Re: An uncountable countable set

On Tue, 31 Oct 2006 10:30:08 -0500, Tony Orlow <tony@xxxxxxxxxxxxx>
wrote:

[. . .]

Tony, I'm going to post several replies to this one post because I've
come up with a couple of ideas which may (or may not) appeal to you.

First off why not change your approach in the following way. It seems
to me that you could arrange all the naturals on the x axis. Then
instead of trying to cram in all the transcendentals on the same axis,
try putting transcendental infinites on the ordinal y axis instead.

However if you try this approach you may find that you need another
mutually orthogonal z axis to accommodate another class of infinites.
I don't know if this is going to work completely or not. But I think
it holds considerably more promise than trying to accommodate it all
on one more or less circular x axis alone.

In any event this is the end of this particular suggestion. I hope it
helps and sheds some light on what I think is going on in mechanical
terms. In any event I'll get back to your original message now plus
what I think will turn out to be definitive mechanical arguments on
the subject of transcendentals and conventional linear analysis of the
reals.

~v~~
.

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