Cantor Confusion
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From: mueckenh on 5 Jan 2007 07:40 Virgil schrieb: > >Otherwise I had to assume that the union of all finite binary > > trees is identical to the complete binary tree, as far as nodes and > > egdes are concerned, but that the trees are not identical as far as > > paths are concerned. > > What is wrong with assuming what is easily provable? As every edge and > node is a member of some finite path of some finite tree, each must be > in the union. So it is. > But no infinite path is a member of any finite tree, so > none can be members of a union of finite trees. So where are the nodes and edges which make the infinite paths longer than any finite path? > > I cannot accept ghosts in mathematics, but, of course, I cannot prove > > that they do not exist. So we are finshed with this topic. > > WE, on the other hand, can prove that what WM regards as ghosts do exist > in several versions of set theory. That makes these versions of set theory vakueless. >As WM has no specific version of his > own, he effectively has none at all. There is no version of infinity other than by belief in ghosts (lacking mathematical spirit) Regards, WM
From: mueckenh on 5 Jan 2007 07:45 Virgil schrieb: > > > Not all natural numbers in unary representation 0.1, 0.11, 0.111, ... > > exist. > > They do in ZFC or NBG. Is that the theory which requires different paths from identical nodes in the binary tree? Virgil, if you believe that stuff, then any discussion with you will be in vain, in particular in fields where the contradictions are not so obvious. Regards, WM
From: Franziska Neugebauer on 5 Jan 2007 07:48 mueckenh(a)rz.fh-augsburg.de wrote: > Franziska Neugebauer schrieb: >> mueckenh(a)rz.fh-augsburg.de wrote: >> >> > David R Tribble schrieb: >> >> David R Tribble schrieb: >> >> >> Well, now I'm confused. Could you provide an example of a >> >> >> natural number that does not exist? >> >> > >> >> >> >> mueckenh wrote: >> >> > Take the first 10^100 digits of pi (if you can - but you >> >> > cannot). It is impossible to bring this number to existence in >> >> > the whole universe. >> >> >> >> Can you "bring into existence" the number 1? >> > >> > Here it is: >> > >> > . >> >> [X] a dot > > One clear representation of number 1, sufficient to identify it. Not > only a name. A: Can you bring into existence God? WM: Here it is: - FN: [X] a dash [ ] God WM: One clear representation of God, sufficient to identify it. Not only a name. F. N. -- xyz
From: mueckenh on 5 Jan 2007 07:52 Franziska Neugebauer schrieb: It is without any value to follow your text. 1) My "ideas" are identical with what you call irrational numbers. 2) But these numbers are not numbers, because they cannot be approximated to any given epsilon. I will not withdraw (1) or (2), and they do not constitute a contradiction. Regards, WM
From: Franziska Neugebauer on 5 Jan 2007 07:57
mueckenh(a)rz.fh-augsburg.de wrote: > Franziska Neugebauer schrieb: > > It is without any value to follow your text. LOL. Head-in-the-sand? > 1) My "ideas" are identical with what you call irrational numbers. > 2) But these numbers are not numbers, because they cannot be > approximated to any given epsilon. > > I will not withdraw (1) or (2), and they do not constitute a > contradiction. Until you show an error in my proof ,----[ <459c29b6$0$97261$892e7fe2(a)authen.yellow.readfreenews.net> ] | Your three answers together state | | P & Q & Q' | | According to the rules of logic which still are in effect | | a & b & c -> a & b | | regardless of the truth of c. Hence from stating | | P & Q & Q' | | it follows that you also state | | P & Q | | Since P <-> ~Q you are stating a contradiction: | | P & ~P `---- your answers P and Q constitute a contradiction. F. N. -- xyz |