Cantor Confusion
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From: David Marcus on 23 Oct 2006 21:56 Dik T. Winter wrote: > In article <1161518008.776999.238550(a)k70g2000cwa.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: > > Dik T. Winter schrieb: > > > In article <1161435575.019298.164830(a)e3g2000cwe.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: > > > > > You think so. The irrational numbers are defined to be the limits > > > > > of some particular sequences (or rather as equivalence classes of > > > > > sequences). I > > > > > > > > Equivalence classes of sequences with same limit like > > > > lim {t --> oo} a_t. > > > > > > Wrong. > > > > Wrong is wrong. The limit *is* the irrational number. You can use > > these and only these numbers in a Cantor list, not the equivalence > > classes of sequences. > > You really do not understand how the reals are defined. The limit is > *not* the irrational number. The limit does not even exist. Indeed. If we already had irrational numbers, we wouldn't need to define them as equivalence classes of Cauchy sequences of rationals. -- David Marcus
From: David Marcus on 23 Oct 2006 22:01 Han de Bruijn wrote: > David Marcus wrote: > > mueckenh(a)rz.fh-augsburg.de wrote: > >>MoeBlee schrieb: > >>>First you say the notion of 'rational relation' (whatever that means) > >>>"cannot be expressed by mathematical notion". Then you challenge me to > >>>say what part of your proof is in conflict with set theory. What is the > >>>notion of 'rational relation' that "cannot be expressed by mathematical > >>>notion"? Are defining a certain relation in set theory or are you > >>>definining a relation you claim not to exist in set theory? > >> > >>Meanwhile there are many who understand the binary tree. Perhaps you > >>will follow the discussion, then you may understand it too. > > > > But, no one seems to understand your binary tree. Please state your > > claim and its proof using standard terminology and words that you > > clearly define. For example, use the terminology that Halmos uses in > > "Naive Set Theory". If you don't like that book, then pick a book you > > like and tell us what it is. > > There are many readers here who DO understand Mueckenheim's binary tree. > And no, binary trees will not be found in Halmos' "Naive Set Theory". > Because it's too naive, I suppose .. You mean all the cranks think they understand it. If they really understood it (and it made sense--a rather big assumption that), they could explain it in standard language. It isn't even that much fun to banter with Mueckenheim because so little of what he says is even understandable. -- David Marcus
From: David Marcus on 23 Oct 2006 22:06 Han de Bruijn wrote: > And no, binary trees will not be found in Halmos' "Naive Set Theory". > Because it's too naive, I suppose .. I don't see how you would know it is not there since you said that while you own the book, you've never read it. Funny how books aren't much use if you don't actually read them. Anyway, I didn't say binary trees were in the book. I said that if Muckenheim wants to talk using the mathematical concepts of sets, functions, and relations, he should use standard terminology, where "standard" means the same as in some mathematics book. It is like saying that if he wants to speak in English he should use words according to the meanings as given in an English dictionary. Or, he could continue to do as Humpty Dumpty did and use his own meanings for words without telling people what they are. -- David Marcus
From: David Marcus on 23 Oct 2006 22:08 Han de Bruijn wrote: > Bob Kolker wrote: > > Han de Bruijn wrote: > >> > >> True. And you haven't seen any binary tree either. > > > > Bullshit. One can trivially construct finite binary trees. To "see" one > > is to think one. We can think binary trees as simply as we can think of > > a triangle with one of its sides removed. Three points, two sides. V for > > victory. > > Did I say that _you_ haven't seen any binary tree? I thought this was > a response to David Marcus, who hasn't seen any, it seems. No idea why you think that. You might try reading what I actually write. -- David Marcus
From: David Marcus on 23 Oct 2006 22:12
mueckenh(a)rz.fh-augsburg.de wrote: > Here are short answers to further postings which I put together in this > one because after 15 postings I am always cut off for hours. Could someone explain how come MB is cut off after 15 postings? His parents take away his computer? -- David Marcus |