Re: Ordinals

From	Richard Damon <richard@damon-family.org>
Newsgroups	sci.math
Subject	Re: Ordinals
Date	2024-03-01 09:44 -0500
Organization	i2pn2 (i2pn.org)
Message-ID	<urspko$e433$1@i2pn2.org> (permalink)
References	(6 earlier) <b8dMn7_7dL9kYr-1qK_KxCDw7gU@jntp> <urptma$abti$2@i2pn2.org> <2NRiNAMtOqLljuoKQ0Z4UbqiHbE@jntp> <urrh33$cbpp$7@i2pn2.org> <LBmDFtF_MpgLzTOD9gc34iqo3Cw@jntp>

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On 3/1/24 3:47 AM, WM wrote:
> Le 01/03/2024 à 04:12, Richard Damon a écrit :
> 
>> And evvery natural number is finite and thus namable and thus visible.
> 
> That concerns potential infinity only.

No, it applies to ALL Finite numbers, which of course, being finte, 
never actally REACH infinite, so if you want to invent a term for that 
as "Potential Infinity", so be it.

But ALL

> 
>> It is the SET that "completes infinity", and the set isn't any of the 
>> individual number.
> 
> The set is nothig but the collection of its elements. 

But it is, it is the COLLECTION of ALL its elements AT ONCE.

Thus, it converts the potential infinity of the individal Natural 
Numbers, none of which are themselves infinite, into the ACTUAL infinity 
of the set itself, and its size.

So, I guess your "dark" numbers, the ones that can only be talked about 
as sets, are to collectively is the final collection (and its size).

Thus, your "NUF(x)" function is "dark" and you can't use its values 
individually, so NUF(x) = 1 is an invalid statement.

> The complete set 
> requires that no element is missing. That proves, via ∀n ∈ ℕ: 1/n - 
> 1/(n+1) = d_n > 0, the existence of a smallest unit fraction.

Why does it require a smallest unit fraction?

Your equation proves to opposite.

Given that for all n 1/n - 1/(n+1) > 0

we can say that for all n (by addin 1/(n+1)

1/n > 1/(n+1)

Since for all n, n+1 exists (from the definition of the natural numbers)

Thus, there can not be a smallest 1/n

Smallest here only applies to finite sub-sets, not the final actually 
infinite set.

> 
> Regards, WM
> 
> 
>

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Re: Ordinals "markus...@gmail.com" <markusklyver@gmail.com> - 2024-02-20 11:35 -0800
  Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-20 20:54 +0100
    Re: Ordinals "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-20 11:59 -0800
  Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-20 12:15 -0800
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    Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-20 17:02 -0500
      Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-20 19:36 -0800
        Re: Ordinals Mild Shock <bursejan@gmail.com> - 2024-02-21 05:47 -0800
          Re: Ordinals Mild Shock <bursejan@gmail.com> - 2024-02-21 05:50 -0800
            Re: Ordinals Mild Shock <bursejan@gmail.com> - 2024-02-21 06:16 -0800
        Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-21 10:24 -0800
          Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 09:03 +0100
            Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 09:11 +0100
            Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 10:16 -0800
              Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 19:20 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 19:22 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 19:40 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:00 +0100
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 10:55 -0800
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:08 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:13 +0100
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 11:01 -0800
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:11 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:13 +0100
            Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-22 14:34 -0500
              Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 11:39 -0800
              Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-23 00:41 +0100
      Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-21 08:33 +0000
        Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-21 12:59 -0500
          Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-22 13:00 +0000
            Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-22 11:13 -0500
              Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-23 08:47 +0000
                Semanticists candy (Was: Ordinals) Mild Shock <janburse@fastmail.fm> - 2024-02-26 12:58 +0100
                Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-27 14:25 -0500
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-27 11:59 -0800
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-27 20:05 +0000
                Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-27 17:24 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-28 09:48 +0000
                Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-28 06:52 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-28 17:24 +0000
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-02-28 17:07 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-29 08:23 +0000
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-02-29 07:35 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-29 19:25 +0000
                Re: Ordinals "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-29 13:48 -0800
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-02-29 22:12 -0500
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-29 19:36 -0800
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 20:38 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 20:52 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 21:08 +0100
                Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-03-01 15:56 -0500
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 22:53 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 23:11 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 23:33 +0100
                Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-03-01 19:41 -0500
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-01 20:15 -0800
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-02 10:49 -0800
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-02 20:40 +0100
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-01 14:45 -0800
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-01 08:47 +0000
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-03-01 09:44 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-01 18:29 +0000
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-03-01 14:00 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-02 12:36 +0000
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-03-02 09:22 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-02 15:25 +0000
  Re: Ordinals "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-20 17:21 -0800
    RSemanticists candy (Re: Ordinals) [Addendum] Mild Shock <janburse@fastmail.fm> - 2024-02-26 13:01 +0100

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