Cantor Confusion
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From: Eckard Blumschein on 7 Dec 2006 08:57 On 12/7/2006 1:54 AM, Dik T. Winter wrote: > > Could you read a pdf version? > Yes. I will add it to M283 as soon as possible. > > It started with the question how to deal with the nil in case of > > splitting IR into IR+ and IR-. I got as many different and definitve > > answers as there are possibilities. I expected that there is only one > > correct answer, and I found a reasoning that compellingly yields just > > one answer in case of rationals and a different one in case of reals. > > Oh, well. In Bourbaki's mathematics R+ and R- both contain 0. So you > are a follower of Bourbaki after all? But of course the 0's are the > same. If they were different you would have quite a few problems with > limits and continuity. According to my reasoning, any really real number is not unique but must rather be void because even the tiniest interval is thought to contain indefinitely not just many rational numbers but indefinitely much of real numbers. Therefore, unreachable the very nil on top of the nested intervals has not any significance at all. It cannot even be distinguished from numbers 0- and 0+ left and right from it, respectively, because the diffence is zero. So I agree with the Bourbakis perhaps for the first time: 0+ and 0- are indiscriminable in IR. However among the rationals, the nil is the first negative number according to my reasoning and my old encyclopedia.
From: Bob Kolker on 7 Dec 2006 09:47 mueckenh(a)rz.fh-augsburg.de wrote: > > > You cannot imagine the integer [pi*10^10^100]. That is not an integer, dummkopf. It is an irrational real number. Bob Kolker
From: David Marcus on 7 Dec 2006 10:02 mueckenh(a)rz.fh-augsburg.de wrote: > MoeBlee schrieb: > > > > > There is nothing in that that shows that a set is not a fixed entity. > > > > > > The universe of all sets can grow. Define: "The universe of all sets is > > > called the set of all sets", and you see it. > > > > As to what Fraenkel, Bar-Hillel, and Levy wrote, they are underscoring > > the fact that different axioms yield different universes of sets. That > > is what they mean by the universe of sets "growing" (scare quotes in > > original text). > > You should try to distinguish between "to differ" and "to grow". You > may scream as loud as you can. These verbs are different and denote > different processes. That is amusing: someone whose native language is not English explaining to native English speakers what the words in a book written in English mean. > > > An easy example which > > > should not escape you: The set of states of the EC has been growing and > > > probably will continue to grow. > > > > Which you'll have a hard time proving to be a set in Z set theory. > > Of course in set theory there are variables denoting sets. In any book > on ZF set theory you can find sentences like: "The letters X and Y in > these expressions are variables; they stand for (denote) unspecified, > arbitrary sets." By such tools it is very easy to deal with a set like > the set of states of the EC in ZF. It turns out again and again that > you have very little knowledge about set theory and its philosophy. Another language problem: you completely misunderstand what the word "variable" means in this context. Variables don't vary. They are simply names. > I am sorry but as your behaviour parallels your expertise I will no > longer discuss with you. Again, a promise to stop posting. If only you would keep such promises. > A last hint may help you to become a decent > person and socialize with your surrounding: You should know that it is > not appropriate to speak out everything one thinks. In general it is > not useful to injure persons. What would it help if I publicly uttered > what I think of you? Oh, I'm sure we already know. -- David Marcus
From: David Marcus on 7 Dec 2006 10:09 Eckard Blumschein wrote: > On 12/5/2006 8:52 PM, Virgil wrote: > > In article <1165322064.705072.182240(a)80g2000cwy.googlegroups.com>, > > mueckenh(a)rz.fh-augsburg.de wrote: > > > >> The number of your contributions has increased by 1 with your post I > >> just answer. The same holds for the set of your contributions. > > > > Such time dependent "sets" are not the same as sets under the rubric of > > set theories, as they do not, for example, obey the axiom of > > extensionality. > > Fraenkel 1923, p.190: > "Dieses Axiom besagt, dass eine Menge m als vollst�ndig festgelegt gilt, > sobald bestimmt ist, welche Elemente in ihr enthalten sind." How is that relevant? Anyway, you should stop quoting from books that you obviously don't understand. Try to stick to simple things. -- David Marcus
From: David Marcus on 7 Dec 2006 10:13
stephen(a)nomail.com wrote: > Nobody but you has talked about "growing" sets. Sets, like numbers, do not > grow. You, like many other people who do not understand set theory, > think of sets as mutable objects, that change as we perform operations > on them. This is akin to thinking that numbers change when we perform > addition. If I add 3 to 7, neither 3 or 7 changes. It is such an odd belief. Why use a set for something that a function is naturally for? I don't really understand why cranks insist on using sets for everything, while at the same time insisting that sets are useless or illogical or whatever. -- David Marcus |