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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: Thu, 17 Oct 2024 21:26:18 -0400
Organization: i2pn2 (i2pn.org)
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On 10/17/24 2:22 PM, WM wrote:
> On 17.10.2024 00:39, Jim Burns wrote:
> 
>> No natural number is
>> the first to not.have a natural.number.double.
> 
> True.
> 
>>>
>>>> When doubling all natural numbers
>>>> we obtain only natural numbers.
>>>
>>> That is impossible.
>>
>> There is no first natural number from which we obtain
>> (by doubling) anything not.a.natural.number.
> 
> True.
>>
>> The only set of natural numbers with no first
>> is the empty set..
> 
> No, the set of dark numbers is another set without smallest element.
>>
>> There is no ▒▒▒▒▒ natural number from which we obtain
>> (by doubling) anything not.a.natural.number.
> 
> Correct is: There is no such _definable_ natnumber.

But all Natural Numbers are definable.

You are just creating your "darknesss" to try to hide your stupdity, but 
it doesn't work.

> 
> There is a general rule not open to further discussion:
> When doubling natural numbers we obtain even numbers which have not been 
> doubled.
> In potential infinity we obtain more even natural numbers than have been 
> doubled.
> In actual infinity we double ℕ and obtain neither ℕ or a subset of ℕ.
> 
> Regards WM
> 
> 

Your general rule not open to further discussion is what put you outside 
the realms of logic.

It is the sharpanel from the explosion to smithereens of your logic 
system from the contradiction you have put into it.