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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The reality of sets, on a scale of 1 to 10 [Was: The
 non-existence of "dark numbers"]
Date: Tue, 25 Mar 2025 08:27:29 -0000 (UTC)
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Am Mon, 24 Mar 2025 20:17:45 +0100 schrieb WM:
> On 23.03.2025 22:28, Alan Mackenzie wrote:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>> On 22.03.2025 12:31, joes wrote:
>> 
>>>> for infinite sets "reality" and cardinality don't have to correspond.
>>> So it is! Substance and cardinality have nothing in common because
>>> sets of very different substance have same cardinality.
>> What is this "reality" or "substance" of which you speak?
> Substance is by far the better word. It denotes the number of elements.
> The set {1, 2, 3} has more substance than the set {7, 14}. For many sets
> the relative substance cannot be determined. But this drawback is less
> disastrous than to lump every countable set together.
You can just say subsets.

>> The cardinality of N is aleph-0.
>> What is the "reality" (in this sense) of N?
> The substance of ℕ is |ℕ|. It is larger than every finite set. The
> substance of the set of prime numbers is far less than |ℕ| but larger
> than every finite set. These are useful mathematical findings.
What's the use?

-- 
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.