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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Simple enough for every reader?
Date: Sat, 17 May 2025 23:27:57 -0700
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On 5/17/2025 11:20 PM, Chris M. Thomasson wrote:
> On 5/17/2025 12:06 PM, FromTheRafters wrote:
>> After serious thinking Chris M. Thomasson wrote :
>>> On 5/17/2025 10:35 AM, WM wrote:
>>>> On 17.05.2025 19:20, Alan Mackenzie wrote:
>>>>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>>>>> Are you aware of the fact that in
>>>>>
>>>>>> {1}
>>>>>> {1, 2}
>>>>>> {1, 2, 3}
>>>>>> ...
>>>>>> {1, 2, 3, ..., n}
>>>>>> ...
>>>>>
>>>>>> up to every n infinitely many natural numbers of the whole set
>>>>>
>>>>>> {1, 2, 3, ...}
>>>>>
>>>>>> are missing? Infinitely many of them will never be mentioned
>>>>>> individually. They are dark.
>>>>>
>>>>> <Yawn>
>>>>
>>>> Exciting. Many readers claim(ed) that all natural numbers could be 
>>>> used as individuals. Further this would be a precondition for 
>>>> countability of infinite sets.
>>>
>>> Show me a dark natural number?
>>
>> 666
> 
> Another natural number could be first number non-zero, roll a 10 sided, 
> faces { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }, die until you get non zero. 
> Then, roll 10 sided die evermore...
> 
> So build the natural number, roll, oh shit got a zero, roll again, got a 2:
> 
> 2
> 
> Now Roll, roll, roll, roll, ...
> 
> 279304...
> 
> We are building a natural number digit by digit using random rolls, the 
> first roll needs to be higher that zero... Fair enough? They will all be 
> natural numbers, right?

So, how could my process "break" when the natural numbers are infinite 
any at any step of the process, its within that domain? N is taking the 
naturals to infinity, as that has all of them, so my process is in that 
domain even when taken to infinity, or does it somehow "break free"? So 
to speak?