Galileo's Paradox
in [Math]
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From: Virgil on 5 Dec 2006 17:51 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.
From: Virgil on 5 Dec 2006 17:53 In article <45759B75.5010005(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > > All numbers are ficticious so call a number or a set of numbers > > ficticious is redundant and conveys no information. > > > > Bob Kolker > > > > 1,000,000.00 Mark were paid for spreading this fog. And cheap at the price.
From: Virgil on 5 Dec 2006 17:55 In article <45759C29.7040003(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/4/2006 9:54 PM, Bob Kolker wrote: > > Eckard Blumschein wrote: > >> > >> You are right if you consider each time the complete set. Neither the > >> integers not the rationals are actually complete. So both complete sets > > > > Really? Tell me an integer or rational that is not in the set of > > integers or rationals? Which ones did we miss? > > > > Bob Kolker > > Read carefully: I did not write set of integers, I just wrote the > integers. The complete set of integers is something quite different. When you speak of "the integers" do you mean all of them on not. If you do mean "all, then the set of all of them is all of them.
From: Virgil on 5 Dec 2006 18:01 In article <45759E91.309(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/4/2006 9:49 PM, David Marcus wrote: > > >> According to my reasoning, the power set is based on all elements of a > >> set. > > > > "Based"? > > 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. And oo is NaN, 2^oo has no meaning. > > > > >> 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? > > > > >> 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? to consist of an actually infinite amount of fictitious > elements. > > My topic is not relegion but outdated quasi-religious mathematics. When you can rid yourself of them, you will be better off.
From: Virgil on 5 Dec 2006 18:03
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. |