Re: Forgotten to answer?

Am Sun, 26 Jan 2025 09:31:45 +0100 schrieb WM:

On 25.01.2025 18:03, FromTheRafters wrote:

WM pretended :

On 22.01.2025 19:01, Python wrote:
>
 > If you have three coins of 2 euros not a single one is "necessary"
 > to pay a 3 euros drink
>
This failing analogy has been repeated again an again, first by
Rennenkampff, because their authors do not understand the principle:
Cantor's theorem concerns the set of indices or ordinal numbers, not a
set of sets.

 
Then how are these 'Cantor's Theorem' ordinals contructed?

 
That can be done in an arbitrary way. For the above sets of euros or for
{a, b}, {b, c}, {c, a} the first necessary is the second.

Only in that order. You only mean that one can drop only one of the sets,
but not two.

For FISONs
F(n) I use the index n. But we can attach the ordinals in an arbitrary
way. There is no first necessary and no first sufficient either. All
FISONs fail to complete the set ℕ if it is fixed and greater than all
FISONs.

Every single FISON is not equal to N. But not if you take all of them.

The potentially infinite collection UF(n) however is obviously
produced.

And it is equal to N.

--
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.