Re: An uncountable countable set


Virgil schrieb:

You have posited an infinite sequence of infinite sequences of
transpositions to perform your alleged miracle. As you can never even
finish the first subsequence in finite time, you must reorder your
transpositions into a single sequence to even consider its effect.

I did so.

When? Since reordering disrupts the effect of sequences of overlapping
transpositions (non-commutativity), you have not done so to anyone's
satisfaction but your own.

(1,2)
(2,3)
(1,2)
(3,4)
(2,3)
(1,2)

....

No I have only one infinite sequence of transpositions. They
are as well defined and as fast to be executed as Cantors sequence of
replacements of digits.

Cantor does not have a list. Only those who challenge him need to have
lists. What Cantor does is to refute each list presented to him...

Cantor does have a list, it was the first one, constructed by himself:

E1 = (a1,1, a1,2, . . .,a1,nu, . . .),
E2 = (a2,1, a2,2, . . .,a2,nu, . . .),
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E??? = (a???,1, a???,2, . . .,a???,???, . . .),
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

That is not a list so much as an N by N matrix over the decimal digits
into which any list can be fitted.

It is an abstract list. You should learn to think in abstract terms.

And your notation sucks.

There were Greek letters, mu and nu, but completely irrelevant for
recognizing the list as a list (if one is able to think in abstract
notions - and of no further help, if one is not).

Regards, WM

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