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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: Tue, 8 Oct 2024 17:21:26 -0400
Organization: i2pn2 (i2pn.org)
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On 10/8/24 3:44 PM, Chris M. Thomasson wrote:
> On 10/8/2024 5:57 AM, Richard Damon wrote:
>> On 10/8/24 3:29 AM, Moebius wrote:
>>> Am 08.10.2024 um 02:38 schrieb Chris M. Thomasson:
>>>> On 10/7/2024 4:01 PM, Richard Damon wrote:
>>>
>>>>> 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.
>>>
>>> It can.
>>>
>>> This idiot should read Peter Suber's Infinite Reflections:
>>>
>>> "Conclusion
>>>
>>> Properly understood, the idea of a completed infinity is no longer a 
>>> problem in mathematics or philosophy. It is perfectly intelligible 
>>> and coherent. Perhaps it cannot be imagined but it can be conceived; 
>>> it is not reserved for infinite omniscience, but knowable by finite 
>>> humanity; it may contradict intuition, but it does not contradict 
>>> itself. To conceive it adequately we need not enumerate or visualize 
>>> infinitely many objects, but merely understand self-nesting. We have 
>>> an actual, positive idea of it, or at least with training we can have 
>>> one; we are not limited to the idea of finitude and its negation. In 
>>> fact, it is at least as plausible to think that we understand 
>>> finitude as the negation of infinitude as the other way around. The 
>>> world of the infinite is not barred to exploration by the equivalent 
>>> of sea monsters and tempests; it is barred by the equivalent of 
>>> motion sickness. The world of the infinite is already open for 
>>> exploration, but to embark we must unlearn our finitistic intuitions 
>>> which instill fear and confusion by making some consistent and 
>>> demonstrable results about the infinite literally counter-intuitive. 
>>> Exploration itself will create an alternative set of intuitions which 
>>> make us more susceptible to the feeling which Kant called the 
>>> sublime. Longer acquaintance will confirm Spinoza's conclusion that 
>>> the secret of joy is to love something infinite."
>>>
>>> Source: http://legacy.earlham.edu/~peters/writing/infinity.htm
>>>
>>>  > 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?
>>>
>>> Right.
>>
>> Which just says that it is something we can understand to exist, but 
>> not understand itself.
>>
>> It is like it is behind an impenetrable glass wall so we can not touch 
>> it or feel it, but just dimly observe it.
> 
> We can sure ponder on about it. Just like we know for sure that there is 
> no largest natural number. We can stare that fact in the face and 
> observe it quite clearly indeed. :^)
> 

Yes, it is something we can think about, and perhaps get some insight 
into, but what we end up studying will normally be the processes of 
potential infinity, as that is something that is rooted in what we know.

The Actual Infinity is on the other "end" of that infinite process, that 
only the infinite can travel.

> 
>>
>> Such a thing doesn't exist for us to use in our logic, so effectively 
>> doesn't exist execpt to convince us that there are things beyond our 
>> understanding.
>