Re: Cantor and the binary tree

In article <1118165340.899108.271300@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Virgil wrote:
> > In article <1118049210.758102.82150@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> > mueckenh@xxxxxxxxxxxxxxxxx wrote:
> >
> > > Robert Kolker wrote:
> > > > mueckenh@xxxxxxxxxxxxxxxxx wrote:
> > > > >
> > > > >
> > > > > You have shown that set theory is inconsistent. Congratulations.
> > > >
> > > > Not so. There are always more paths than nodes.
> > >
> > > The basic element of the binary tree is the branching where a path is
> > > separated.
> > > /
> > > B
> > > /\
> > > Separated means separately visible, distinct from the others.
> > > You need not define which of the two paths going out it is. All we need
> > > to know is that the number of separated paths has increased by 1. The
> > > number of separated paths is equal to the number of branchings.
> > >
> > > Set theory requires: The number of separated paths is larger than the
> > > number of branchings. That is not counterintuitive. That is wrong.
> >
> > Only in WM's world where intuition overpowers logic.
>
> Oh, you have a logic argument, to be drawn *from the tree*, to receive
> more paths than paths origins?

In a maximal binary tree, or, indeed, any tree, every maximal path
originates at the root, so if there are as many as 2 maximal paths,
there are more than the number of path origins. That proves nothing.
.

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