? Pair, power, union? > >>> They all stay in the finite domain if you start with existence of the > >>> empty (or any other finite) set. Comprehension or replacement cannot go > >>> further. So, how would you like to achieve it? > >>> > >>> Regards, WM > >>> > >> Inductive subdivision of the unit continuum? We certainly seem to be > >> able to specify, or approximate arbitrarily closely, some values with > >> infinite strings of digits. It seems obvious that any finite interval in > >> the continuum has more than any finite number of points within it. So, > >> isn't that an actually infinite set, albeit with linear finite measure > >> and bounds? > > > > > > Sorry Tony, you are in error. We cannot approximate sqrt(2) arbitrarily > > close. We can visualize it by the diagonal of a square and we can name > > it. But we cannot approximate it better than to an epsilon of > > 1/10^10^100. It woud be nice if we could, but assuming we can manage > > it, only because otherwise mahematics becomes too difficult, is a bit > > too simple. > > > > Regards, WM > > > > Can you justify that limit of accuracy in mathematical terms, without > resorting to discussions of the size of the universe? I see no > theoretical, mathematical reason for it. Mathematics is unavoidably tied to the universe. No mathematics without matter. Please visit my website on MatheRealism http://www.fh-augsburg.de/~mueckenh/MR.mht Regards, WM |