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NNTP-Posting-Date: Sat, 07 Sep 2024 15:34:00 +0000
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sat, 7 Sep 2024 08:34:05 -0700
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On 09/07/2024 05:57 AM, Richard Damon wrote:
> On 9/6/24 11:00 PM, Ross Finlayson wrote:
>> On 09/06/2024 07:01 PM, Richard Damon wrote:
>>> On 9/6/24 8:07 AM, WM wrote:
>>>> On 06.09.2024 05:08, Richard Damon wrote:
>>>>> On 9/5/24 10:08 AM, WM wrote:
>>>>
>>>>>> NUF(x) must grow. It cannot grow by more than 1 at any x.
>>>>
>>>>> This is NOT the "ancient" idea of infinity,
>>>>
>>>> NUF(x) must grow. It cannot grow by more than 1 at any x.
>>>> Right or wrong in your opinion?
>>>>
>>>> Regards, WM
>>>>
>>>
>>> Only if it exists.
>>>
>>> If it does, it must be counting some sub-finite values as "unit
>>> fractions" that are not the reciprocal of the Natural Numbers (since
>>> there is no smallest of those unit fractions to count from).
>>>
>>> So, either it is counting some sub-finite values (actually a lot of them
>>> a countable infinity of them) or it just doesn't exist.
>>>
>>> Maybe that is your dark numbers, these sub-finite numbers that are
>>> reciprocals of some post-finite values above the infinite set of Natural
>>> Numbers (which have no upper bound) and are below Omega.
>>
>> That's a remarkable supposition, I wonder how you'd imagine
>> both to satisfy to yourself and others that thusly is a
>> "consistent" form, of course which only requires "internal
>> consistency" for its own sake, then besides, to suffer the
>> running of the gauntlet, of those who'd insist it contradicted
>> theirs. For, their are simple inductive arguments that nothing
>> ever happens or is, at all.
>>
>> I sort of appreciate the sentiment, though, that "infinite"
>> is big enough to have quite a range.
>>
>>
>
> The problem with "consistancy" is that WM's mathematicss isn't
> consistent with the full Natural Numbers, and unlikely to be helped with
> the addition of something even more esoteric.
>
> His work doesn't define the set well enough to actually define how it
> must work, and the best answer is likly to just adopt one of the
> existing set of sub-finite number, it just needs to have a countably
> infinite subset of values that can be reasonable defined as "unit
> fractions".


Maybe it'd do better with less.

How about this, imagine it was your duty to convince a panel of
mathematicians that something that made for the most properties
possible of the notion of an iota-value or least-positive-rational,
had a way to define this thing. Is it any different than f(1) for
n/d, d-> oo, n -> d, modeling a not-a-real-function as a limit of
real functions?

Or does that just mean crazy-town to you? The crazy-town here
is actually sort of crazy-town, like, you walk out on the streets
and at various intervals encounter derelict indigents who are
entirely insane, on most given Tuesdays.

How do you keep your sanity in crazy-town, or help rehabilitate
crazy-town? Among the ideas that nothing can be crazy if it's
all consistent, in the infinite, get into things like Hausdorff's
constructible universe, and Skolem's countable universe, or,
"model of ZF", if "universe" makes no sound to you.