Re: The non-existence of "dark numbers"

Am Wed, 19 Mar 2025 23:21:30 +0100 schrieb WM:

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.

Not a proof, not a valid implication, and nonsense follows.
N *is defined* as the smallest inductive set.

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.

It's both wrong and awfully worded. Perhaps you meant that no finite
number of FISONs "empties" N; but there is an infinite number of them.

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.

Derivation of that limit?

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

You cannot believe in mathematics? Then try another occupation.

I'll leave you to your physics.

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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.