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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: Mon, 28 Oct 2024 20:21:19 -0400
Organization: i2pn2 (i2pn.org)
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On 10/28/24 3:47 PM, WM wrote:
> On 28.10.2024 12:21, Richard Damon wrote:
>> On 10/28/24 6:32 AM, WM wrote:
>>> On 27.10.2024 18:08, Moebius wrote:
>>>> Am 27.10.2024 um 17:12 schrieb WM:
>>>>> Am 27.10.2024 um 14:54 schrieb Moebius:
>>>>
>>>>>> Hint: For each and every x e IR, x <= 0: NUF(x) = 0
>>>>>> and for each and every x e IR, x > 0: NUF(x) = aleph_0.
>>>>>
>>>>> That [...] would require that [for each and every x > 0] [there] 
>>>>> exist [ℵo unit fractions] between 0 and x
>>>>
>>>> Exactly!
>>>>
>>> This requirement is impossible to satisfy because every unit fraction 
>>> is an x > 0.
> 
>> Of course it isn't.
> 
> In order to maintain your nonsense, you have even to deny that all unit 
> fractions are positive or to believe that many sit between 0 and (0, oo).

Nope, we just need to recognize that since the number line is an 
infinite and dense set, that (0, 1] doesn't have a lowest number in it.

Its greatest lower bound is 0, which is outside the set, so there is no 
"boundary" point at the bottom of the set, which is thus "unbounded"

> 
>> You just don't understand how infinity works. Things without ends just 
>> behave differently then things with finite ends,
> 
> But never so.

Only to your stuck finite mind.

> 
> Regards WM
> 
>