An uncountable countable set
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From: Virgil on 20 Oct 2006 03:35 In article <11006$4538774e$82a1e228$25512(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > MoeBlee wrote: > > > Han de Bruijn wrote: > > > >>MoeBlee wrote: > >> > >>>All cardinals are ordinals (while not all ordinals are cardinals). The > >>>set of natural numbers is the set of finite ordinals which is the set > >>>of finite cardinals. This is standard set theory. > >> > >>Ah! Therefore we can limit ourselves to the naturals and forget all the > >>fuzz about ordinals and cardinals. Because the infinite counterparts of > >>these beasties do not exist in _my_ universe anyway. > > > > Do what you want in _your_ universe. Meanwhile, if you ever get around > > to formulating a mathematical theory, do let us know. > > I've formulated more than one, _without_ set theory. Lets see what assumptions it requires. If it requires the consent of physics, it is worthless to anyone but physicists.
From: Virgil on 20 Oct 2006 03:40 In article <9806$45387805$82a1e228$25512(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > MoeBlee wrote: > > > Han de Bruijn wrote: > > > >>The confusion stems from the fact that I cannot and shall not understand > >>the _infinite_ counterparts of the finite cardinals and ordinals. > > > > How can you understand if you won't read a book that explains it? (By > > the way, Halmos is a good book, but it's just an overview; it doesn't > > give you the full explanations that you need.) > > > > So you seem to think it is better to spout nonsense on the Internet > > about a subject you cannot possibly understand since you insist that > > you won't. > > How can you say this? One word at a time. > I understand very well that infinite cardinals and ordinals simply do > not exist. And we understand that, while they have no more physical existence than any other mathematical ideas, they do have just as much mathematical existence as any other mathematical ideas.
From: Ross A. Finlayson on 20 Oct 2006 04:16 Virgil wrote: > In article <a4bdc$453876fe$82a1e228$25512(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > MoeBlee wrote: > > > > > > You won't read a textbook in set theory because it's confusing? So, > > > you'd rather remain confused and completely ignorant about set theory, > > > while spouting nonsense about it every day on the Internet? > > > > Uh, I'm spouting *sense*. > > Whatever it may be when HdB spouts it, it is nonsense by the time it > appears here. > > > > > Anyway, what is confusing about the theorem that there exist finite > > > ordinals and that there exist infinite ordinals? > > > > The latter. > > HdB is too easily confused. Virgil, that's worthless. Han: put the ordinals 1-1 to the naturals. Ross
From: Ross A. Finlayson on 20 Oct 2006 04:32 Ross A. Finlayson wrote: > MoeBlee wrote: > > Han de Bruijn wrote: > > > The confusion stems from the fact that I cannot and shall not understand > > > the _infinite_ counterparts of the finite cardinals and ordinals. > > > > How can you understand if you won't read a book that explains it? (By > > the way, Halmos is a good book, but it's just an overview; it doesn't > > give you the full explanations that you need.) > > > > So you seem to think it is better to spout nonsense on the Internet > > about a subject you cannot possibly understand since you insist that > > you won't. > > > > MoeBlee > > Did you find that statement in the book about s? > > Skolemize, any model is countable. > > There is no "everything" in ZF. > Well, this thread is getting pretty long. I think I can sum it up by saying nothing. Warm regards, Ross Finlayson
From: imaginatorium on 20 Oct 2006 10:35
Ross A. Finlayson wrote: > Ross A. Finlayson wrote: > > MoeBlee wrote: > > > Han de Bruijn wrote: <chop> > Well, this thread is getting pretty long. I think I can sum it up by > saying nothing. Hmm. If you said nothing, Ross, we would all miss your witticism. I think you mean: "I think I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can sum it up by posting a note commenting that I can [message length exceeded] |