Re: Cantor and the binary tree

In article <1118840953.771858.21920@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Virgil wrote:
>
> > Is it the "bunches" or the "paths" that WM is alleging do not exist as
> > individuals?
>
> The bunches.

So no set of paths (equivalent to a bunch of paths according to WM) can
exist as an individual set? Very odd set theory that WM uses. Doesn't
agree with anyone else's.
> >
> > If WM is speaking of paths, then the a maximal binary tree, by his
> > standards, has no paths at all, since no path exists in a maximal binary
> > tree which does not share each "edge" with some other path, though the
> > particuar other path depends on which "edge" is to be shared.
>
> I am glad to say that you are fully correct.

I have been correct all along. It is just that WM's self-delusions have
previously prevented him from seeing it.

> Paths which do not differ
> by any edge are due to binary representations which cannot be
> distinguished. But why do you want to distinguish them, if you know you
> cannot?

WM seems to be deluding himself again.

Two paths in a maximal binary tree are distinct if and only if there is
a node at which one branches left and the other branches right.

If this does not happen there is no "them" to distinguish, only an "it"
which cannot be distinguished from itself.
>
> Regards, WM
.

Relevant Pages

  • Re: Cantor and the binary tree
    ... here is one of many points where Cantorians differ. ... > Let us speak of bunches as non-empty subsets of paths. ... > In this way any bunch of paths gets its personal branch. ... node is also the root node to a maximal binary tree so each bunch is ...
    (sci.math)
  • Re: Cantor and the binary tree
    ... >>> Each edge is mapped on that bunch which contains that edge. ... >> Not all non-empty subsets are bunches. ... Since there is an easy bijection from the paths in any one bunch to the ... is equivalent to a maximal binary tree with that node as root node. ...
    (sci.math)
  • Re: Cantor and the binary tree
    ... The bunches. ... > If WM is speaking of paths, then the a maximal binary tree, by his ... > standards, has no paths at all, since no path exists in a maximal binary ...
    (sci.math)