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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Simple enough for every reader?
Date: Sun, 15 Jun 2025 18:15:39 +0200
Organization: A noiseless patient Spider
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In-Reply-To: <102m7g4$rqqe$1@dont-email.me>

On 15.06.2025 12:32, Mikko wrote:
> On 2025-06-14 14:00:36 +0000, WM said:

>> Of course the border between visible and dark numbers depends on time 
>> and system.
> 
> And therefore has no mathenatical meaning.

That is only true if mathematics is restricted to definable numbers. But 
that is not the usual approach. The undefinable prime numbers for 
instance belong to present mathematics.
> 
>> But the mathematically interesting fact is that never all numbers can 
>> become visible because completeness, well-order and infinity are 
>> mutually incompatible.
> 
> What kind of comleteness do you mean?

The complete set of numbers / prime numbers is infinite. If each number 
were known and subtracted, a last one would appear.

>> Therefore not all can have a known well-order.
> 
> Then can as they do. The arithmetic order of natural numbers is a known
> well-order. But a well-order does not imply that there is a last one.
> only that there is a first one.

But this does: ℕ \ {1, 2, 3, ...} = { }	.

Regards, WM