Date: Dec 28, 2012 10:07 PM
Subject: Re: The Diagonal Argument
On Dec 28, 5:13 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
> > Hancher, the "puke parrot" bit is largely for comedic effect, yes it
> > seems clear that you do actually read the attempts of others to
> > develop frameworks and structures of what would be developments in
> > mathematics, but it is as well clear that you definitely have a
> > penchant for tearing down said arguments without building them up.
> It is the duty of every mathematician to tear down such bad mathematics
> as is thrust upon him or her.
> And both you and WM thrust a lot of it here.
Cantor's nested intervals theorem <-> Finlayson's EF as counterexample
Cantor's antidiagonal argument <-> Finlayson's EF as counterexample
continued fractions <-> Finlayson's EF as counterexample
Cantor's indicator function theorem <-> Finlayson's symmetrical
mapping as counterexample
Zuhair's binary tree theorem <-> Finlayson's BT = EF as counterexample
Cantor's powerset theorem <-> Finlayson's powerset as order type as
successor construction, and a dialetheic ur-element
Russell's negated correlates <-> Finlayson's note on statement of
structurally true languages
irrationals uncountable <-> Finlayson's "A function surjects the
rationals onto the irrationals"
I've been busy. And, that's not bad mathematics.
Now, I am very interested in:
a) results standardly establishing uncountability
b) applications solely due transfinite cardinals
Basically, that's with the notion that this symmetry between limit
ordinals has particular results for the diagonal arguments and may
well be a general consideration about them, and particularly a
generally unique result about them, and then, that applications solely
due transfinite cardinals would be of incredible interest for the
possibility they might advance science in, say, physics.