An uncountable countable set
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From: Virgil on 5 Oct 2006 15:08 In article <1160044514.105544.245260(a)c28g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Dik T. Winter schrieb: > > > > > > > (There are exactly twice so > > > > > much > > > > > natural numbers than even natural numbers.) > > > > > > > > By what definitions? You never state definitions. > > > > > > By the only meaningful and consistent definition: A n eps |N : > > > |{1,2,3,...,2n}| = 2*|{2,4,6,...,2n}|. > > > Do you challenge its truth? > > > > No, I never did. But you draw conclusions about it about the set N. > > Indeed, > > for each finite n, it is true. > > And N is nothing but the collection of all finite n. That does not require that what is true for every member of a set be true for the set itself. {2,4,6} is an odd sized set, despite all its members being of even size.
From: Virgil on 5 Oct 2006 15:10 In article <d01ff$4524e557$82a1e228$25988(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Not liked by Carl Friedrich Gauss as well. I'm in fairly good company. > > Han de Bruijn Gauss is long since dead. From the neck up, HdB emulates him.
From: Virgil on 5 Oct 2006 15:12 In article <59d4a$4524e9b1$82a1e228$26891(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > Appeals to dead authorities aside, you're choosing not to explain what > > is meant by "mathematics without the discipline". Why? > > Why not? Apparently HdB does not choose to accept working within his own discipline.
From: Virgil on 5 Oct 2006 15:15 In article <9e0d8$4524f775$82a1e228$18464(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Mike Kelly wrote: > > > Han de Bruijn wrote: > > > >>Mike Kelly wrote: > >> > >>>Appeals to dead authorities aside, you're choosing not to explain what > >>>is meant by "mathematics without the discipline". Why? > >> > >>Why not? > > > > It seems very silly to post seemingly silly messages to usenet and then > > refuse to explain what non-silly meaning they have behind them. People > > will think you utterly silly. > > No: What's the beef in explaining something that is self explanatory? > > Han de Bruijn As there is plenty of discipline in those parts of honest mathematics that HdB deems without it, some explanation of how his notion of discipline differs from current mathematical discipline is needed if his claim is to be considered as anything but sour grapes.
From: Virgil on 5 Oct 2006 15:19
In article <9bab5$45250b9a$82a1e228$23627(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Mike Kelly wrote: > > > Bullshit. There is no bijection between the naturals and the set of all > > binary strings. > > Theorem: > There is no bijection between the naturals > and the set of all binary strings. > > Proof: > Bullshit. > > See? That's how Mike Kelly's mathematics works. Quite convincing. > > Han de Bruijn It is how HdB's "mathematics" works at all event, as he declares all sorts of things without any proofs other than claims of "that's the way it is." Which as justification is just what Mike said it was. |