Cantor Confusion
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From: Virgil on 26 Oct 2006 16:29 In article <1161885287.076956.190220(a)i3g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > 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 it proves nothing about the cardinalities of any sets. > > > But for infinite ones, you must do one > > more transfinite step. > > No. Yes! > Any real number has only finite digit positions, according to Dik And is Dik your "Authority"? > > Indeed, i is not simple. Au contraire! > Do we need transfinite induction for all the > reals? Not to establish their existence.
From: Virgil on 26 Oct 2006 16:32 In article <1161885731.614220.103620(a)b28g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > > 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 The world of ideas exists within the universe, but is not constrained to mimic it.
From: MoeBlee on 26 Oct 2006 16:54 David Marcus wrote: > mueckenh(a)rz.fh-augsburg.de wrote: > > I guess I can see now the reason of your problems: You don't > > understand because you are looking for a tanslation always. There is no > > translation required. The tree is that mathematics which deserves this > > name. It is outside of your model, independent of ZFC, but generally > > valid and, therefore; covering ZFC too. > > Thank you for finally admitting that your argument can't be given within > ZFC. I don't recall the exact quote. If it is convenient for you, would you quote him saying that his argument is within Z set theory? As I recall, I sure thought that was what he said. It sure seemed clear enough to me that he was claiming to make an argument within Z set theory, which is the only reason I wasted my time trying to make sense of his argument. It would be nice to have his exact words and their context right in front of us. MoeBlee
From: Lester Zick on 26 Oct 2006 18:48 On 26 Oct 2006 13:25:43 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: >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. You don't define much of anything in mechanically exhaustive terms that I can tell. >> "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. "Pure syntax"? What is that supposed to mean? >> >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. So "cardinality" is not a predicate symbol? So "least" is not a predicate symbol? So "ordinal" is not a predicate symbol? So "equinumerosity" is not a predicate symbol? Then what did you think you were using to designate various predicates? > Whatever "cardinality=least ordinal >equinumerosity" is meant by you, the phrase is not something that >renders a formula of set theory. Well that I sure as hell believe. You don't know what predicate symbols are but you sure as hell use them anyway. >> 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. Cardinality(x)=least ordinal(y) with equinumerosity(z). >> 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. Yeah, I know, Moe, like pages 1-99 are filled with nicknames and single place operations that you prefer to use instead of exhaustive terminology. >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. You mean I should disregard silence on your part as a preference for my not justifying your own opinions on the subject of your beliefs? ~v~~
From: MoeBlee on 26 Oct 2006 19:18
Lester Zick wrote: > You mean I should disregard silence on your part as a preference for > my not justifying your own opinions on the subject of your beliefs? Yes. Exactly. You hold the key to all that is true. MoeBlee |