Re: Ultimate debunking of Cantor's Theory

On 18 Jul., 01:13, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
Consider the list
0.0
0.1
0.11
0.111
...

(1) Is the diagonal of the list an entry in the list? No, of course
it's not, since the diagonal is a denumerable sequence and each entry
in the list is a finite sequence.

That is one statement. The other claim is that the infinite diagonal
cannot exist without an infinite number of list entries and an
infinite number of 0's adjacent to 1's. This second claim proves the
existence of a sequence of infinitely many 1's. Why do you think this
second claim is wrong?

Whose claim?

The claim of those who see how the diagonal is constructed. The
diagonal cannot exist without lines which are as long as each initial
segment of the diagonal including the complete diagonal.

You have not shown that your list refutes uncountability.

I did not intend to show this by the list, because, if it turns out
that Cantor's arguing fails (because the diagonal cannot exist without
infinite sequences of 1's in the list), then there is no reason to
contradict uncountability --- it simply vanishes.

Then what is the point of your list if not to refute undecidability?

The list, more precisely the following matrix,
1
11
111
....

shows (by simple bijection of initial segments of the diagonal and
lines) that an infinite diagonal cannot exist unless there were also
an infinite line. Hence actual infinity is disproved. With it
uncountable infinity is disproved also.

Regards, WM

.

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