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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Replacement of Cardinality
Date: Tue, 3 Sep 2024 23:04:38 -0400
Organization: i2pn2 (i2pn.org)
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On 9/3/24 7:27 AM, WM wrote:
> On 02.09.2024 20:47, Chris M. Thomasson wrote:
>> On 9/2/2024 9:56 AM, WM wrote:
>>> On 01.09.2024 21:09, Chris M. Thomasson wrote:
>>>> On 8/31/2024 8:27 PM, Moebius wrote:
>>>
>>>>> In general, for all x e IR, x > 0: NUF(x) = aleph_0.
>>>
>>> Don't get confused by that nonsense. Everybody knows that unit 
>>> fractions are different from each other. Therefore they cannot be 
>>> counted at the same x, let alone at less than all positive x, i.e., 
>>> at zero.
> 
>> I suppose you think you can prove there is a largest natural number as 
>> well? 
> 
> The proof with unit fractions is more convincing because 0 has been 
> better accepted than ω. And it is really simple: At 0 there are no unit 
> fractions. Then their set increases but all have different positions.
> 
> Regards, WM
> 

But there isn't a "first" from that direction, just like there is no 
"last" Natural Number.

That is just your problem, you don't understand the fact that "finite" 
means can get arbitrary small, and thus there doesn't need to be a 
"smallest", and in fact, there CAN'T be in the infinite set.