Re: The non-existence of "dark numbers"

On 19.03.2025 21:15, joes wrote:

Am Wed, 19 Mar 2025 20:30:27 +0100 schrieb WM:

I use Cantor's ℕ which is larger than all its inductive subsets.

It can't be larger. It contains nothing apart from the inductive set.

Cantor thought so too, but both of you are in error.
Proof: UF = ℕ  ==>  Ø = ℕ.

 

Obviously

Please prove that it is obvious.

>
For Cantor's ℕ we have:
|ℕ \ {1}| = ℵo |ℕ \ {1, 2, 3, ..., n}| = ℵo ==>
|ℕ \ {1, 2, 3, ..., n+1}| = ℵo
>
All FISONs fail to empty ℕ when applied one after the other.

Awful wording.

Correct description of mathematical facts.>

All FISONs fail to empty ℕ when applied at once, because mathematics is
not time-dependent.

Only you haven't "applied" all of them.

When applied one after the other, all FISONs fail. Therefore they also fail when being applied at once.

That would be
N \ {1, 2, 3, ...}

You cannot believe in mathematics? Then try another occupation.
Regards, WM