An uncountable countable set
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From: mueckenh on 5 Oct 2006 12:45 MoeBlee schrieb: > A CONTRADICTION? From what AXIOIMS? Please show a derivation of a > sentence P and ~P from the axioms. Oh, that's right, by "contradiction" > you don't mean a contradiction in the sense of a sentence and its > negation; you mean something that doesn't sit with your personal > intuition. > + 1 Gedankenexperiment: Put 10 balls in A and remove two, one of which is put in B and the other one is put in C. P: At noon all balls are in B. ~P: At noon all balls are in C. Regards, WM
From: MoeBlee on 5 Oct 2006 13:57 mueckenh(a)rz.fh-augsburg.de wrote: > The axiom of infinity does only state n+1 exists if n is given. What axiom of infinity is that? What you just said is not part of any axiom of infinity I've ever heard of. MoeBlee
From: MoeBlee on 5 Oct 2006 14:05 mueckenh(a)rz.fh-augsburg.de wrote: > I used "k + omega " as the ordinal number of {-k, -k+1, ..., 0, > 1,2,3,...}. > If you can't understand that, try to increase your knowldge of set > theory. What book about set theory do you recommend that mentions such an ordinal? Also, perhaps I missed it, but what is your definition of '-k' for an ordinal k? > > > But subtraction of a set of positive numbers from the set omega is > > > expressed, as I did, by -k + omega. > > > > Ah, apparently you are defining something new here. > > New for you probably. As omega + k is different from k + omega, we > should not write omea - k for -k + omega. So, again, what is the definition of '-k'? > Here it is, but some greek symbols may be misprinted. > > Die Subtraktion kann nach zwei Seiten hin betrachtet werden. Sind > ï?¡ï? und ï?¢ irgend zwei ganze Zahlen, ï?¡ï? < ï?¢, so überzeugt man > sich leicht, daÃ? die Gleichung > > ï?¡ï? + ï?¸ = ï?¢ > > immer eine und nur eine Auflösung nach ï?¸ zuläÃ?t, wo, wenn > ï?¡ï? und ï?¢ Zahlen aus (II) sind, ï?¸ eine Zahl aus (I) oder (II) > sein wird. Diese Zahl ï?¸ werde gleich ï?¢ï? - ï?¡ gesetzt. > > 202 Betrachtet man hingegen die folgende Gleichung: > > ï?¸ï? + ï?¡ = ï?¢ > > so zeigt sich, daÃ? dieselbe oft nach ï?¸ gar nicht lösbar ist, z. B. > tritt dieser Fall bei folgender Gleichung ein: > > ï?¸ï? + ï?· = ï?· + 1. That came out with just boxes for the symbols, and unfortunately I don't read German. Would you give us this information in ASCII and English? MoeBlee
From: MoeBlee on 5 Oct 2006 14:16 mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > > A CONTRADICTION? From what AXIOIMS? Please show a derivation of a > > sentence P and ~P from the axioms. Oh, that's right, by "contradiction" > > you don't mean a contradiction in the sense of a sentence and its > > negation; you mean something that doesn't sit with your personal > > intuition. > > > > + 1 Gedankenexperiment: Put 10 balls in A and remove two, one of which > is put in B and the other one is put in C. > > P: At noon all balls are in B. > ~P: At noon all balls are in C. I take it that you mean that "At noon all balls are in C" implies ~P. Anyway, none of what you mentioned are formulas of set theory nor have you stated any axiomatic theory here. Just as I said about the other poster, you find a conflict with your intuitions (here, regarding a thought experiment), but no actual contradiction in an axiomatized theory. MoeBlee
From: Virgil on 5 Oct 2006 14:35
In article <d648a$4524bbca$82a1e228$30728(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Virgil wrote: > > > In article <22028$4524b4dc$82a1e228$28724(a)news1.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>In real time there are no singularities. With the Balls in a Vase there > >>is a singularity at noon. Therefore the quantity called "time" resembles > >>real time sometimes, but not always. > > > > There is no part of the gedankenexperiment as stated that can be run in > > "real time", so the constraints allegedly imposed by properties of > > "real time" are irrelevant. > > Precisely! Such as the constraint that something must happen at noon. As that is a constraint imposed by the experiment, and not by "real time", it is both relevant to the experiment and inevitable within the experiment. |