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From: WM <invalid@no.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sun, 27 Oct 2024 17:20:17 +0100
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Am 27.10.2024 um 12:38 schrieb Richard Damon:
> On 10/27/24 3:38 AM, WM wrote:
>> Am 26.10.2024 um 21:35 schrieb Chris M. Thomasson:
>>> On 10/26/2024 9:04 AM, WM wrote:
>>>> On 26.10.2024 05:21, Jim Burns wrote:
>>>>> On 10/25/2024 3:15 PM, WM wrote:
>>>>
>>>>>> Mainly, among other points, the claim that
>>>>>> all unit fractions can be defined and the claim that
>>>>>> a Bob can disappear in lossless exchanges.
>>>>>
>>>>> The proof that all unit fractions can be defined
>>>>> is to define them
>>>>> as reciprocals of positive countable.to.from.0 numbers.
>>>>>
>>>>> That describes all of them and only them.
>>>>
>>>> No, you falsely assume that all natnumbers can be defined.
>>>
>>> Huh? Confusing to me. Humm... Are you trying to suggest that a 
>>> natural number can _not_ be a natural number?
>>
>> No. But most natnumbers cannot be defined. This can best be understood 
>> by the unit fractions.
> 
> So, what is the line between the DEFINED natural numbers and the "not 
> defined"?

There is no line. The defined natural numbers are a potentially infinite 
set, i.e. it can grow without end.

Regards, WM