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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Tue, 08 Oct 2024 06:26:46 -0400
Organization: Peripheral Visions
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Moebius wrote :
> Am 08.10.2024 um 09:30 schrieb Moebius:
>> Am 08.10.2024 um 09:29 schrieb Moebius:
>>> 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:
>> 
>> "Perhaps it cannot be imagined but it can be conceived; it is not reserved 
>> for infinite omniscience, but knowable by finite humanity..."
>> 
>>> "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?
>
> "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." :-P

Yes, consider "Lather, Rinse, Repeat" is infinite unless and until we 
restrict it to "Lather, Rinse, Repeat 5 times" or Lather Rinse Repeat 
until bottle is empty" or some such recursion bailout is reached or 
iteration count completes.