Article <v8p63d$a0fn$2@dont-email.me>

Warning: mysqli::__construct(): (HY000/1203): User howardkn already has more than 'max_user_connections' active connections in D:\Inetpub\vhosts\howardknight.net\al.howardknight.net\includes\artfuncs.php on line 21
Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connections
Warning: mysqli::query(): Couldn't fetch mysqli in D:\Inetpub\vhosts\howardknight.net\al.howardknight.net\index.php on line 66
Article <v8p63d$a0fn$2@dont-email.me>

Deutsch English Français Italiano

<v8p63d$a0fn$2@dont-email.me>

View for Bookmarking (what is this?)
Look up another Usenet article

Path: ...!2.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Mon, 5 Aug 2024 02:24:13 +0200
Organization: A noiseless patient Spider
Lines: 48
Message-ID: <v8p63d$a0fn$2@dont-email.me>
References: <hsRF8g6ZiIZRPFaWbZaL2jR1IiU@jntp>
 <-qUZ96ARwcjh9QPfyWRnijjNwoY@jntp>
 <6b837540-3d9a-4b8e-9a70-88d52e81a1a4@att.net>
 <xQQT0K_Q_k2FbMcCUXF8j3CEg84@jntp>
 <9822f5da-d61e-44ba-9d70-2850da971b42@att.net>
 <p36L63dXamDAkHDhkZhDKqx-h-o@jntp>
 <d8bbe664-a601-4590-9a7f-d5312b4dae54@att.net>
 <F6pqEi9Vg1YMcYTcIPQNs6NU_vI@jntp>
 <4f606ef2-ef6c-487b-b959-d109e374929f@att.net> <v8mh6f$3mmj9$2@dont-email.me>
 <I2JWgvxiRMkr8F2KSK6i7i5b1n0@jntp> <v8p1jp$9gvr$1@dont-email.me>
Reply-To: invalid@example.invalid
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Mon, 05 Aug 2024 02:24:13 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="781e31630972fbca343b535050bc8635";
	logging-data="328183"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+6KSy/Up+1OA1iXTX7cZMl"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:laE1x6ylRYJJS5ih+ysDD6g5nqA=
Content-Language: de-DE
In-Reply-To: <v8p1jp$9gvr$1@dont-email.me>
Bytes: 2866

Am 05.08.2024 um 01:07 schrieb Chris M. Thomasson:
> On 8/4/2024 8:35 AM, WM wrote:
>> Le 04/08/2024 à 02:15, Moebius a écrit :
>>> Am 03.08.2024 um 21:54 schrieb Jim Burns:
>>>> On 8/3/2024 10:23 AM, WM wrote:
>>>
>>>>> NUF(x) = ℵ₀ for all x > 0 is wrong.
>>>
>>> Nonsense.
>>>
>>> Actually, Ax > 0: NUF(x) = ℵ₀.
>>
>> You mean that there are ℵ₀ unit fractions smaller than all positive x?

Obviously not.

What I mean is that for all positive x there are ℵ₀ unit fractions 
smaller than x.

>> Impossible. [...] Not even one unit fraction can be smaller than all positive x.

No one (except WM) claimed that there's a unit fraction which is smaller 
than all positive x.

> Huh?

WM is constantly mixing up

          ∀x > 0: ∃^ℵ₀ u ∈ ⅟ℕ: u < x   (true)
with
          ∃^ℵ₀ u ∈ ⅟ℕ: ∀x > 0: u < x   (false) .

(Here ⅟ℕ = {1/n : n e IN} is the set of all unit fractions.)

> Say x = 1/2, there are infinite smaller unit fractions, say, 1/4, 
> 1/5, 1/6, ect... However there is only one larger one, 1/1. See? No 
> smallest one for 1/0 is not a unit fraction! There is a largest one, 1/1...
> 
> They tend to zero, but there is no smallest one...

Yeah.

Proof: If s is a unit fraction then 1/(1/s + 1) is a unit fraction which 
is smaller than s (for each and every s).

> See?