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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: The existence of dark numbers proved by the thinned out harmonic,
 series
Date: Tue, 18 Mar 2025 12:12:27 -0700
Organization: A noiseless patient Spider
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On 3/18/2025 8:41 AM, WM wrote:
> On 18.03.2025 16:14, FromTheRafters wrote:
>> After serious thinking WM wrote :
>>> On 18.03.2025 13:18, Alan Mackenzie wrote:
>>>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>>
>>>>> All elements of ℕ are there. That is the assumption. If no greatest 
>>>>> can
>>>>> be identified, then the reason are dark numbers.
>>>>
>>>> No, the reason is that there is no greatest element.
>>>
>>> How can that be realizied? If all are there and all are smaller than 
>>> omega, then there is a greatest one
>>
>> That is just your intuition making you think that. Try mathematical 
>> thought.
> 
> Apply it and explain how a fixed set can be well-ordered striving for 
> omega but not reaching it.

You sure seem to be locked in the world of finite thought. N is all the 
natural numbers where the word "all" does NOT imply a greatest 
natural... :^)