Galileo's Paradox
in [Math]
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From: Bob Kolker on 6 Dec 2006 12:02 Mike Kelly wrote: > > > By "b)" I was referring to the statement > > "(b) proper subsets are smaller than their supersets " what do you mean by "smaller"? If you mean the cardinality, what you say is just plain wrong. The set of even integers has the same cardinality as the set of integers, for example. > > that was made several posts earlier in the thread. SixLetters doesn't > see why this leads to a contradiction. I tried to explain it. Whatever you "explanation", if you are referring to cardinality you are just plain wrong. Bob Kolker >
From: Eckard Blumschein on 6 Dec 2006 12:03 On 12/6/2006 12:01 AM, Virgil wrote: > In article <45759E91.309(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >> Yes. The power set algorithm does not change what mathematicians still >> used to call cardinality. 2^oo=oo. > > What "algorithm does EB refer to? Power sets come from axioms, not > algorithms. 2^aleph_0 does not come from axioms. Look for Pascal's triangle. > > And oo is NaN, 2^oo has no meaning. You are a knowing-all. >> >> In case of an infinite set, there are nor all elements available. >> > >> > "Available"? >> >> Yes. You cannot apply the algorithm until you have all numbers. > > What "algorithm? For calculating binominal coefficients. >> >> > >> >> Nonetheless I can do so as if they would exist, and I am calling them a >> >> fiction. >> > >> > "Exist"? "Fiction"? >> >> Exist means, they have their numerical address within a rational order. >> Fiction means, they don't have it but it is reasonable to do so as if. >> >> > >> >> Fictions are uncountable. >> > >> > "Uncountable"? >> >> The continuum cannot really be resolved into countable elements. > > What do you mean by the "uncountability" of one element? How can one > element sometimes be countable and sometimes not? Your question is justified. In order to be part of a counted or at lest countable plurality, each element has to be discrete and addressable. So the number 1 may belong to a finite set as well as to a cuntable infinite set. However 1.000... with perfectly oo much of significant nils is not immediately a countable element. It rather belongs to a fictitious uncountable continuum which also includes the not really existent but merely fictitious irrational "numbers" like pi. The plurality arount number 1 obeys trichotomy. The 1.000... does not. This makes the latter fictitious. > > to consist of an actually infinite amount of fictitious >> elements. > >> >> My topic is not religion but outdated quasi-religious mathematics. > > When you can rid yourself of them, you will be better off. Fortunately, I was never trained in set-quasi-religion.
From: Eckard Blumschein on 6 Dec 2006 12:04 On 12/6/2006 12:03 AM, Virgil wrote: > In article <4575A9EE.5090102(a)et.uni-magdeburg.de>, > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > >> > What are fictitious real numbers? >> >> Fictitious real numbers are defined by DA2 > > 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.
From: Georg Kreyerhoff on 6 Dec 2006 12:05 Eckard Blumschein schrieb: > Fortunately, I was never trained in set-quasi-religion. So you admit that you don't know what you are talking about. Georg
From: Bob Kolker on 6 Dec 2006 12:08
Eckard Blumschein wrote: > > > Fortunately, I was never trained in set-quasi-religion. Set theory is not a religion. It is one of many abstract mathematical systems. You might as well refer to group theory as a "quasi-religion". In a sense all mathematical systems are "quasi-religions" so calling one of many mathematical systems a quasi-religion says nothing. Your use of pejoratives is unsabstantial and reveals to all who see that you are a shallow silly person. Bob Kolker |