Re: Another stab at Cantor


georgie wrote:
Virgil wrote:
In article <1158683687.456621.233970@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"georgie" <geo_cant@xxxxxxxxx> wrote:

Arturo Magidin wrote:
In article <1158683189.567305.51540@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
georgie <geo_cant@xxxxxxxxx> wrote:

Arturo Magidin wrote:

(ii) The strings Dk, where D1 is obtained via the diagonal process
from L1, and D(k+1) is obtained via the diagonal process from the
list that has D(k+1-j) in the j-th position, j=1,...,k, and L1(n) in
the (k+n)th position.

"the list that has D(k+1-j) in the j-th position, j=1,...,k, and L1(n)
in the
(k+n)th position." is an attempt to describe L_Omega.

No, Georgie boy. It is an accurate description of the list considered
in step k+1 of the procedure described. The list described in (ii) is
used ONLY in order to construct the string D(k+1).

Do you use the "No, Georgie boy." proof often? Does it get published?
According to you, (ii) does not describe a list in the limiting case.

You said
yourself that the limiting case, L_Omega, is not a list so (ii) is not
valid.

No, Georgie-boy. You are grasping at straws and choking on air.

So were you wrong before, when you said L_Omega was not a list,
or are you wrong now that you deny it?

If L_Omega is not a list and its members cannot be listed, then it is
already uncountable, and Cantor wins.

If black is defined as white, and white is defined as black, then black
is
black and white is whate and black is white and white is black.
Therefore,
Cantor Wins.
QED

But what about the limiting case not being a list and therefore not
subject to diagonalizaion.
Oh yeah. I almost forgot. There's
a bunch of explanations:

1. That's trolling.
2. It doesn't apply because we said it doesn't.
3. It wasn't proven that the final set has all the reals so we don't
want to explain any further.
4. We can come up with personal attacks and diversions that
deflect away from that fact.
5. Cantor Wins.

There is also the explanation that was actually given.
Either the limiting case is not countable, and we
don't care whether or not it contains all the reals,
or the limiting case is countable, and *whether or
not* the limiting case is a list, the limiting case can
be turned into a list.



-William Hughes

.

Relevant Pages

  • Re: Another stab at Cantor
    ... and Dis obtained via the diagonal process from the ... Georgie boy." ... does not describe a list in the limiting case. ... already uncountable, and Cantor wins. ...
    (sci.math)
  • Re: Another stab at Cantor
    ... and Dis obtained via the diagonal process from the ... Georgie boy." ... does not describe a list in the limiting case. ... already uncountable, and Cantor wins. ...
    (sci.math)
  • Re: Another stab at Cantor
    ... Arturo Magidin wrote: ... and Dis obtained via the diagonal process from the ... Georgie boy." ... does not describe a list in the limiting case. ...
    (sci.math)
  • Re: Another stab at Cantor
    ... and Dis obtained via the diagonal process from the ... yourself that the limiting case, L_Omega, is not a list so is not ... the set of reals is not countable. ... Either way, Cantor wins. ...
    (sci.math)
  • Re: Another stab at Cantor
    ... Arturo Magidin wrote: ... and Dis obtained via the diagonal process from the ... Georgie boy." ... does not describe a list in the limiting case. ...
    (sci.math)
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