Re: The set of necessary FISONs

Am Wed, 05 Mar 2025 22:05:04 +0100 schrieb WM:

Am 05.03.2025 um 13:25 schrieb Richard Damon:

On 3/4/25 4:07 AM, WM wrote:

 

Wrong, Cantor shows that the number of Natural Numbers generated by the
iterative method of, we have 0, and for every number we have its
successor, is not one of those finite numbers, but is another number
Aleph0

Below you contradict yourself.

Nope.

We call that phenomenon potential infinity.

WHich is just infinity,

>
Cantor denies your claim.
"Nevertheless the transfinite cannot be considered a subsection of
what is usually called 'potentially infinite'. Because the latter is
not (like every individual transfinite and in general everything due
to an 'idea divina') determined in itself, fixed, and unchangeable,
but a finite in the process of change, having in each of its current
states a finite size; like, for instance, the temporal duration since
the beginning of the world, which, when measured in some time-unit,
for instance a year, is finite in every moment, but always growing
beyond all finite limits, without ever becoming really infinitely
large." [G. Cantor, letter to I. Jeiler (13 Oct 1895)]
Here he is right.

 
Which doesn't mean what you think it means.

He means what he says.

He doesn't say what you say.

He is pointing out that these "transfinite" concepts aren't part of the
infinite set built by iteration (the "potential infinity") but is
beyond it.

Therefore iterartion fails to produce actual infinity.

As an element, but not as the number of elements (=the size of the set).

We SEE the "potentially infinite" via a process, where each step is
finite, but the final result of it *IS* an infinite thing.

There is no final result. You are unable to understand infinity.

Speak for yourself. You are evidently unable to understand limits and
infinite "processes".

Because the latter is a finite in the process of change, having in each
of its current without ever becoming really infinitely large.

No, infinity isn't finite and doesn't change.

None of the members of N are themselves infinite, but the set itself
is.

Not by recursion or induction! Therefore UF is a proper subset of ℕ. UF
= ℕ  ==> Ø = ℕ

Wrong. Of course induction "is infinite". UF is not empty.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.