Cantor Confusion
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From: Lester Zick on 10 Nov 2006 13:22 On Fri, 10 Nov 2006 02:41:34 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote: >In article <1163098294.339005.143210(a)e3g2000cwe.googlegroups.com> "MoeBlee" <jazzmobe(a)hotmail.com> writes: > > mueckenh(a)rz.fh-augsburg.de wrote: [. . .] >What surprises me is that opposition against it in this way comes from >especially the German posters in this group. They all want to stress >the difference between actual infinity and potential infinity, that >are indeed not mathematical terms, and most other posted do not know >the difference. Is it still the old religious issue? I think so, >based on the postings of at least one of the German posters. It's amazing that 21st century mathematikers cannot analyze the truth of contentions without playing cards:the race card, the religion card, the homeland card, etc. My last name is Zick. I'm American. Period. When it comes to mathematics I'm universalist. Patriotism and religion among others are the last resort of scoundrels. In mathematics these kinds of issues are historical anachronisms unless you can't establish truth in universal terms which it would seem mathematikers can't. ~v~~
From: Lester Zick on 10 Nov 2006 13:28 On Fri, 10 Nov 2006 08:51:29 -0500, Bob Kolker <nowhere(a)nowhere.com> wrote: >Dik T. Winter wrote: >> >> What surprises me is that opposition against it in this way comes from >> especially the German posters in this group. They all want to stress >> the difference between actual infinity and potential infinity, that >> are indeed not mathematical terms, and most other posted do not know >> the difference. Is it still the old religious issue? I think so, >> based on the postings of at least one of the German posters. > >If Cantor's last name had been Shickelgrueber or von Richthoffen, none >of this would be written. Would you care to play the race card next, oberfuehrer? If you can't argue truth in universal terms you might just as well play cards, Bob. ~v~~
From: MoeBlee on 10 Nov 2006 13:30 mueckenh(a)rz.fh-augsburg.de wrote: > That is what I said. omega is a limit. omega is a limit ordinal. 'is a limit ordinal' has a specific definition. > In modern set theory there are > limits. Yes. > Further this (Cantor's) definition supports my definition of > definition. Your "definition" of 'definition'. Oh boy, another gem from the Pandora's box that is your mind. MoeBlee
From: Lester Zick on 10 Nov 2006 13:31 On Thu, 9 Nov 2006 19:11:01 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >Lester Zick wrote: >> On Thu, 9 Nov 2006 00:09:14 -0500, David Marcus >> <DavidMarcus(a)alumdotmit.edu> wrote: >> >> >mueckenh(a)rz.fh-augsburg.de wrote: >> >> William Hughes schrieb: >> > >> >> > It is not true that a set cannot exist unless it has a maximum element. >> >> >> >> It is true, at least if all of its elements do exist. >> > >> >The set of natural numbers does not have a maximum element, so what you >> >just wrote is clearly false. Want to try again? >> > >> >> But in order to force you to understand that simple truth, >> > >> >Calling something a "simple truth" does not make it more believable, >> >especially when it is so easy to give an example to show that it is >> >false. >> >> Look who's talking. Is believability your criterion of truth in >> mathematics? > >Nope. In mathematics, we use proof. Proof of what pray tell? >> Is "no contrary examples to show that it is false" your >> criterion of truth in mathematics? > >Nope. But, a contrary example is a proof that the statement is false. Well not exactly. It's at best only proof of inconsistency with your particular axiomatic assumptions. >> I suspect mathematics requires some >> criterion of truth more substantial than your naive credulity. > >Indeed. That is why we prove things using axioms. Oh I see. So you're axiomatic assumptions are true? ~v~~
From: MoeBlee on 10 Nov 2006 13:37
mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > > > > This number does not exist. The diagonal has not omega positions. > > > > So I guess the answer to my question is that you are not prepared to > > show that my proof has anything more than first order logic applied to > > Z set theory nor are you prepared to demonstrate a contradiction in Z > > set theory. > > Your proof shows either a contradiction in Z or it shows that Z is > false. You've shown no contradiction in Z. And if 'false' means 'in conflict with WM's intuitions', then, we'll just have to live with the fact that Z is in conflict with your intuitions. > Z contains a contradiction to your proof, if one can show in Z that a > diagonal of a matrix has not more elements than every line. You've not shown that. > Z is false, > if one cannot show that. Z is in conflict with your intuitions then. > So, why further bother about Z? Yes, you should not bother about Z. MoeBlee |