Date: Dec 13, 2012 2:58 PM
Author: Virgil
Subject: Re: On the infinite binary Tree

> On Dec 13, 9:56 am, WM <> wrote:


> No. I proved that the number of infinite paths is countable by
> constructing all nodes of the Binbary Tree by a countable set of
> infinite paths.

WM goofs an argument again!!!

You claim to have shown that the set of paths can be SURJECTS ONTO the
set of nodes.
But such a claim only argues that the set of paths is at least as large
as the set of nodes, but not, as yo claim, that it cannot be larger.

Note that any nonempty set can be surjected onto any one element set,
but that does not prove that every nonempty set has ONLY one member, it
only proves that every nonempty set has AT LEAST one member.

To prove what you claim you must also show that the set of paths INJECTS
INTO to the set of nodes, which you cannot do because it is not true!