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 : 03. Nov 2024, 01:17:09
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <488abfa68c5ce1c17697b463db2176396e26a99e@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 23 24 25 26 27
User-Agent : Mozilla Thunderbird
On 11/2/24 5:37 PM, WM wrote:
On 02.11.2024 21:30, Richard Damon wrote:
On 11/2/24 1:56 PM, WM wrote:
On 02.11.2024 17:02, Richard Damon wrote:
On 11/2/24 6:23 AM, WM wrote:
>
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.
>
Right, NUF(x)is 0 at x - 0, and Aleph_0 at any x > 0, since as you said, for any positive finite x, there are Aleph_0 unit fractions below it.
>
No, neither did I say so nor is it correct. Only for x > x₀ are ℵ₀ smaller unit fractions existing.
 
So, for what finite number x > 0 is there less than that?
 Those numbers are dark.
But how are they even a number.
You are just trying to assign "black magic" to you dark numbers to blaim them for the things your logic can't handle.
They just break your logic.

>
There isn't one, as we CAN PROVE that for all x > 0, there exist and infinite number of unit fractions less that x
 For every visible number x larger, much larger than x₀ you can prove that.
Nope, I can prove it for EVERY x.
You logic assumes there is no infinity, as you can't actually have all the natural numbers. Thus your concept of "actual infinity" is just a lie.
Sorry, that *IS* what you logic is saying.

 Regards, WM
 

Date Sujet#  Auteur
2 Sep 24 * How many different unit fractions are lessorequal than all unit fractions?2198WM
2 Sep 24 +* Re: How many different unit fractions are lessorequal than all unit fractions?2094Richard Damon
2 Sep 24 i`* Re: How many different unit fractions are lessorequal than all unit fractions?2093WM
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
3 Sep 24 i i `* Re: How many different unit fractions are lessorequal than all unit fractions?3Richard Damon
3 Sep 24 i i  `* Re: How many different unit fractions are lessorequal than all unit fractions?2WM
4 Sep 24 i i   `- Re: How many different unit fractions are lessorequal than all unit fractions?1Richard Damon
3 Sep 24 i `* Re: How many different unit fractions are lessorequal than all unit fractions?2087Jim Burns
3 Sep 24 i  `* Re: How many different unit fractions are lessorequal than all unit fractions?2086WM
3 Sep 24 i   `* Re: How many different unit fractions are lessorequal than all unit fractions?2085Jim Burns
4 Sep 24 i    `* Re: How many different unit fractions are lessorequal than all unit fractions?2084WM
4 Sep 24 i     +* Re: How many different unit fractions are lessorequal than all unit fractions?2080Jim Burns
5 Sep 24 i     i`* Re: How many different unit fractions are lessorequal than all unit fractions?2079WM
5 Sep 24 i     i `* Re: How many different unit fractions are lessorequal than all unit fractions?2078Jim Burns
5 Sep 24 i     i  `* Re: How many different unit fractions are lessorequal than all unit fractions?2077WM
6 Sep 24 i     i   +* Re: How many different unit fractions are lessorequal than all unit fractions?2075Python
6 Sep 24 i     i   i+* Re: How many different unit fractions are lessorequal than all unit fractions?4Moebius
6 Sep 24 i     i   ii`* Re: How many different unit fractions are lessorequal than all unit fractions?3Moebius
6 Sep 24 i     i   ii `* Re: How many different unit fractions are lessorequal than all unit fractions?2WM
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?2070WM
6 Sep 24 i     i   i +* Re: How many different unit fractions are lessorequal than all unit fractions?2062joes
6 Sep 24 i     i   i i`* Re: How many different unit fractions are lessorequal than all unit fractions?2061WM
6 Sep 24 i     i   i i `* Re: How many different unit fractions are lessorequal than all unit fractions?2060Python
6 Sep 24 i     i   i i  `* Re: How many different unit fractions are lessorequal than all unit fractions?2059WM
7 Sep 24 i     i   i i   `* Re: How many different unit fractions are lessorequal than all unit fractions?2058Python
7 Sep 24 i     i   i i    +* Re: How many different unit fractions are lessorequal than all unit fractions?2WM
7 Sep 24 i     i   i i    i`- Re: How many different unit fractions are lessorequal than all unit fractions?1joes
7 Sep 24 i     i   i i    `* Re: How many different unit fractions are lessorequal than all unit fractions?2055Moebius
7 Sep 24 i     i   i i     +* Re: How many different unit fractions are lessorequal than all unit fractions?55Moebius
7 Sep 24 i     i   i i     i`* Re: How many different unit fractions are lessorequal than all unit fractions?54WM
7 Sep 24 i     i   i i     i `* Re: How many different unit fractions are lessorequal than all unit fractions?53Richard Damon
7 Sep 24 i     i   i i     i  `* Re: How many different unit fractions are lessorequal than all unit fractions?52WM
7 Sep 24 i     i   i i     i   `* Re: How many different unit fractions are lessorequal than all unit fractions?51Richard Damon
8 Sep 24 i     i   i i     i    `* Re: How many different unit fractions are lessorequal than all unit fractions?50WM
8 Sep 24 i     i   i i     i     +* Re: How many different unit fractions are lessorequal than all unit fractions?21Richard Damon
9 Sep 24 i     i   i i     i     i`* Re: How many different unit fractions are lessorequal than all unit fractions?20WM
9 Sep 24 i     i   i i     i     i +* Re: How many different unit fractions are lessorequal than all unit fractions?13Richard Damon
9 Sep 24 i     i   i i     i     i i`* Re: How many different unit fractions are lessorequal than all unit fractions?12WM
9 Sep 24 i     i   i i     i     i i +* Re: How many different unit fractions are lessorequal than all unit fractions?8joes
9 Sep 24 i     i   i i     i     i i i`* Re: How many different unit fractions are lessorequal than all unit fractions?7WM
9 Sep 24 i     i   i i     i     i i i +* Re: How many different unit fractions are lessorequal than all unit fractions?5joes
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10 Sep 24 i     i   i i     i     i i  `* Re: How many different unit fractions are lessorequal than all unit fractions?2WM
11 Sep 24 i     i   i i     i     i i   `- Re: How many different unit fractions are lessorequal than all unit fractions?1Richard Damon
9 Sep 24 i     i   i i     i     i `* Re: How many different unit fractions are lessorequal than all unit fractions?6joes
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8 Sep 24 i     i   i i     i     `* Re: How many different unit fractions are lessorequal than all unit fractions?28joes
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