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NNTP-Posting-Date: Sun, 29 Dec 2024 18:12:32 +0000
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary, effectively, super-standard)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 29 Dec 2024 10:12:21 -0800
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On 12/29/2024 04:34 AM, Richard Damon wrote:
> On 12/29/24 6:01 AM, WM wrote:
>> On 28.12.2024 20:17, Richard Damon wrote:
>>> On 12/28/24 11:50 AM, WM wrote:
>>
>>> Every Natural Number is less that almost all other natural numbers,
>>> so its %-tile of progress is effectively 0, but together they make up
>>> the whole infinite set.
>>
>> All definable numbers (FISONs) stay below 1 %. Every union of "below 1
>> %" stays below 1 %.
>>
>> Regards, WM
>
> Since 0 is Less than 1, you are sort of correct, but that fact doesn't
> prove your claim.
>
> The problem is that when you get to *ALL* you are now talking abut
> infinite mathematics, which your logic just can't handle, because you, a
> finite being, can't do all of an infinite set individually, so it isn;t
> something you can talk about.

Duns Scotus:  infinity is in
Spinoza:  infinity is in
Leibniz:  infinity is in


Most people point to some like these when saying
"yes we can talk about infinity, mathematically".

Since at least "Medievel times"


The Aristotleans sort of have that it's not in,
yet, it's approached in many ways, and Zeno gives
reasonings why it is what it is.

Then, there's also that after Russell that it's
so that there are no "standard models" only
"fragments and extensions:  super-standard".

https://www.youtube.com/watch?v=9r-HbQZDkU0&list=PLb7rLSBiE7F4_E-POURNmVLwp-dyzjYr-&index=29

"Logos 2000:  natural infinities": in this podcast
is explained "three natural infinities".


The "effectively" infinite shows up in any
consideration of the "negligence" of terms.
Then about related rates and here the convolutive,
symmetrical about 0 <-> oo, there's that the usual
trolling here is rather lacking, yet the soft-ball
straw-man fallacy isn't for making a "false rejection
fallacy".


So, according to your own reasoning about infinitary
reasoning, either acknolwedge its greater surrounds
and fuller dialectic or "it's trolls all the way down".


Because here it's turtles, though an inverted turtle
is a rather helpless creature, ....