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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?
Date: Mon, 7 Oct 2024 21:00:55 -0400
Organization: i2pn2 (i2pn.org)
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On 10/7/24 8:43 PM, Chris M. Thomasson wrote:
> On 10/7/2024 4:08 PM, Richard Damon wrote:
>> On 10/7/24 4:05 PM, Chris M. Thomasson wrote:
>>> 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... ;^)
>>>
>>>
>>
>> The problem with his "Actual infinity" is you need to get rid of 
>> the ... (as that is generative) and put in the full list of the number.
>>
>> Because you have a full list of the numbers, he think that means there 
>> is a last one to that list.
> 
> Odd to me! He must think 1/6 is dark wrt the list, right? Am I getting 
> closer to WM's strange way of thinking? Well, 1/6 is not so dark anymore 
> because I wrote it here... ;^) Wow.
> 
> 
>>
>> The problem is that the full list can not be presented to a finite 
>> being, and thus, that "Actual infinity" can't be comprehended by it.
> 
> A fill list:
> 
> all of the natural numbers.
> 
> That is a finite term for all of them. WM, well, he might explode?

Yep, that is part of the problem. We can only think of "lists" as finite 
lists, but the "actually infinite" list just goes on and on. This means 
we can't GET to that far end to start counting from there.

It just with the unit fractions, it isn't the "distance" that gets 
infinite, it is the scale gets infinitely small, so we can't get down to 
find that region, and that makes it easier to decieve yourself about its 
properties.

> 
> 
>>
>> You need to b infinite, to actually have a fully generated infinite.
>>
>> We can handle infinities by generative processes (his potential 
>> infinity) because we don't need to actually get to the end, we just 
>> know the process can continue forever and there will be no end, except 
>> after infinite work is done.
>>
>>>
>>>>
>>>> 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.
>>>
>>
>>
>