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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Sun, 27 Oct 2024 09:39:19 -0400
Organization: Peripheral Visions
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Richard Damon has brought this to us :
> 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"?

If 'not defined' could be a proper subset of the naturals, then there 
would be a first such 'not defined' in that subset. Of course WM can't 
substantiate any of his wild claims. He's clearly lost his mind.

>> Try to understand the function NUF(x) = Number of Unit Fractions between 0 
>> and x, which starts with 0 at 0 or less and after NUF(x') = 1 cannot change 
>> to 2 without pausing for an interval consisting of uncountably many real 
>> points. The reason is this: ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.
>
> And isn't defined, since there is no finite number x, such that NUF(x) has 
> the value of 1.
>
> Your logic just assumes the existance of something that doesn't exist, and 
> thus is unsound, just like your own mind,

What there is left of it.