Re: Simple enough for every reader?

On 30.06.2025 23:25, joes wrote:

Am Mon, 30 Jun 2025 20:21:09 +0200 schrieb WM:

On 29.06.2025 12:25, Mikko wrote:

On 2025-06-28 13:56:57 +0000, WM said:

On 28.06.2025 11:56, Mikko wrote:

On 2025-06-27 19:36:41 +0000, WM said:

On 27.06.2025 09:33, Mikko wrote:

On 2025-06-26 13:09:32 +0000, WM said:

>

If we subtract in the order that is used for enumerating then a
last one is necessary.

No, there is no last one in an infinite enumeration.

Then it is not finished or completed.

No, but it can be continued.

Yes it is actually. That is why it's called infinite. You have to take
it, like Cantor, as it's own "finished" thing. That is where you fail.

You fail. Finished = finite and infinite = not finished supplies a clear contradiction.

 

The notion set can only be applied to complete sets. i.e., sets which
cannot be continued.

Saying that every set is "complete" does not mean anything,

It means that no further element can be found later on.

Elements aren't "found", they either are or are not.

That means finished.

Then it cannot be. If it is that all natural numbers are subtracted in
their order, then it is that a last one is subtracted.

For the infinitieth time: no, that does not follow.

It follows fo every not completely blinded brain.

There is no "last"
number, and yet you can "subtract" an infinity of elements - in an
infinity of "steps", naturally.

Either there is a last one, or not all are subtracted.

     But Cantor already knew that there are incomplete, i.e.,
potentially infinite sets like the set of all cardinal numbers. He
called them "absolutely infinite".

Nah. It just has a higher cardinality.

The collection of alle alpehs has no cardinality. Cantor knew that.

 

Yes. both bijection and one-to-one imply completeness.

Do you think N \ {0} and N \ {3} can not be bijected?

A complete set with one element subtracted is again a complete set.

 

In all these example "eindeutig and vollständig" is an feature of the
correspondence, not of any set.

A bijection is a set too.

A set of pairs.

Yes, a set.

So no example of a set of being "complete".

Without completeness countability and uncountability both would be
meaningless

How so?

Read Cantor: Vollständig, ohne Ausnahme.

Uncompleted does not apply to sets. Therefore I use the notion
collection for the potentially infinite.

Too bad nobody else does.

Try to learn more.

Yes. If all prime numbers could be known, the same contradiction would
arise.

Primes are not infinite themselves.

But the known primes are a potentially infinite collection.
Regards, WM