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

On 1/5/25 2:47 PM, WM wrote:

On 05.01.2025 18:39, Richard Damon wrote:

On 1/5/25 12:26 PM, WM wrote:

On 05.01.2025 13:47, Richard Damon wrote:

On 1/5/25 5:31 AM, WM wrote:

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

>
Because you never actually USED *ALL* FISONs,

>
All FISONs are smaller than 1 % of |ℕ|.
Find a FISON {1, 2, 3, ..., n} such that {1, 2, 3, ..., 100n} is a superset of ℕ.

 

I never said there was,

 You said that I never used all FISONs. But I do. All are insufficient.

No, you DON'T use all. Because ALL has an infinite number of members, and you need to process them one by one, and you can't do infinite work
YOU always have a highest eleement "n" that you have gone to, but there is no highest Natural Number, so you LIE when you say you used ALL.

 

but your claim doesn't match your conclusion, as the union of *ALL* the FISIONs will reach the size of the Natural Numbers, even though no finite subset reaches a measurable percentage of it.
>

How do they do it? Do one or more FISONs grow during the union process? (One would be sufficient.)

Nope, they are just infinite in number. Since there isn't a last FISON, there isn't a largest FISON, so they just include all the elements.
You are just stuck in your stupid finite world, thinking you have escaped its bars, which you are just putting yourself in.
You are just showing that your mental processe just can't handle the truth, and think your lies have to be true.

 Regards, WM