Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Collatz conjecture question
Date: Mon, 24 Mar 2025 16:53:01 +0100
Organization: A noiseless patient Spider
Lines: 22
Message-ID: <vrrv4t$17041$1@dont-email.me>
References: <vrnt34$199cq$1@dont-email.me> <vron6n$23ve9$1@dont-email.me>
 <vrpr97$2n9lu$1@dont-email.me>
 <j4ecneBTbq93EH36nZ2dnZfqnPadnZ2d@giganews.com>
 <vrq7cn$3hsgc$1@dont-email.me>
 <e5adnQPxQcNeJH36nZ2dnZfqn_ednZ2d@giganews.com> <vrr5lp$g34g$1@dont-email.me>
 <3Wby9Zhhb6vBuGxbBIcxRJcPWMg@jntp> <J3LuPdUqdDI9uyAseojZhGPD7b0@jntp>
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, 24 Mar 2025 16:53:01 +0100 (CET)
Injection-Info: dont-email.me; posting-host="c8d33bf3036d3ff7f40cb6616576354d";
	logging-data="1278081"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19WZ1GVx0V0gUPXFZAxZqUH"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:3gPkbJGx/TgsgurQwYwpR5C+nDo=
Content-Language: de-DE
In-Reply-To: <J3LuPdUqdDI9uyAseojZhGPD7b0@jntp>
Bytes: 1993

Am 24.03.2025 um 16:27 schrieb Python:
> Le 24/03/2025 à 15:47, Richard Hachel a écrit :

>>  (-5)² = 25
>>
>>  Then -5 = 5

Huh?!

Did this idiot even went to school?

Hint at RH: The function f: IR -> IR defined with f(x) = x^2 (for all x 
e IR) does not have an inverse. Hence from a² (with any a e IR) you 
can't "derive" /a/ by applying a "sqrt" inverse function (since there is 
no such function).

On the other hand there's the function sqrt: {x e IR: x >= 0} --> {x e 
IR: x >= 0} defined in a way such that sqrt(a^2) = a for all a e {x e 
IR: x >= 0}.

Hence we may get sqrt(25) = 5, but certainly NOT sqrt((-5)²) = -5. 
<facepalm>