Date: Jan 13, 2013 4:34 PM
Subject: Re: Matheology � 191
Zuhair <email@example.com> wrote:
> What mean nothing more than saying that we have Countably many FINITE
> paths of the complete binary infinite tree, nothing less nothing more.
> However the complete infinite binary tree does have paths that are not
> finite, and those are Uncountably many.
Actually, the proper usage demands that a path be of maximal length, so
that proper subpaths, starting at the root node but not of maximal
length, are not paths at all, but only initial pieces of them.
WM tends to conflate paths with proper subpaths at every opportunity.
To be clear, one should always distinguish between a full path and a
proper subpath, perhaps by using "subpath" when appropriate.