Cantor Confusion
in [Math]
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From: WM on 11 May 2007 11:56 On 11 Mai, 15:48, William Hughes <wpihug...(a)hotmail.com> wrote: > On May 11, 2:54 am, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > > This is > > contradicted by the fact that every node of p which you can ask for is > > shared by the same path p'. > > Up to now we have been talking about the set > "every node of p". We can continue to so so. > > You have now introduced the Wolkenmuekenheim > set "every node of p which you can ask for". Do you think that this set is different from the set "every node of p". > This set > is bounded above by the maximum node. Of course the > maximum node can change to something bigger (this > makes sense in Wolkenmuekenheim) and when it does > the set "every node of p which you can ask for" changes. > > So the set "every node of p which you can ask for" can change. > When it does the "same path p' " may have to change. What are numbers you cannot ask for? Regards, WM
From: William Hughes on 11 May 2007 12:04 On May 11, 11:53 am, WM <mueck...(a)rz.fh-augsburg.de> wrote: <snip> > > p* is that path which consists of all the nodes at which p is not > single p is never single. Therefore "all the nodes at which p is not single" is all the nodes of p. >(so that there is also another path). Is it impossible or > forbidden by ZFC or third order logic or pink elephants to construct a > path p* from this set of nodes? Nope, the path which you contruct from all the nodes of p is p. Look! Over there! A pink elephant.! The path you contruct is not equal to p. - William Hughes
From: William Hughes on 11 May 2007 12:22 On May 11, 11:46 am, WM <mueck...(a)rz.fh-augsburg.de> wrote: > On 11 Mai, 14:36, William Hughes <wpihug...(a)hotmail.com> wrote: > > > > > On May 11, 5:35 am, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > Definition: p* is a path in the binary tree which is with path p at > > > the next node K(p, n+1) in the binary tree, whatever node K(p, n) you > > > investigate. > > > > Lemma: In the binary tree for every path p there exists at least one > > > path p* as defined. > > > > Proof: Choose a node K(p, n) of path p in the binary tree. There is a > > > path p* which is with p at node K(p, n+1) too such that K(p, n+1) = > > > K(p*, n+1). This path p* has been with p at all nodes m < n too. The > > > choice of n is arbitrary. Therefore the Lemma holds for all nodes K(p, > > > n) of p with n in N. > > > > Remark: This proof is independent of the number of nodes. > > > Look! Over there! A pink elephant! > > You should consult an eye doctor. > > > > > Remark: When you change n, p* never has to change. > > It cannot change? Nope. By definition p* is a path. A path is something that cannot change. - William Hughes
From: franz_lemmermeyer on 11 May 2007 12:30 On 11 Mai, 19:22, William Hughes <wpihug...(a)hotmail.com> wrote: > Nope. By definition p* is a path. A path is > something that cannot change. Well, in Mueckenmathics it can change. Even the number 2 can change if you take lim[n -> oo]. A very dynamic theory, that mueckenmathics, with flexible definitions that mean whatever the reincarnation of Humpty Dumpty at the FH Augsburg wants them to mean. franz
From: William Hughes on 11 May 2007 12:40
On May 11, 11:56 am, WM <mueck...(a)rz.fh-augsburg.de> wrote: > On 11 Mai, 15:48, William Hughes <wpihug...(a)hotmail.com> wrote: > > > On May 11, 2:54 am, WM <mueck...(a)rz.fh-augsburg.de> wrote: > > > > This is > > > contradicted by the fact that every node of p which you can ask for is > > > shared by the same path p'. > > > Up to now we have been talking about the set > > "every node of p". > > We can continue to so so. So we can continue to conclude that, there is no single fixed path p'=/=p which shares *every* node of p. - William Hughes |