Virgil
Posts:
4,482
Registered:
1/6/11
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Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Posted:
Jan 11, 2013 4:20 AM
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In article
<9bd35385-3fae-4236-82ff-f1be4dacd7ac@f19g2000vbv.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> > We cannot determine whether a path is missing until we have a list of
> > the paths which are not missing
>
> Paths are determined, in mathematics, by nodes.
Paths in a Complete Infinite Binary Tree can be determined in any one of
a large number of ways, not all of which require listing nodes but all
of them determining the pattern of left or right branching of a path.
And until WM lists his paths, by whatever method he chooses to identify
them, he has not proved his set of paths from a Complete Infinite Binary
Tree is countable. And if it is countable, it is necessarily incomplete
by some variation of the diagonal argument.
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