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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Mon, 29 Jul 2024 19:16:02 +0200
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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*