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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: Sat, 2 Nov 2024 20:17:12 -0400
Organization: i2pn2 (i2pn.org)
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On 11/2/24 5:39 PM, WM wrote:
> On 02.11.2024 21:34, Richard Damon wrote:
>> On 11/2/24 1:42 PM, WM wrote:
>>> On 02.11.2024 14:50, Moebius wrote:
>>>> Am 02.11.2024 um 14:21 schrieb joes:
>>>>> Am Fri, 01 Nov 2024 18:03:26 +0100 schrieb WM:
>>>>
>>>>>> If an invariable set of numbers is there, then there is a smallest 
>>>>>> and a
>>>>>> largest number of those which are existing.
>>>>
>>>> or each and every n e IN there is an n' e IN (say n' = n+1)
>>>
>>> Actual infinity is not based on claims for each and every, but 
>>> concerns all.
> 
>> But if it applies to ALL, it must apply to ANY, so a property of ANY 
>> must apply to each on of the ALL.
>>
>> So, for ALL the Natural Numbers, there can't be a highest, because for 
>> ANY Natural Number there is a following one
> 
> That cannot be true for all dark numbers.
> 
> Regards, WM
> 

But dark numbers don't actually exist, at least not by your description.

The statement does hold for *ALL* Natural Numbers, by there definition.

This just proves that you idea of "dark numbers" just does't work. If 
you want try to actual come up with some definitions for them, go ahead, 
but just trying to blame them for everything that breaks your logic and 
your need to lie about the actual Natural Numbers doesn't work.

Your problem is that you logic can't make the Natural Numbers, and blows 
its self, and your mind, when you try to make it do so, and the darkness 
of your numbers is just the hole it left behind.