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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Tue, 29 Oct 2024 11:53:11 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Tue, 29 Oct 2024 09:42:07 +0100 schrieb WM:
> On 29.10.2024 01:21, Richard Damon wrote:
>> On 10/28/24 3:52 PM, WM wrote:
>>> On 28.10.2024 12:21, Richard Damon wrote:
>>>> On 10/28/24 6:36 AM, WM wrote:
>>>
>>>>> NUF increases by 1 or more, but more would violate mathematics.
>>>> No, NUF(x) jumps from 0 to Aleph_0 in the domain of finite numbers,
>>>> because there is no finite x where it has the value of 0.
>>> It has the value 0 for all x =< 0. And it cannot jump by more than 1
>>> at any point.
>> Of course it can. just not at any finite value.
> There are no others on the real line.
That's the point (pun unintended).

>>> No, but the first steps happen at undefinable x.
>> No, it happens at an x that isn't a finite number.
> The nit is dark.
I.e. infinitesimal.

>> If you allow your NUF to accept infintesimal numbers
> No, that is strongly forbidden.
Then there is no x with NUF(x)=1.

>>>>> This infinity between 0 and (0, 1] is not what I can accept.
>>>> Note, it isn't an "infinity between" it is that the "bottom" of (0,
>>>> 1] doesn't exist as a definable point.
>>> That is true. The bottom is dark.
>> No, the bottom is outside the set.
> Then it is dark bottom.
>> Your "Darkness" is just your attempt to hide the problems with your
>> logic.
> And your bottom outside the set is what?
The infimum is 0.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.