Re: Replacement of Cardinality

Am 28.07.2024 um 20:17 schrieb Jim Burns:

On 7/28/2024 8:17 AM, WM wrote:

ω-1 ∈ ℕ

Holy shit!
What does "ω-1" even mean?
A "reasonable" interpretation might be:
       ω-1 is the natural number k such that k+1 = ω.
The only problem with this interpretation is that there is no natural number k such that k+1 = ω.
So (in a mathematical context) we can't define:
       ω-1 =df the natural number k such that k+1 = ω.

'Defining into existence' that which doesn't exist
makes nonsense of whatever meaning one's words have.

Right.

ℕ = {1, 2, 3, ..., ω-1}

*sigh*