An uncountable countable set
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From: Han de Bruijn on 5 Oct 2006 08:15 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
From: Mike Kelly on 5 Oct 2006 08:21 Han de Bruijn 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? "Mathematics without the discipline" is about as self-explanatory as "A little bit of physics would be no idleness in mathematics". I have no idea what you are talking about, so I asked for clarification. -- mike.
From: Dik T. Winter on 5 Oct 2006 08:43 In article <J6n1Ft.8zB(a)cwi.nl> "Dik T. Winter" <Dik.Winter(a)cwi.nl> writes: > I did not know because there is no definition presented nor available. > Addition is defined between ordinal numbers. Ordinal numbers are (by > their very definition) larger than or equal to 0. But you want to > define addition between ordinal numbers and non-ordinal numbers. Pray > go ahead, and supply your definitions. (I still have not found the time > to see how Cantor defined omega - 1.) I have looked how Cantor defines subtraction. (x the unknown). (1) a + x = b, a < b, always solvable; x = b - a, and so: omega - 1 = omega. (2) x + a = b, a < b. Not always solvable, and when solvable there are in most cases multiple solutions. The smallest possible solution is chosen, and notated: b_(-a). (_ meaning subscript) So when Mueckenheim writes: (-k) + omega = x he is meaning the solution of k + x = omega (I think), which (according to Cantor) is notated as omega - k, and so is omega. omega_(-k) does not exist. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Han de Bruijn on 5 Oct 2006 09:41 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
From: Dik T. Winter on 5 Oct 2006 10:16
In article <1160043857.204324.235890(a)m73g2000cwd.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: > Dik T. Winter schrieb: .... > > Apparently you did not see the questions at all. You stated as your > > definition something like: > > "numbers are in trichotomy with each other" > > and I answered something like "so omega is a number". But I never did > > see an answer. > > Omega is not in trichotomy with 1 + omega. Why not? omega = 1 + omega. > > I asked for a mathematical definition of number. You never gave one (and > > also your paper does not give any mathematical definition), your only > > mathematical definition was about the trichotomy. > > I am not sure about the definition of a number. Therefore I cannot give > it. What I can give and have given, is a criterion what a number has to > satisfy and I can give some examples which do not satisfy that > criterion and which, therefore, are not numbers But omega satisfies that criterion. > > Oh. I did not know that slow internet access made long threads more > > difficult to follow than short threads. > > It lasts a long while until all is loaded again, after I have posted. > This problem, however, exists only during the weekends. But this thread > is too long. I am not able and willing to read all contributions. O, I am also not reading all contributions. > > I see no reason to shift the > > subject. And certainly not to a subject for which a thread already does > > exist. > > The original subject of this thread is no longer under discussion here. Nevertheless, the subject of a thread should never change to an already existing subject... -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ |