Re: The non-existence of "dark numbers"

Am 12.03.2025 um 22:31 schrieb Alan Mackenzie:

WM <wolfgang.mueckenheim@tha.de> wrote:

If you were able to learn, then you would have the chance here:
ℕ \ {1} = ℵo

 Where do you get that from?  You're trying to say a subset of N is
identical to the first transfinite cardinal.  That cannot be true.

Should read: |ℕ \ {1}| = ℵo

and if ℕ \ {1, 2, 3, ..., n} = ℵo>> then ℕ \ {1, 2, 3, ..., n+1} = ℵo.

 Where do you get that from?  It is clearly false - the first of these
sets contains an element, n+1, that the second one doesn't.  Therefore
they are distinct sets.

Should read: and if |ℕ \ {1, 2, 3, ..., n}| = ℵo then |ℕ \ {1, 2, 3, ..., n+1}| = ℵo.

Induction cannot cover all natural numbers but only less than remain
uncovered.

Gibberish.

The second part of that sentence is gibberish.  Nobody has been talking
about "uncovering" numbers, whatever that might mean.  [...]