Re: An uncountable countable set


Virgil schrieb:

That does not make their sizes infinite. It is completely irrelevant
here.

What IS irrelevant is the notion that in order to have infinitely many
naturals (more than any finite number of them) one must somehow have one
of them being infinitely large.

Then consider a set without an infinitely large element: {1,2,3,...,n}.
It is finite.
Remember: Sets are fixed entities. They do not grow.


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. 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,, . . .),
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Regards, WM

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