Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

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Sujet : Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.math
Date : 11. Oct 2024, 23:12:16
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <120c574f31c494e2fb70824dc2280afa905569ba@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
User-Agent : Mozilla Thunderbird
On 10/11/24 2:02 PM, Jim Burns wrote:
On 10/11/2024 7:06 AM, Richard Damon wrote:
On 10/10/24 11:19 PM, Chris M. Thomasson wrote:
On 10/10/2024 6:38 PM, Richard Damon wrote:
On 10/10/24 2:32 PM, WM wrote:
 
If not all do exist,
te doubling yields larger natnumbers,
some of which have not existed before.
But that means potential infinity.
>
But there aren't any natural numbers that
have not existed before. That is just showing that
your "actual infinity" is a finite set that you grabbed on the way to infinity,
but didn't get there yet.
>
Actual infinity means
you need to wait until you get there.
The problem is
finite creatures can't do that,
so can't handle actual infinity.
 
What do you mean?
I can say all the natural numbers.
That was pretty fast for all of them. ;^)
>
Which names the set,
but not actually list the contents of that set.
 Is a set
without a finite list  but
with a finite description
potential or actual?
Having not the INFINITE list, but just a finite description of the set is a potential infinity in the systems he is referring. Actual infinity has the completely enumerated list of all the infinite number of members of the set, which can not be changed. (and it turns out, can not be observed by a finite being)

 It looks to me as though the consensus is:
we don't care what the answer is.
It may not to you, but it does to him.
The issue is that his concept of the complete list takes on the properties of a finite list, even though it IS an infinite list, and thus not "perceivable" to a finite being.

 We have a description of ℕ and its elements,
free of mentions of 'potential' and 'actual'.
 From its description,
we can reason about it and its elements.
Which puts it in his classification as just a potential infinity.

"Potential ℕ" vs. "actual ℕ" leaves unchanged
which claims we reason to.
No, the claim is that if we have at hand the complete list of all the elements, we don't need to "reason" about things, but can just observe the facts about them.
The problem is that we can't actually "observe" the things, as actual infinity turns out to not be observable by finite beings, so he ends up looking at showdows of it and thinks he is looking at the real thing.
Those shaddow confuse the infinite for bigger than we can imagine, and then we imagine we got there and see the end that wasn't really there.

 I see them as in the same vein as
weekday.mathematics and Sunday.mathematics.[1]
A distinction without a difference.
At least with the casual mathematician (whch I will admit being one) is that they tend to pick up the tools that are normally in use, and may us them a bit ineptly, but will generally listen to correction. Sometimes they may pick up an arcane tool, and the "pros" may not remember that being used that way, and there might be a bit more work to figure out what is going on.
Wackos (like WM) seem to pick up some of these tools (or tools discarded for not being useful) and not really understanding how they were supposed to work just wail away, and refuse to accept the corrections showing the errors found in history, as they think they no better.

 And I see that indifference as there _by design_
It is why unwelcome mathematical results are accepted
not because mathematicians are paragons of rectitude
(no offense)
but because there is no weasel.ability in mathematics.
 ⎛ Not everyone appreciates that lack of weasel.ability.
⎝ Those who don't self.select to be non.mathematicians.
 [1]

⎜ Most writers on the subject seem to agree that
⎜ the typical “working mathematician” is
⎜ a Platonist on weekdays and a formalist on Sundays.
⎜ That is, when he is doing mathematics,
⎜ he is convinced that
⎜ he is dealing with an objective reality
⎜ whose properties he is attempting to determine.
⎜ But then, when challenged to give
⎜ a philosophical account of this reality,
⎜ he finds it easiest to pretend that
⎜ he does not believe in it after all.

https://core.ac.uk/download/pdf/82047627.pdf
Some Proposals for Reviving the Philosophy of Mathematics
REUBEN HERSH
Department of Mathematics, University of New Mexico,
Albuquerque, New Mexico 87131
 

Date Sujet#  Auteur
2 Sep 24 * How many different unit fractions are lessorequal than all unit fractions?2203WM
2 Sep 24 +* Re: How many different unit fractions are lessorequal than all unit fractions?2098Richard Damon
2 Sep 24 i`* Re: How many different unit fractions are lessorequal than all unit fractions?2097WM
2 Sep 24 i +* Re: How many different unit fractions are lessorequal than all unit fractions?5Richard Damon
3 Sep 24 i i`* Re: How many different unit fractions are lessorequal than all unit fractions?4WM
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3 Sep 24 i `* Re: How many different unit fractions are lessorequal than all unit fractions?2091Jim Burns
3 Sep 24 i  `* Re: How many different unit fractions are lessorequal than all unit fractions?2090WM
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5 Sep 24 i     i`* Re: How many different unit fractions are lessorequal than all unit fractions?2083WM
5 Sep 24 i     i `* Re: How many different unit fractions are lessorequal than all unit fractions?2082Jim Burns
5 Sep 24 i     i  `* Re: How many different unit fractions are lessorequal than all unit fractions?2081WM
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7 Sep 24 i     i   ii  `- Re: How many different unit fractions are lessorequal than all unit fractions?1Richard Damon
6 Sep 24 i     i   i`* Re: How many different unit fractions are lessorequal than all unit fractions?2074WM
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6 Sep 24 i     i   i i`* Re: How many different unit fractions are lessorequal than all unit fractions?2064WM
6 Sep 24 i     i   i i `* Re: How many different unit fractions are lessorequal than all unit fractions?2063Python
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7 Sep 24 i     i   i i    i`- Re: How many different unit fractions are lessorequal than all unit fractions?1joes
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9 Sep 24 i     i   i i     i     i`* Re: How many different unit fractions are lessorequal than all unit fractions?20WM
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9 Sep 24 i     i   i i        i i   i +* Re: How many different unit fractions are lessorequal than all unit fractions?3Chris M. Thomasson
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