Cantor Confusion
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From: MoeBlee on 26 Oct 2006 19:25 Lester Zick wrote: > >Please quote what I said about 'cardinality' in general terms that is > >not handled by my definition. > > Cardinality(x)=least ordinal(y) with equinumerosity(z). I didn't post that or anything else nonsensical like that. Please don't do that.
From: MoeBlee on 26 Oct 2006 19:25 Lester Zick wrote: > >Please quote what I said about 'cardinality' in general terms that is > >not handled by my definition. > > Cardinality(x)=least ordinal(y) with equinumerosity(z). I didn't post that or anything else nonsensical like that. Please don't do that. MoeBlee
From: MoeBlee on 26 Oct 2006 19:25 Lester Zick wrote: > >Please quote what I said about 'cardinality' in general terms that is > >not handled by my definition. > > Cardinality(x)=least ordinal(y) with equinumerosity(z). I didn't post that or anything else nonsensical like that. Please don't do that. MoeBlee
From: David Marcus on 26 Oct 2006 19:28 MoeBlee wrote: > wrote: > > mueckenh(a)rz.fh-augsburg.de wrote: > > > I guess I can see now the reason of your problems: You don't > > > understand because you are looking for a tanslation always. > > > There is no translation required. The tree is that mathematics > > > which deserves this name. It is outside of your model, > > > independent of ZFC, but generally valid and, therefore; covering > > > ZFC too. > > > > Thank you for finally admitting that your argument can't be given > > within ZFC. > > I don't recall the exact quote. If it is convenient for you, would > you quote him saying that his argument is within Z set theory? As I > recall, I sure thought that was what he said. It sure seemed clear > enough to me that he was claiming to make an argument within Z set > theory, which is the only reason I wasted my time trying to make > sense of his argument. It would be nice to have his exact words and > their context right in front of us. Not sure if he ever said precisely "within Z set theory", but he certainly said things very similar. Below are a few messages that I found. There are probably others. In the first, he says that "standard mathematics contains a contradiction". In the next two, he states there are "internal contradictions of set theory". In the next, I say that he says that "standard mathematics contains a contradiction", and he does not dispute this. David Marcus ---------------------------------------------------------------------- From: mueck...(a)rz.fh-augsburg.de Subject: Re: Cantor Confusion Date: Mon, Oct 9 2006 8:54 am Groups: sci.math David Marcus schrieb: > mueck...(a)rz.fh-augsburg.de wrote: > > David Marcus schrieb: > > > mueck...(a)rz.fh-augsburg.de wrote: > > > > David Marcus schrieb: > > > > > mueck...(a)rz.fh-augsburg.de wrote: > > > > > > Hi, Dik, > > > > > > I would like to publish our result to the mathematicians > > > > > > of this group in order to show what they really are > > > > > > believing if they believe in set theory. > > > > > > There is an infinite sequence S of units, denoted by S = > > > > > > III... > > > > > > This sequence is covered up to any position n (included) > > > > > > by the finite sequences I II III > > > > > > ... > > > > > What do you mean by "cover"? > > > > A covers B if A has at least as many bars as B. A and B are > > > > unary representations of numbers. > > > > Example: A = III covers I and II and III but not IIII. > > > > > > But it is impossible to cover every position of S. > > > > > > So: S is covered up to every position, but it is not > > > > > > possible to cover every position. > > > So, your conclusion is that no finite sequence of I's will cover > > > S. Correct? > > > Is this your entire theorem or is there more to the conclusion? > > My conclusion is: Either (S is covered up to every position <==> S > > is completely covered by at least one element of the infinite set > > of finite unary numbers <==> S is an unary natural) ==> > > Contradiction, because S can be shown to be not a unary natural. > Are you saying that standard mathematics contains a contradiction Yes, obviously. > or that you think mathematics should be done differently? Not mathematics but set theory. Regards, WM ---------------------------------------------------------------------- From: David Marcus Subject: Re: Cantor Confusion Date: Thurs, Oct 12 2006 3:01 am Groups: sci.math mueck...(a)rz.fh-augsburg.de wrote: > William Hughes schrieb: > > mueck...(a)rz.fh-augsburg.de wrote: > > > William Hughes schrieb: > > > > > > In my view we have not gotten very far. We still have the > > > > > > result that there is no list of all real numbers > > > > > That is not astonishing, because there are only those few > > > > > real numbers which can be constructed. > > > > Few? Few compared to what. > > > Compared to the assumed set of uncountably many. > > Funny, you claim that the term "uncountably many" has no > > meaning, but you use it. > You believe in its meaning and in the great set R. > > > > The real numbers that cannot > > > > be constructed? According to you they don't exist. But even > > > > these "few" real numbers cannot be listed! > > > Nevertheless the diagonal proof shows only that there are > > > elements of a countable set which have not yet been constructed.\ > > No, it is much stronger. It shows that any list of constructable > > numbers > > is not complete. > Because it had not been constructed. Nevertheless it shows that the > constructed number belongs to a countable set. Therefore all can be put > in bijection with N --- after the conxtruction is complete. > > > > > > (we need to reinterpret our terms, real numbers are > > > > > > computable real numbers, and a list is a computable > > > > > > function from the natural numbers to the (computable) real > > > > > > numbers). > > > > > > If it gives you a warm fuzzy to say that > > > > > > "Every ball will be removed at some time before noon", > > > > > No. To say that every ball will be removed, is wrong, because there is > > > > > not every ball. > > > > If it gives you a warm fuzzy to say > > > > "For any natural N, the ball numbered N will be removed from > > > > the vase before noon" > > > There is not "any natural" but only those which we can define. > > O, so there are now > not only now but always > > only a finite number of naturals, not even an arbitrarially large > > number. But you continue to prattle on about limits. > > > There is a largest natural which ever will be defined. Hence > > > mathematics in the universe and in eternity has to do with only > > > a very small sequence of naturals. > > > Writing 1,2,3,... is but cheating > > If you want to deal with a system in which there is an unknown > > but largest natural, knock yourself out. > That is nonsense. There is no largest natural! There is a finite set of > arbitrarily large naturals. The size of the numbers is unbounded. > > But you have a long > > way to go before you are even close to being consistent. > It is just the reality. It is impossible to have more than 10^100 > numbers represented by all the bits of the universe. > > And don't attempt to use results from this system to say that > > results from another system are wrong. > > Note that according to you the bal
From: MoeBlee on 26 Oct 2006 19:30
Duplicate posts unintentional. MoeBlee |