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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: Sat, 02 Nov 2024 14:11:50 -0400
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After serious thinking Ross Finlayson wrote :
> On 11/02/2024 06:54 AM, FromTheRafters wrote:
>> WM was thinking very hard :
>>> On 01.11.2024 22:53, FromTheRafters wrote:
>>>> WM explained on 11/1/2024 :
>>>>> On 01.11.2024 19:39, FromTheRafters wrote:
>>>>>> WM formulated the question :
>>>>>
>>>>>>>> Infinite subsets don't do that for you, even if you wish really
>>>>>>>> hard.
>>>>>>>
>>>>>>> They cannot evade if they are invariable.
>>>>>>
>>>>>> Sets don't change.
>>>>>
>>>>> Therefore the elements do not depend on us and our knowledge. "If I
>>>>> find x, then I can find x + 1" is not relevant. "For every x (that I
>>>>> find) there is x + 1" is no relevant. All elements are there,
>>>>> independent of what we know or do. Therefore the first and the last
>>>>> are also there independent of us. If they weren't, their existence
>>>>> would depend on some circumstances and could change.
>>>>
>>>> Circumstances like "there is no last element"?
>>>
>>> That means, there is always another element. Potential infinity.
>>
>> Sets don't change. Forget about amplifying 'not finite' with such as
>> 'actual' and potential' -- infinite simply means not finite and
>> 'actual/potential' is a distinction without a difference. A useless
>> concept outside of math philosophy.
>>
>>>> the set of denominators have no largest element to 'start' with.
>>>
>>> If all unit fractions are existing, then a smallest unit fraction is
>>> existing. If NUF(x) has grown to ℵ₀ at x₀, then ℵ₀ unit fractions must
>>> be between 0 and x₀. Hence at least ℵ₀ points with ℵ₀ intervals of
>>> uncountably many points must be between 0 and x₀. That cannot happen
>>> at x₀ = 0.
>>>
>>> Is that too hard to understand?
>>
>> Apparently, for you.
>
> Au contraire, there are multiple law(s) of large numbers,
> and in mathematics like emergence after convergence,
> the potential / practical / effective / actual distinction,
> of "infinity", is a thing.
>
> You know who discovered mathematics? Philosophers.

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AI Overview
Learn more…
While philosophers like Pythagoras played a significant role in the 
early development of mathematics by exploring its concepts and 
principles, it's not accurate to say that philosophers "discovered" 
math; rather, mathematics evolved from practical applications across 
different civilizations, with philosophers contributing to its 
theoretical understanding and philosophical implications.
Key points to consider:

    Historical context:
    Ancient civilizations like the Egyptians and Babylonians used 
mathematics for practical purposes like measuring land and calculating 
taxes before the emergence of formal philosophical inquiry.

Philosophical contributions:
Thinkers like Pythagoras and Plato later examined the nature of 
mathematical concepts, leading to philosophical discussions about the 
existence and universality of mathematical truths.

Debate on discovery vs. invention:
Today, philosophers of mathematics still debate whether mathematics is 
"discovered" (existing independently of humans) or "invented" (a human 
construct).

    Philosophy of mathematics - Wikipedia
    Pythagoras is considered the father of mathematics and geometry as 
he set the foundation for Euclid and Euclidean geometry. Pythag...
    Wikipedia

Platonism in the Philosophy of Mathematics
Jul 18, 2009 — Platonism about mathematics (or mathematical platonism) 
is the metaphysical view that there are abstract mathematical ...
Stanford Encyclopedia of Philosophy
Is Math a Human Invention or a Natural Phenomenon?
Jan 8, 2023 — There is ongoing debate among philosophers and 
mathematicians about whether mathematics is discovered or invented. 
Some...
Medium

    Show all

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