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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Mon, 7 Oct 2024 13:05:35 -0700
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On 10/7/2024 4:20 AM, Richard Damon wrote:
> On 10/7/24 5:51 AM, WM wrote:
>> On 07.10.2024 11:36, FromTheRafters wrote:
>>> WM formulated the question :
>>>> On 06.10.2024 19:03, FromTheRafters wrote:
>>>>> A set is a collection of well-defined objects, meaning we must be 
>>>>> able to determine if an element belongs to a particulr set.
>>>>
>>>> But you can't determine the smallest unit fraction although it is a 
>>>> singleton set, a point on the real axis.
>>>
>>> There is no smallest unit fraction.
>>
>> If there are only fixed points, then there is a point such that 
>> between it and zero there is no further point.
>>
>> Regards, WM
>>
> 
> Nope, not if you have an INFINITE set of fixed points.
> 
> The problem is we can't have an infinite set of fixed points, as we are 
> finite.

If each one of these is "fixed" in your line of thinking:

1/1, 1/2, 1/3, 1/4, 1/5, ...

Well, there are infinitely many of them... ;^)



> 
> So, your "actual infinity" is something beyond what we can have, so it 
> doesn't exist for us, and logic that assumes it is just breaks.