Galileo's Paradox
in [Math]
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From: MoeBlee on 11 Dec 2006 15:04 Tony Orlow wrote: > A formal language is a set of strings: > http://en.wikipedia.org/wiki/Formal_language > I suppose now you're going to tell me I'm using nonstandard language.... Wikipedia. What a lousy basis for the subject of formal languages. MoeBlee
From: Virgil on 11 Dec 2006 15:21 In article <457D504B.2040402(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/6/2006 9:08 PM, Virgil wrote: > > In article <4576F7E0.3090102(a)et.uni-magdeburg.de>, > > Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > >> > And oo is NaN, 2^oo has no meaning. > >> > >> You are a knowing-all. > > > > oo is, at best, ambiguous. > > In what respect? Which of the several separate notions of infinite is it supposed to represent? Cardinal? Ordinal? Real compactification? Geometric? Etc. > > > >> >> >> In case of an infinite set, there are not all elements available. > >> >> > > >> >> > "Available"? > >> >> > >> >> Yes. You cannot apply the algorithm until you have all numbers. > >> > > >> > What "algorithm? > >> > >> For calculating binominal coefficients. > > > > What does one need that for in accepting the axiom of the power set? > > Is there evidence for the reals as characterised by DA2 to actually fit > ZFC? How is that relevant to your "calculating binomial coefficients" claim? Avoiding a question by asking an unrelated one is a copout. > > This is Bolzano's religious thinking. It is far preferrable to EB's religious thinking. > Pi is not isolated within e.g. the > system of decimal numbers but merely like a problem. EB isolates himself among the kooks, which is only part of his problems. > > > >> Fortunately, I was never trained in set-quasi-religion. > > > > No mathematicians have been either, but mathematicians also have not > > been trained in your anti-set-actual-religion either.
From: Virgil on 11 Dec 2006 15:29 In article <457D53C3.3060308(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/6/2006 5:48 AM, David Marcus wrote: > >> Exist means, they have their numerical address within a rational order. > > > > Define "numerical address" and "rational order", please. > > The words are self-explaining. If EB cannot explain them then they men nothing. If EB will not explain them, it must be because he dare not. > > > >> Fiction means, they don't have it but it is reasonable to do so as if. > > > > So, "fiction" means "not exist, but reasonable to do so as if". What > > does "reasonable to do so as if" mean? > > Exactly what e.g. Leibniz or Vaihinger or to some extent Robinson > understood. But which EB is incapable of explaining. > > "uncountable" mean? > > Uncountable is > definitely not a property of numbers. Numbers are always countable. > Nonetheless a single real "number" is uncountable. Typical self-contradiction. "Uncountable" of an object means that it is a set whose members cannot be injected into the set of naturals. Which Dedekind cuts does EB claim are uncountable by this definition? > > >> >> So this power set has no chance but > >> >> to be also uncountable. > >> >> Try to get the title cardinal Kolker, or at least Bob the Builder and I > >> >> will possibly convert. > >> > > >> > When you tire of religion, you could always learn some math. > >> > >> My topic is not relegion but outdated quasi-religious mathematics. > > > > You are the one reading old papers by Cantor instead of reading modern > > mathematics texts. Why do you think that what you read has any relevance > > to modern, current, up-to-date mathematics? > > Some basic errors were not yet eradicated. Those that EB keeps making are the only ones currently visible.
From: stephen on 11 Dec 2006 15:39 MoeBlee <jazzmobe(a)hotmail.com> wrote: > Tony Orlow wrote: >> A formal language is a set of strings: >> http://en.wikipedia.org/wiki/Formal_language >> I suppose now you're going to tell me I'm using nonstandard language.... > Wikipedia. What a lousy basis for the subject of formal languages. > MoeBlee In the theory of computation, a language is simply a set of strings. The phrase "formal language theory" is used to describe the subject matter of regular expressions, grammars and Turing Machines, and in all those cases a language is simply a set of strings. For plenty of examples of this usage, see http://www.bestwebbuys.com/Language_Arts-General-N_10016622-books.html Stephen
From: Virgil on 11 Dec 2006 15:40
In article <457D57A7.8080605(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > On 12/6/2006 5:17 PM, Tez wrote: > > Eckard Blumschein 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. > > > > "The" power set "algorithm"? Could you write out "the" algorithm here > > for us so that you and I can flesh out your claims in detail? > > If you have N elements, you will get 2^oo combinations > (cf. Pasqual's triangle) How does EB think he can deduce that N = oo? EB must think he has deduced it as Pascal's triangle requires that the power set of a set of n members has 2^n members, not 2^m for m != n. > > In mathematics existence means common properties. What about the reals, > we have to distinguish genuine and putative reals. > > Genuine reals are those which were assumed for DA2 and are indeed > uncountable since they have an actual infinite number of decimals. > > Putative reals are defined by Dedekind's cut, nested intervals, Cauchy > limits if the tiny word fictitious is missing and the like. Then let us eliminate all "genuine" reals, which according to EB are individually uncountable objects and restrict ourselves to what EB calls putative reals, the Dedekind cuts, each of which is, as a set, countable with cardinality 2. It is quite easy, via cantors first proof, to prove the uncountability of the set of Dedekind cuts even though each cut, being a finite set, is countable. |