An uncountable countable set
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From: imaginatorium on 20 Oct 2006 02:41 MoeBlee wrote: > You wrote too many confused and uninformed things for me to even care > to sort through. You don't say who "you" is... let me spend a little while guessing. Oh, but I'll read on while I'm guessing. > I'll take you up on your last line, though: > > > You > > say you set theory texts define "cardinality" in a certain way which > > is pretty much circular if relying on cardinality for equinumerosity. > > I don't say that. And the definition of 'cardinality of' does use > 'equinumerosity', but the definition of 'equinumerosity' does not use > 'cardinality of', so there is not the circluarity you just arbitarily > claim there to be. I've already been over the subject of mathematical > definitions with you in other threads. But please do consider all your > points, objections, and conceptions to be vindicated by my increasing > apathy to try to bring you to reason about anything at all. Good news, Lester! I think you're going to win!! Brian Chandler http://imaginatorium.org
From: Han de Bruijn on 20 Oct 2006 03:13 MoeBlee wrote: > Han de Bruijn wrote: > >>MoeBlee wrote: >> >>>Han de Bruijn wrote: >>> >>>>But why are the finite ordinals not equivalent with the naturals (I mean >>>>in mainstream mathematics)? >>> >>>The set of finite ordinals IS the set of natural numbers. >>> >>>x is a natural number <-> x is a finite ordinal. >>> >>>Why don't you just read a textbook? >> >>It's all very confusing. Because there also "exist" infinite ordinals, >>they say. > > 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*. > Anyway, what is confusing about the theorem that there exist finite > ordinals and that there exist infinite ordinals? The latter. Han de Bruijn
From: Han de Bruijn on 20 Oct 2006 03:14 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. Han de Bruijn
From: Han de Bruijn on 20 Oct 2006 03:17 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? I understand very well that infinite cardinals and ordinals simply do not exist. Han de Bruijn
From: Virgil on 20 Oct 2006 03:33
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. |