Cantor Confusion
in [Math]
|
From: David Marcus on 16 Feb 2007 12:52 Andy Smith wrote: > > sticking my nose in again, smack it if you wish. > > As I understand it : > > P(1) is the set of all numbers of 1 bit length - 2 elements (0.0 & 0.1) > P(2) is the set of all numbers of 2 bits length - 4 elements (0.00, > 0.01, 0.10, 0.11) > P(n) is the set of all numbers of n bits length - with 2^n elements. > > The set P(n) includes all P(m) for m<n, if a right fill of 0 for the > bits is inferred (i.e. 0.0 is the same as 0.00 is the same as 0.00..) > > For any bit-length (path-length) n, P(n) is countable, so for any finite > n, P(n) is countable. > But, real numbers require an infinite number of bits to represent them If you want to be able to represent all of them. Some reals only need a finite number of bits. > (or, if you prefer, we can define the set of reals as the set of numbers > with an infinite random binary expansion). Don't think so. Not sure what "random" means here. > But if the number of bits is > not finite, neither is P(oo), and the reals are uncountable. -- David Marcus
From: David Marcus on 16 Feb 2007 16:34 G. Frege wrote: > On Fri, 16 Feb 2007 05:07:47 +0100, G. Frege <nomail(a)invalid> wrote: > > > Actually I was referring to (1) the insight that there really a > > problem is lurking and (2) the idea of using quotation marks to > > prevent such confusion. :-) > > > > See: > > http://plato.stanford.edu/entries/quotation/ > > Would you PLEASE follow the link before talking even more nonsense? > > The following should be a correct quote from "Through the Looking > Glass". > > ------------------------------------------- > > The name of the song is called "HADDOCKS' EYES."' > > 'Oh, that's the name of the song, is it?' Alice said, trying to feel > interested. > > 'No, you don't understand,' the Knight said, looking a little vexed. > 'That's what the name is CALLED. The name really IS "THE AGED AGED > MAN."' > > 'Then I ought to have said "That's what the SONG is called"?' Alice > corrected herself. > > 'No, you oughtn't: that's quite another thing! The SONG is called > "WAYS AND MEANS": but that's only what it's CALLED, you know!' > > 'Well, what IS the song, then?' said Alice, who was by this time > completely bewildered. > > 'I was coming to that,' the Knight said. 'The song really IS > "A-SITTING ON A GATE": and the tune's my own invention.' > > ------------------------------------------- Maybe Carroll should have written 'I was coming to that,' the Knight said. 'The song really IS A-SITTING ON A GATE: and the tune's my own invention.' -- David Marcus
From: Dik T. Winter on 16 Feb 2007 20:15 In article <awrH2HXUwd1FFwXf(a)phoenixsystems.demon.co.uk> Andy Smith <Andy(a)phoenixsystems.co.uk> writes: > In message <JDKBA5.MwM(a)cwi.nl>, Dik T. Winter <Dik.Winter(a)cwi.nl> writes .... > > > P(n) is the set of all paths of the tree T(n) with n levels. > > > P(0) is a set with one path, namely p(0) = {0.} > > > P(1) is a set with two paths, namely p(1) = {0.0} and q(1) = {0.1} > > > P(2) is a set with four paths, namely p(2) = {0.00}, and some others. > > > >Using that representation for paths is misleading, As you state that > >each path is a set of nodes, and if that is the case, with that notation > >0.00 is a node, and each path is a set containing a single node. > As I understand it : > > P(1) is the set of all numbers of 1 bit length - 2 elements (0.0 & 0.1) > P(2) is the set of all numbers of 2 bits length - 4 elements (0.00, > 0.01, 0.10, 0.11) > P(n) is the set of all numbers of n bits length - with 2^n elements. That is neither Wolfgang's model, nor mine. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Michael Press on 16 Feb 2007 21:05 In article <1171468278.284645.273750(a)v33g2000cwv.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > On 13 Feb., 21:17, Virgil <vir...(a)comcast.net> wrote: > > In article <1171364856.226197.135...(a)l53g2000cwa.googlegroups.com>, > > mueck...(a)rz.fh-augsburg.de wrote: [...] > > > What about all existing sets with 3 objects, i.e., the fundamenal set > > > of 3? > > > > What fundamental set of 3 does WM refer to? > > Olease read before writing. The set of all existing sets with 3 > objects. How many sets with three elements are there? -- Michael Press
From: Michael Press on 16 Feb 2007 21:11
In article <virgil-E37A5B.15421415022007(a)comcast.dca.giganews.com>, Virgil <virgil(a)comcast.net> wrote: > In article <1171576194.042084.91330(a)a34g2000cwb.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: [...] > > It seems you are in a very deep confusion. > > It is called transference. Technically, it is called projection. Transference is when A treats B as if B were someone else from A's life. Transference could be in play, but this exchange is not evidence. -- Michael Press |