Cantor Confusion
in [Math]
|
From: Virgil on 15 Feb 2007 17:35 In article <1171575875.054198.56510(a)q2g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > The tree contains a path which *is* the union of the p(i), namely > p(oo). The tree, i.e., the union of finite trees is or establishes the > paths q(oo), r(oo), ... too. Therefore it establishes all elements of > the set P(oo). Repeating this silliness does not make it any less silly.
From: Virgil on 15 Feb 2007 17:42 In article <1171576194.042084.91330(a)a34g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > On 14 Feb., 20:20, Virgil <vir...(a)comcast.net> wrote: > > In article <1171468278.284645.273...(a)v33g2000cwv.googlegroups.com>, > > > > > > > > > > > > mueck...(a)rz.fh-augsburg.de wrote: > > > On 13 Feb., 21:17, Virgil <vir...(a)comcast.net> wrote: > > > > In article <1171364856.226197.135...(a)l53g2000cwa.googlegroups.com>, > > > > > > mueck...(a)rz.fh-augsburg.de wrote: > > > > > On 12 Feb., 21:22, Virgil <vir...(a)comcast.net> wrote: > > > > > > In article <1171283208.696664.25...(a)a75g2000cwd.googlegroups.com>, > > > > > > > > mueck...(a)rz.fh-augsburg.de wrote: > > > > > > > On 12 Feb., 04:13, "Dik T. Winter" <Dik.Win...(a)cwi.nl> wrote: > > > > > > > > In article > > > > > > > > <1171205918.124082.214...(a)a75g2000cwd.googlegroups.com> > > > > > > > > mueck...(a)rz.fh-augsburg.de writes: > > > > > > > > > > > On 11 Feb., 03:06, "Dik T. Winter" <Dik.Win...(a)cwi.nl> > > > > > > > > > wrote: > > > > > > > > ... > > > > > > > > Well, I would concede that the above three things are > > > > > > > > representaions of > > > > > > > > the > > > > > > > > number three, using some convention. Anyhow, they are *not* > > > > > > > > the > > > > > > > > number > > > > > > > > three. > > > > > > > > > What has "the number three" that is not expressed above? > > > > > > > > Universality. Just as no single man represents mankind, > > > > > > > I did not say that III expresses all numbers. It expresses all that > > > > > the number 3 can express. > > > > > > Not to me. > > > > > What is missing? > > > > For one thing, WM is missing the knowledge that a name is not the object > > named. > > > Is this valid for names too? Ask Korzybski. > > ===================== > > By showing that the cardinal of that set is larger, as a cardinal, than > > any natural, even or odd. > > Would you do so please for |N|? Been there! Done that! Got the T-shirt. > > ========================== > > > >Set theories which deny the existence of all existing sets should be > >> abolished first. > > > > Then WM embraces such naive set theories as those which Russell's > > paradox, for example, proves self-contradictory. > > Would you mind to read my text please? Or do you in fact deny the > existence of *existing* sets? I don't but WM does. > > It seems you are in a very deep confusion. It is called transference. > > Regards, WM
From: Carsten Schultz on 15 Feb 2007 18:11 MoeBlee schrieb: > On Feb 15, 1:42 pm, mueck...(a)rz.fh-augsburg.de wrote: >> Every set of finite even numbers contains numbers which are larger >> than the cardinal >> number of the set, if the set has a cardinal number. > > Since even numbers are natural numbers, thus finite, I suppose that > what you actually mean is: I think you are wrong. > Every finite set of even numbers has a > member greater than the cardinality of the set. > > But that's not even true. > > {0 2} is a finite set of even numbers and no member is greater than > the cardinality of the set. Guess why WM does not want 0 to be a natural number. [...] >> Could you please look up the proof that the actually infnite set N >> has a cardinal number larger than every natural? Usually it is done by >> induction, and it starts: Certainly 0 < |N|. This is the fundamental >> error. No, certainly 0 is not less than |N|. No axiom and no proof >> lead to this statement. > > You're nuts. You are right on this one. Which is why your first statement was probably wrong. Best, Carsten -- Carsten Schultz (2:38, 33:47) http://carsten.codimi.de/ PGP/GPG key on the pgp.net key servers, fingerprint on my home page.
From: William Hughes on 15 Feb 2007 18:32 On Feb 15, 4:42 pm, mueck...(a)rz.fh-augsburg.de wrote: > On 14 Feb., 18:24, "William Hughes" <wpihug...(a)hotmail.com> wrote: > > > > > On Feb 14, 11:15 am, mueck...(a)rz.fh-augsburg.de wrote: > > > > On 14 Feb., 02:21, "William Hughes" <wpihug...(a)hotmail.com> wrote:> On Feb 13, 11:58 am, mueck...(a)rz.fh-augsburg.de wrote: > > > > > > On 10 Feb., 15:31, "William Hughes" <wpihug...(a)hotmail.com> wrote: > > > > > And you have snipped again. I conclude: > > > > > You now agree the statement > > > > > Every set of finite even numbers > > > > contains numbers which are larger than the cardinal > > > > number of the set. > > > > > is false. > > > > No, it is true. How can you conclude it was wrong? > > > Because it does not imply that the set of even finite numbers > > has a cardinality, it is not true for E, and E is a set > > of finite even numbers. > > It is true for every form of existence E can assume. But in order to > avoid any misunderstanding: > > Every set of finite even numbers contains numbers which are larger > than the cardinal > number of the set, if the set has a cardinal number. > > And since in Wolkenmeukenheim all cardinal numbers are finite this reduces to the trivial Every finite set of finite even numbers contains numbers which are larger than the cardinal number of the set. > > > > > > Correct. And it can be shown that the sparrow is not lager than any > > > > > natural number. > > > > > No. The sparrow of E is an equivalence class. This equivalence > > > > class is different than any equivalence class containing a set > > > > with cardinality a (fixed) finite number. If we extend injection and > > > > surjection > > > > in the same way we extended bijection (in-transforms, and sur- > > > > transforms) > > > > we can put a ordering on the sparrows such that the sparrow > > > > of E is larger than the sparrow of any set whose cardinality > > > > is a natural number. > > > > Absolutely wrong. > > > > Correct is: The equivalence class |E| > > > |E| is your notation for the cardinality of E. We are > > not talking about the cardinality of E (your definition) > > but the sparrow of E. > > Could you please look up the proof that the actually infnite set N > has a cardinal number larger than every natural? Which bit of the sparrow of E is not |E| did you fail to understand? > Usually it is done by > induction, and it starts: Certainly 0 < |N|. This is the fundamental > error. No, certainly 0 is not less than |N|. No axiom and no proof > lead to this statement. > > >of > > >is different from any > > > equivalence class containing a set with cardinality a (fixed) finite > > > number. This is trivially true because |E| is not a fixed number. > > > |E| is not the sparrow of E. The sparrow of E, as you have > > agreed, is fixed. > > The sparrow is fixed. It is a songbird and it sings: The number of > elements of my set is not fixed. > Your set is a member of the equivalence class, it is not the equivalence class. The sparrow of E is an equivalence class which contains your set and many other sets. Any property your set may have is totally irrelevent. The fact that the number of elements in your set is not fixed does not mean that the number of sets in the equivalence class is not fixed. > > > > > > > Why should we decide to call it a number? Well, i is > > > > > also called a number, but would we name it a number, if we had the > > > > > choice today? > > > > !!! > > > Yes, why not? > > Because vectors and tensors are closely related to complex numbers, > Quaternions and Cayley numbers, but are not called numbers. > In my > opinion, all numbers should be ordered by size. > But we are not interested in what is true in Wolkenmuekenheim. It is quite natural to call the algebraic completion of the real a set of numbers. > > > > > > > > > E is all components of E. What holds for all components (not only for > > > > > each component!) holds for E. > > > > > No. E.g. All components of E have a fixed maximum. E does > > > > not have a fixed maximum. What holds for all components of E > > > > does not necessarily hold for E. > > > > > > > and the fact that the compenents of E have a given > > > > > > property does not mean that E has that property > > > > > > More precisely: If all initial segments of E have that property and if > > > > > no element of E is outside of every initial segment, then E has that > > > > > property. > > > > > No. E.g. All inital segments of E have a fixed maximum. No element > > > > of > > > > E is outside of every initial segment. However, E does not have > > > > a fixed maximum. > > > > Every element of E is finite. Show me a part of E which is outside of > > > every finite initial segment. > > > My second statement was "No element of E is outside of every initial > > segment." > > The fact that no element of E is outside of every initial segment does > > not > > mean that E has a fixed maximum. > > Correct. But as all existing elements trivially exist, and as all > elements are in trichotomy, there must be a greatest > element. Of > course it cannot be fixed. Hence there is a not fixed largest element. True and absolutely irrelevent. Which of the following do you disagree with? All initial segments of E have a fixed maximum E does not have a fixed maximum If every initial seqment of E has a fixed maximum then E has a fixed maximum - William Hughes
From: Dik T. Winter on 15 Feb 2007 20:03
In article <m6r8t2dl73493se98005o0ngn8bu94an2h(a)4ax.com> G. Frege <nomail(a)invalid> writes: > On Thu, 15 Feb 2007 13:05:34 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> > wrote: > > >> > >> When seen as a set of curly brackets it has 3 at the left sinde and 3 > >> at the right. > >> > Seems that WM is mixing up the name with the named object again. :-) Moreso because {{{}}} is 2. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ |