Re: Ultimate debunking of Cantor's Theory

On Jul 15, 9:42 am, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 15 Jul., 15:05, Don Stockbauer wrote:
There are just two flavors of infinity:
1. The potential

which is not infinite.

2. The actual

Which is not there.

The problem I have with all this, not knowing much
about the various theories of sets, is that some
people will make declarations, such as that there
are no infinite sets, or there are only potentially
infinite sets, as if they are speaking absolute
truths.

They don't say, along with those declarations, that
they mean 'according to this or that set theory'.
They say it as if it is revealed truth. Then, when
someone challenges the declarations, they start
talking about sets of axioms in various theories,
and so demonstrate their knowledge, which is
undeniable.

But, in spite of high IQs, and vast and subtle
accumulated knowledge about the deepest aspects of
all known theories of sets, the fact remains that
with only limited knowledge, and only average IQ,
anyone who thinks about it at all, knows that the
totality of natural numbers is an infinite totality.

(The word 'totality' here is not used in the sense
of a sum, but in the sense of 'all'.)

If I'm forbidden from using the word 'set', so be it,
but there is an 'all' of natural numbers, and it is
infinite.

.

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