Cantor Confusion
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From: Eckard Blumschein on 8 Dec 2006 06:29 On 12/8/2006 1:06 AM, David Marcus wrote: > mueckenh(a)rz.fh-augsburg.de wrote: >> Virgil schrieb: >> > In article <4576BC30.2000101(a)et.uni-magdeburg.de>, >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> > >> > It is evident that EB understands "infinity" even less that Cantor. >> >> That is a hard attack! To understand the infinite even less than >> Cantor??? Yes. Sometimes he made reasonable remarks like: Infinity is a gulf. (He did not refer to GIs.) Sometimes he revealed his much too intuitive way of thinking: I see it but I cannot believe it. If he really understood infinity as good as an average student of electrical engineering he would never have been so presumptious as to declare one infinity larger than an other one. His approach was wrong, and his decisive proofs were fallatiously interpreted. >> I don't know anybody who understood the infinite better than Cantor, >> not even approximately as well. If so, then tell me what is wrong with Spinoza's definition. > Then why do you disagree with Cantor's results? This is a good question.
From: Bob Kolker on 8 Dec 2006 06:30 Eckard Blumschein wrote: > > > Read completely what I wrote and be ashamed of your arrogance. You have not defined the concept "exact numerical address". You have waved your hands. Define the concept without giving "examples". Bob Kolker
From: Eckard Blumschein on 8 Dec 2006 06:35 On 12/8/2006 1:05 AM, David Marcus wrote: > Eckard Blumschein wrote: >> On 12/5/2006 9:23 PM, Virgil wrote: >> >> >> Do not confuse Cantor's virtue of belief in god given sets with my power >> >> of abstraction. >> > >> > Cantor's religious beliefs are as irrelevant as EB's beliefs in his own >> > infallibility. >> >> I am not infallible. Show me my errors, and I will express my gratitude. > > Show you your errors or convince you that they really are errors? The > former is simple, but the latter appears to be impossible. We can't > force you to learn, if you don't wish to. I can force you to either refute e.g. my hint that Cantor's definition of a set has been declared untenable or tacitly accept this fact.
From: Eckard Blumschein on 8 Dec 2006 06:53 On 12/8/2006 12:54 AM, David Marcus wrote: > Eckard Blumschein wrote: >> 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. > > I'm sure Dik can't wait. > >> > > 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. > > That's gibberish. Trying speaking English. In English much refers to uncountables while many belongs to countables. I intended to stress that rationals are countable while reals are uncountable. Of course, my corresponding wording is hard to swallow if you not just imagine numbers countable what they certainly are but also real numbers numbers what the reals according to Kronecker not really are. >> Therefore, unreachable the very nil on top of the nested >> intervals has not any significance at all. > > More gibberish. Or, maybe poetry. No, just 'the' illposed. I meant: Therefore, the unreachable very zero on top of... >> It cannot even be >> distinguished from numbers 0- and 0+ left and right from it, >> respectively, because the diffence is zero. > > Are you saying that there are numbers 0- and 0+? Are these rational? > Real? What are their definitions? Limits from the left and from the right. > >> So I agree with the >> Bourbakis perhaps for the first time: 0+ and 0- are indiscriminable in >> IR. > > That's certainly not what Dik said Bourbaki said. Should I read Bourbaki? What book? >> However among the rationals, the nil is the first negative number >> according to my reasoning and my old encyclopedia. > > What is "nil"? Zero? Are you saying zero is negative? If so, define > "negative". Negative is the opposite of positive. Subtraction of a number A from a number B yields a result outside IN iff A is at least as large as is B.
From: Eckard Blumschein on 8 Dec 2006 07:00
On 12/7/2006 10:51 PM, Lester Zick wrote: > On Thu, 07 Dec 2006 10:43:31 -0800, Mark Nudelman > <markn(a)greenwoodsoftware.com> wrote: > >>On 12/7/2006 3:15 AM, Eckard Blumschein wrote: >>> Just try and refute: >>> >>> Reals according to DA2 are fictitious >>> Reals according to DA2 are fictitious >>> With fictitious I meant: They must not have a directly approachable >>> numerical address. This was the basis for the 2nd DA by Cantor afer an >>> idea by Emil du Bois-Raymond. >>> >>> Good luck >>> >> >>Can you define what you mean by a "directly approachable numerical address"? > > The definition of "directly approachable numerical address" is "Q" > since according to David Marcus definitions are "only abbreviations". > > ~v~~ Excellent. Can you tell me what ~v~~ abbreviates? |