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From: Eckard Blumschein on 14 Apr 2005 04:54 On 4/13/2005 6:47 PM, Randy Poe wrote: > Eckard Blumschein wrote: >> On 4/13/2005 2:10 PM, David Kastrup wrote: >> > Nonsense. Cantor never made such a list. >> >> At first he assumed that all reals are represented in his list. >> Then he showed that at least one number is not contained in his list. > > Is proof by contradiction one of the things you don't > understand? > > Do you know that if I begin a proof with: "Assume the > square root of 2 is rational" that it does not mean I > think the square root of 2 is rational? Why do you consider me stoopid? What about proofs, I am requesting you to prove that there are numbers of a higher cardinality than aleph_1. Eckard
From: Giuseppe Bilotta on 14 Apr 2005 05:45 On Thu, 14 Apr 2005 10:54:17 +0200, Eckard Blumschein wrote: > numbers > of a higher cardinality than aleph_1 Given any finite or infinite set A, the set P(A) of the parts of A (the set of all the subsets of A) can be shown to be strictly 'bigger' (of cardinality strictly bigger) than A. So just take the set of the parts of any set with cardinality aleph_1 and you get such a set. -- Giuseppe "Oblomov" Bilotta "They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety." Benjamin Franklin
From: Giuseppe Bilotta on 14 Apr 2005 05:48 On Wed, 13 Apr 2005 19:24:42 +0200, Eckard Blumschein wrote: > You are wrong. The only difference between the decimal representation of > real and rational numbers resides in the number of numerals. It is just > potentially infinite in case of rational numbers but actually infinite > in case of the reals. Accordingly, the series of numerals may be as > large as you like but must be considerd eventually finite in case of > rationals while it never ends in case of reals. As soon as we have > finite numbers of numerals for each number to be represented, one may > name any successor. > The set of real numbers between 0 and 1 is finite. Cool. So for example, 1/3 has a finite representation. Like, 0.333333......3 Which has, say, N digits. So 1/3= 3...3/10^(N+1). Or, 10^(N+1)=9....9 Cool. Very cool. Ah. Would you mind enumerating all the real numbers between 0 and 1? -- Giuseppe "Oblomov" Bilotta [W]hat country can preserve its liberties, if its rulers are not warned from time to time that [the] people preserve the spirit of resistance? Let them take arms...The tree of liberty must be refreshed from time to time, with the blood of patriots and tyrants. -- Thomas Jefferson, letter to Col. William S. Smith, 1787
From: Barb Knox on 14 Apr 2005 05:51 In article <425D55DA.80001(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: [snip] >The set of real numbers between 0 and 1 is finite. Surely you jest. -- --------------------------- | BBB b \ Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | -----------------------------
From: Giuseppe Bilotta on 14 Apr 2005 05:56
On Wed, 13 Apr 2005 18:53:39 +0200, Eckard Blumschein wrote: > I would just like to try and comment > on "enlarging a set" in case of infinite sets: This simply does not work. Like those pills they keep spamming around? :) -- Giuseppe "Oblomov" Bilotta "They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety." Benjamin Franklin |