Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary, effectively)

Am Sun, 05 Jan 2025 11:31:01 +0100 schrieb WM:

On 04.01.2025 11:59, joes wrote:

Am Sat, 04 Jan 2025 09:52:08 +0100 schrieb WM:

On 04.01.2025 05:06, Richard Damon wrote:

On 1/3/25 12:15 PM, WM wrote:

>

Every union of FISONs which stay below a certain threshold stays
below that threshold.

Every union of a finite number of FISONs is just an admssion that you
can't do the actual union of *ALL* FISONs.

For all FISONs:|ℕ \ {1, 2, 3, ..., n}| = ℵo.

But not for the union.

What should make the union larger than all FISONs?

Whatever do you mean? The union is of course larger than every single
FISON, because there are infinitely many.

Every union of FISONs which stay below a certain threshold stays belown
that threshold.

The union of all of them doesn't stay below any threshold.

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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.