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

Am Sun, 05 Jan 2025 11:40:58 +0100 schrieb WM:

On 04.01.2025 14:17, Richard Damon wrote:

On 1/4/25 3:52 AM, WM wrote:

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.
That means there is no exception.

Just like every natural number is finite,
but the set of *ALL* of them is infinite, each FISON is finite,

Not only finite but below 1 % of |ℕ|.

That's a less sharp bound, as it is still infinite.