An uncountable countable set
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From: mueckenh on 13 Aug 2006 12:42 Virgil schrieb: > In article <1155314314.212493.69980(a)75g2000cwc.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: > > > Virgil schrieb: > > > > > > > The "Hilbert Hotel" method allows one always to insert one more and > > > still have rooms for all. > > > > Just this argument shows that the diagonal number of Cantor's list has > > always reserved a place in the list. > > Wrong. It may have a place in a new list, but none in the original list. > > What Cantor does say that is that no list can be complete, but does not > say that there is any number which cannot be listed. We know that the set of *all* those numbers which can ever appear in lists, be it as original entries or as diagonal numbers, is countable. Even you know it! Why do conclude from Cantor's idea such incoherent nonsense? Regards, WM
From: Virgil on 13 Aug 2006 13:11 In article <1155484680.116757.85620(a)p79g2000cwp.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > \ > > > > > This assertion is impossible. Compare the differences of 1 between the > > > > > naturals which would sum up to a natural number infinity if there were > > > > > infinitely many differences possible. > > > > > > > > That makes no more sense > > > > > > and not less > > > > > > > than to say that the sum of infinitely > > > > naturals being infinite prevents existence of infinitely many naturals. > > > > > > Correct. Both conclusions are identical. > > > > And false. > > An infinite sum of 1's is not infinite? "Mueckenh" again proves that he cannot read. It is false and stupid to say that an infinite sum being infinite prohibits infiniteness. But saying that in no way implies that an infinite sum of 1's is not infinite. > > Regards, WM
From: Virgil on 13 Aug 2006 13:14 In article <1155484846.128106.136770(a)m73g2000cwd.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > > At what point do you know that you have all aleph_0 lines? > > > > When you have them all. > > That means never, If "Mueckenh" chooses to be limited himself, he should not think that limits others.
From: Virgil on 13 Aug 2006 13:16 In article <1155484953.596645.146740(a)m73g2000cwd.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > > mueckenh wrote: > > > At what point do you know that you have all aleph_0 lines? > > > > When your list (set, sequence, list) has a line for every natural. > When do you have a line for every natural? When they are all used up. > > When you can show that every line is denumerated by a natural, > How can you show that? AoI.
From: Virgil on 13 Aug 2006 13:19
In article <1155485742.529974.141050(a)i3g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Of course you can index each n. But your "each n" stems from the true > list. And we know that 0.111... is not in the true list, because it is > distinguished from any element of the true list. It can be indexed by the first 1, and each 1 indexed by the next 1 and everything is then indexed. |