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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? (infinitary)
Date: Tue, 8 Oct 2024 12:30:05 -0700
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On 10/7/2024 5:57 PM, Richard Damon wrote:
> On 10/7/24 8:38 PM, Chris M. Thomasson wrote:
>> On 10/7/2024 4:01 PM, Richard Damon wrote:
>>> On 10/7/24 4:27 PM, Chris M. Thomasson wrote:
>>>> On 10/7/2024 4:17 AM, Richard Damon wrote:
>>>>> On 10/7/24 7:13 AM, joes wrote:
>>>>>> Am Mon, 07 Oct 2024 10:13:21 +0200 schrieb WM:
>>>>>>> On 06.10.2024 17:55, joes wrote:
>>>>>>>> Am Sun, 06 Oct 2024 17:26:07 +0200 schrieb WM:
>>>>>>>>> On 06.10.2024 16:52, Alan Mackenzie wrote:
>>>>>>>>>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>>>>>
>>>>>>>>>> This idea of time may be what misleads the mathematically less 
>>>>>>>>>> adept
>>>>>>>>>> into believing that 0.999... < 1.
>>>>>>>>> That is true even in actual infinity.
>>>>>>>>> We can add 9 to 0.999...999 to obtain 9.999...999. But multiplying
>>>>>>>>> 0.999...999 by 10 or, what is the same, shifting the digits 9 
>>>>>>>>> by one
>>>>>>>>> step to the left-hand side, does not increase their number but 
>>>>>>>>> leaves
>>>>>>>>> it constant: 9.99...9990.
>>>>>>>>> 10*0.999...999 = 9.99...9990 = 9 + 0.99...9990 < 9 + 
>>>>>>>>> 0.999...999 ==>
>>>>>>>>> 9*0.999...999 < 9 as it should be.
>>>>>>>> In actual infinity, there is no last 9 (that would not be 
>>>>>>>> infinite).
>>>>>>> Actual means all, but not more. This implies a last before ω. The
>>>>>>> infinity means an end cannot be determined. It is produced by the 
>>>>>>> dark
>>>>>>> numbers.
>>>>>> Actually infinite means infinite, which doesn’t change when you 
>>>>>> add or
>>>>>> subtract a finite number.
>>>>>>
>>>>>
>>>>> Actual infinity doesn't exist for us finite beings.
>>>>
>>>> What do you mean? Are you trying to go the WM route where there is a 
>>>> largest natural number... We just can't see it yet because it's 
>>>> dark? Oh shit.
>>>
>>> I am allowing that an INFINITE being MIGHT be able to comprehend 
>>> something like an actual infinity. But this can not possibly be done 
>>> by a finite being.
>>
>> Well, us as finite beings know that there is not a largest natural 
>> number... That right there is a basic understanding of the infinite: 
>> Fair enough?
> 
> Yes, us "smart" finite beings understand that the logic of there needing 
> to be a "lowest value" unit fraction is incorrect, even if the "logic" 
> of approaching the "existing" list of points from the low side would 
> seem to imply that there should be a first.
> 
> We can't really "see" what is happening there, in a fixed creation point 
> of view, which is what makes that concept not "real" for us.

Humm... Well, I know that there is no smallest unit fraction, yet there 
are infinitely many of them that get closer and closer to zero, yet 
never reach it because no unit fraction will ever actually equal zero. 
That right there helps me as a finite being to understand some basic 
facts about infinity. And yes, WM, actual infinity... ;^)