Galileo's Paradox
in [Math]
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From: Eckard Blumschein on 11 Dec 2006 09:53 On 12/6/2006 8:57 PM, Virgil wrote: > In article <4576EF9A.80408(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/5/2006 11:51 PM, Virgil wrote: >> > In article <45759B2C.1030500(a)et.uni-magdeburg.de>, >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> > >> >> On 12/4/2006 9:56 PM, Bob Kolker wrote: >> >> > Eckard Blumschein wrote: >> >> > >> >> >> >> >> >> >> >> >> 2*oo is not larger than oo. Infinity is not a quantum but a quality. >> >> > >> >> > But aleph-0 is a quantity. >> >> > >> >> > Bob Kolker >> >> >> >> >> >> To those who belive in the usefulness of that illusion. >> > >> > Despite the naysaying of those like EB who have the illusion of their >> > beliefs. >> >> The neys will have it on condition they do not adhere any illusory belief. > > If EB is any representative, then his adhering to as many illusions as > he does represents their utter faliure. Can you reveal just one illusion of mine?
From: Eckard Blumschein on 11 Dec 2006 10:03 On 12/6/2006 8:33 PM, Virgil wrote: > In article <4576E3FF.9090803(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/5/2006 11:14 PM, Virgil wrote: >> > In article <457584A4.3000108(a)et.uni-magdeburg.de>, >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> > >> >> On 12/5/2006 12:16 AM, Virgil wrote: >> >> > In article <4574755B.4070507(a)et.uni-magdeburg.de>, >> >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> > >> >> >> 2*oo is not larger than oo. Infinity is not a quantum but a quality. >> >> > >> >> > Which "infinity" is that? >> >> >> >> We do not need different infinities. >> > >> > Cantor did. And showed why with two separate proofs. >> >> I pointed to the 4th and only correct possibility of interpretation to DA2. > > That is your opinion, but not one accepted by the mathematically > literate. One has to be pretty literate in order to know this well hidden option. > > >> Do not hope for maintaining the proof concerning the power set. > > Do not hope to destroy what you do not understand. Well, I had to understand the illusions first. > >> The reason why the power set is also uncountable is quite simpel > > And Cantor showed it. No. Cantor again merely showed by contradiction that the power set is not countable. The reason is: Already the entity of all natural numbers is an uncountable fiction.
From: Eckard Blumschein on 11 Dec 2006 10:13 On 12/6/2006 9:10 PM, Virgil wrote: > In article <4576F816.5060809(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/6/2006 12:03 AM, Virgil wrote: > >> > DA2 does not define anything. But if they were to b e defined by a >> > theorem, they would already be defined by what I will call DA1. >> >> DA1 dealt with rationals. > > By DA1 I was referring to Cantor's first proof of the uncountability of > the reals, and it deals with far more than the rationals. ??? What paper? Do you mean Cauchy's zig-zag diagonalization?
From: Eckard Blumschein on 11 Dec 2006 10:55 On 12/6/2006 9:16 PM, Virgil wrote: > In article <4576F944.2000607(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> On 12/6/2006 12:06 AM, Virgil wrote: >> > In article <4575B119.2050709(a)et.uni-magdeburg.de>, >> > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> > >> >> On 12/4/2006 11:32 AM, Bob Kolker wrote: >> >> > Eckard Blumschein wrote: >> >> > >> >> >> Notice, there is not even a valid definition of a set which includes >> >> >> infinite sets. Cantor's definition has been declared untennable for >> >> >> decades. >> >> > >> >> > That is simply not so. For example the set of integers. There is is. >> >> >> >> Perhaps, you are honestly bold. Believe me that Fraenkel admitted that >> >> Cantor's definition is untennable. >> > >> > So Fraenkel is wrong! >> >> This time definitely not. > > That is your opinion, but since yours is the opinion of a > non-mathematician, its relevance to anything mathematical is negligible. When communism broke down, the comrads urged us not to start a discussion of their errors. The same is my impression concerning naive set theory. Once mathematicians start, the whole ideology will collapse. >> >> The question is e.g. in case of the >> >> naturals whether they are considered one by one or altogether like an >> >> entity. While a set is usually imagined like something set for good, >> >> this point of view is unrealistic. >> > >> > It is essential. And since all numbers are unrealistic in that they are >> > only imagined, that is no handicap. >> >> Unrealistic means self-contradictory. > > I fail to find self-contradictory anywhere in the following definition > of "unrealistic". Can EB give a citation which does include that meaning? > > <quote> > Proximity/Merriam-Webster U.S. English Thesaurus > > 1 meaning(s) for Unrealistic > > 1. (adj) incapable of dealing prudently with practical matters > (synonym) Impractical, Ivory-tower, Ivory-towered, Ivory-towerish, > Nonrealistic, Unpractical, Viewy > (related) Idealistic, Otherworldly, Quixotic, Romantic, Starry-eyed, > Visionary > (contrast) Commonsensible, Commonsensical, Realistic, Sensible, > Worldly-wise > (antonym) Practical > <unquote> Although biased, Christian Betsch, Fictions in Mathematics is better.
From: Eckard Blumschein on 11 Dec 2006 10:59
On 12/6/2006 8:01 PM, Bob Kolker wrote: > Eckard Blumschein wrote: >> >> I did not say this. Please quote me carefully. >> The set of existing Dedekind cuts is finite. The set of feasible cuts is >> countable. > > The set of Dedikind cuts is not finite. There is a Dedikind cut for each > rational number for starters. Why do you say such stupid things? Because Dedekind himself admitted that he cannot provide any evidence substantiating his basic assumption. There is not a Dedekind cut for each rational number. > > Bob Kolker > |