Re: Ultimate debunking of Cantor's Theory

On Jul 19, 12:39 pm, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 18 Jul., 01:30, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

On Jul 16, 9:41 am, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

On Jul 14, 2:06 am, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:

If I take any finite
subset of S and if there always remains an element s of S not yet
taken, then S is (potentially) infinite.

That is EQUIVALENT to the set theoretic definition of 'infinite' as
'not finite'.

P.S. I'm still curious why you offer a definition of 'potentially
infinite' that is simply equivalent to an ordinary set theoretic
definition of 'infinite'.

The diagonal of
1
11
111
...
is potentially infinite, i.e., never completed, because in that case
there would also a completed infinite line be required by the simple
bijection
between initial segments of the diagonal and corresponding sequences
of 1's in lines.

That's not what I asked about. Please, look at what YOU posted in
response to a request for a definition of 'potentially infinite':

"If I take any finite subset of S and if there always remains an
element s of S not yet taken, then S is (potentially) infinite."

That is equivalent to one of the two standard set theoretical
definitions of 'is infinite', viz. 'S is infinite iff S is not
finite'.

So I'm asking again: Why do you give a definition of 'potentially
infinite' that is just equivalent to an ordinary set theoretic
definition of 'is infinite'?

MoeBlee


.

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