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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Wed, 9 Oct 2024 08:02:56 -0400
Organization: i2pn2 (i2pn.org)
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On 10/9/24 5:28 AM, WM wrote:
> On 08.10.2024 20:01, Richard Damon wrote:
>> On 10/8/24 11:26 AM, WM wrote:
> 
>>> But after the visble natural numbers the dark domain comes, and that 
>>> is what prevents to see the end (which is dark too).
>>
>> Where?
>>
>> The "visible" numbers, per you definition are ALL the numbers, as all 
>> of them can be used individually and are selectable.
> 
> Wrong. Every visible number has infinitely many successors. Therefore 
> there are infinitely many successors beyond every visible number. 
> Otherwise there was a visible number with less successors.

Right, every visible numbers has an infinitely many VISIBLE successors, 
thus no last one.

>>
>> Thus, there aren't any left to be dark, except the ones that don't 
>> actually exist.
>>
>>>>> That shows my point. Infinite sets can be moved. 0.999...999 moved 
>>>>> gives
>>>>> 9.99...9990.
>>>> You have not indicated what this notation means. Where does the zero 
>>>> come
>>>> from?
>>>
>>> The last natural index has lost its 9 by shifting to the left-hand 
>>> side. Hence there is nothing remaining.
>>
>> How did it "lose" it,
> 
> By shifting to the left-hand side.

but it had no end, or it wasn't infinite.

Your problem seems to be that you refuse to understand what "infinite" 
means.

> 
> Regards, WM