Re: Cantor Confusion

In article <1175261931.220013.38850@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:


If you unite natural numbers, you cannot get an infinite number but
only an infinite set of natural numbers. Why is this different for
paths?

Because a path as a set of nodes in an infinite tree, according to any
reasonable definition of paths, can be, and must be, infinite in that
infinite tree, but naturals cannot be infinite anywhere.

Does WM deny that a path, as a set of nodes in a given tree, must be
maximal in that tree in the sense that inserting any other node into
such a set of nodes makes it no longer a path in that tree?

WM must be denying it, as that is the only way his claims make any sense,
but that means what he is calling paths are not the same as what
everyone else is calling paths.

Note that what may be a path in a finite tree need not be a path in any
extension tree {an extention having the same root nodes and including
all of the original nodes, but some or all of the leaf nodes of the
original no longer being leaf nodes).
.