From mboxrd@z Thu Jan 1 00:00:00 1970 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Eduardo Ochs Newsgroups: gmane.emacs.help Subject: Re: (*) -> 1 Date: Tue, 17 Jan 2023 15:28:34 -0300 Message-ID: References: <87r0vuidjc.fsf@eder.anydns.info> <87y1q1kvdm.fsf@web.de> <87h6wpkrlq.fsf@web.de> Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="909"; mail-complaints-to="usenet@ciao.gmane.io" To: Michael Heerdegen , help-gnu-emacs@gnu.org Original-X-From: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane-mx.org@gnu.org Tue Jan 17 19:29:40 2023 Return-path: Envelope-to: geh-help-gnu-emacs@m.gmane-mx.org Original-Received: from lists.gnu.org ([209.51.188.17]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1pHqiJ-000Abg-W8 for geh-help-gnu-emacs@m.gmane-mx.org; Tue, 17 Jan 2023 19:29:40 +0100 Original-Received: from localhost ([::1] helo=lists1p.gnu.org) by lists.gnu.org with esmtp (Exim 4.90_1) (envelope-from ) id 1pHqhk-0005hU-EI; Tue, 17 Jan 2023 13:29:04 -0500 Original-Received: from eggs.gnu.org ([2001:470:142:3::10]) by lists.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.90_1) (envelope-from ) id 1pHqhi-0005h9-OZ for help-gnu-emacs@gnu.org; Tue, 17 Jan 2023 13:29:02 -0500 Original-Received: from mail-yb1-xb34.google.com ([2607:f8b0:4864:20::b34]) by eggs.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_128_GCM_SHA256:128) (Exim 4.90_1) (envelope-from ) id 1pHqhX-0006rk-Eu for help-gnu-emacs@gnu.org; Tue, 17 Jan 2023 13:29:02 -0500 Original-Received: by mail-yb1-xb34.google.com with SMTP id 20so16090604ybl.0 for ; Tue, 17 Jan 2023 10:28:47 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20210112; h=content-transfer-encoding:to:subject:message-id:date:from :in-reply-to:references:mime-version:from:to:cc:subject:date :message-id:reply-to; bh=rNfAVClwICFP9Su8glVr9n8dRljWpxM8L/T4iLLfo+M=; b=HLYQdcrGTs+maAZ2Y3czU8+qIPnwUYnFW9W7JcLv6LgGBMGXHsEMA9o1UEBy7+nMfR VsDuLZRHk/o8zU31T2UODgm+zDnKpYqu0gOJOx4DzaMFlbkpBFxQKy3sUzUJpEH0CIfT HwqV4+lfZAZP7zPbjgiHKu+dP9zAg9wx3dFOOTkEfq8XGn/UY3f4p96XU6/kmapNh38m If7l4IJ1hjb3msT5/+BmRDrUqAkABtQU+JbY6p+YyNwzJQmdWmarizPVrmNW0fyj4QhP zo2iDHSQPt54Cu/Qxnsp9Ne6vp5JsZxbQHMzK0PTEqmcD4d0wt/ha62yeFXdQoVwrEcg hufQ== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20210112; h=content-transfer-encoding:to:subject:message-id:date:from :in-reply-to:references:mime-version:x-gm-message-state:from:to:cc :subject:date:message-id:reply-to; bh=rNfAVClwICFP9Su8glVr9n8dRljWpxM8L/T4iLLfo+M=; b=Ql+ESK9q9B0yNJaFEKxQPgMl9j7cgNRX59BBOZ7QX+OoRBrYWyJsY8Nq7vqtBGIQMt U5dWTY2KFCLhth9C3s7Axr6kSTi0yhwF4fQQ0xZlxUsq2eymAfmhVQcKlPbhS6gXmvDU EojoO7FoLAWRtwyUv3Mz0XykpcmoEoioxDBERpCf8B3m3LKUQ4j+jj3hQ/9G0pLOMDGb Qcn8EztjzCcJBQbpRDX3eikfSpN9K1j6JMxLPNP3dg0lPms8wwWSrQEWh3vEsCtWEpsD SMkbpF8UXms2K4byieNocGcVc8sDMGCzmJ09E9Ne3idBvAsIw48YDjF9eieAgP9TqWEL pbJQ== X-Gm-Message-State: AFqh2kpjpO4Thd+g2Y8V0tTLnhDR44kt+MFkdgC+Ohcs8b7TZvtOUE/g qx5vKnSlP/RJ42EA5/ER5Zr3e0cuOzNqQPyD/YCkYCffE4Y4Ww== X-Google-Smtp-Source: AMrXdXtdUwmdwIXvt8JCiRUM0RVUpO0MEGMwTsGVrcd4x5nkP7rdPpOkfdxqtOBTbsMR2dwDMdxW8EVrKx2jtC0/K3o= X-Received: by 2002:a5b:8c4:0:b0:749:f433:3abb with SMTP id w4-20020a5b08c4000000b00749f4333abbmr553079ybq.239.1673980126094; Tue, 17 Jan 2023 10:28:46 -0800 (PST) In-Reply-To: Received-SPF: pass client-ip=2607:f8b0:4864:20::b34; envelope-from=eduardoochs@gmail.com; helo=mail-yb1-xb34.google.com X-Spam_score_int: -20 X-Spam_score: -2.1 X-Spam_bar: -- X-Spam_report: (-2.1 / 5.0 requ) BAYES_00=-1.9, DKIM_SIGNED=0.1, DKIM_VALID=-0.1, DKIM_VALID_AU=-0.1, DKIM_VALID_EF=-0.1, FREEMAIL_FROM=0.001, RCVD_IN_DNSWL_NONE=-0.0001, SPF_HELO_NONE=0.001, SPF_PASS=-0.001 autolearn=ham autolearn_force=no X-Spam_action: no action X-BeenThere: help-gnu-emacs@gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Users list for the GNU Emacs text editor List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane-mx.org@gnu.org Original-Sender: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane-mx.org@gnu.org Xref: news.gmane.io gmane.emacs.help:142331 Archived-At: On Tue, 17 Jan 2023 at 15:05, Jean Louis wrote: > Ok it has been extended. That is your conclusion. But why? Show me the us= e. Hi Jean, note that we are discussing several different operations called `+'... and sometimes to understand what a mathematical sentence "really means" we have to add annotations to these operations with the same name to distinguish them. The best explanation that I know about this is in the pages 15-20 of these slides: http://math.andrej.com/asset/data/the-dawn-of-formalized-mathematics.pdf#pa= ge=3D15 When I had to explain "neutral elements" to my students a few months ago I started by the operations "for all" and "exists". They understood very quickly that for any proposition P(x) we had: =E2=88=80x=E2=88=88{2,3,5}.P(x) =3D P(2)=E2=88=A7P(3)=E2=88=A7P(5) =E2=88=83x=E2=88=88{2,3,5}.P(x) =3D P(2)=E2=88=A8P(3)=E2=88=A8P(5) where "=E2=88=A7" is "and" and "=E2=88=A8" is "or", and these are the boole= an "and" and "or", that only accept inputs that are truth-values, and the only truth-values are "true" and "false"... so these "=E2=88=A7" and "=E2=88=A8"= are very different from the "and" and "or" from Lisp. Then at some point we started to meet expressions like these ones: =E2=88=80x=E2=88=88{}.P(x) =E2=88=83x=E2=88=88{}.P(x) In a first moment the students didn't know how to interpret them. I told them that this is one of the places in which mathematicians _decide_ to extend a known operation, and in which they _choose_ an extended definition that may look artificial at first - but they choose a definition that turns out to be more well-behaved that the other ones. For the "=E2=88=80" we had (at least) these three possibilities= : =E2=88=80x=E2=88=88{}.P(x) =3D error =E2=88=80x=E2=88=88{}.P(x) =3D false =E2=88=80x=E2=88=88{}.P(x) =3D true and I showed to them why the mathematicians had decided that this one =E2=88=80x=E2=88=88{}.P(x) =3D true would be the best choice. In my argument I used the figures that are here, http://angg.twu.net/LATEX/2022-2-C2-tudo.pdf#page=3D87 but these figures are not self-contained - I also talked a lot, wrote lots of things on the whiteboard, and gesticulated a lot. By the way, I started by "=E2=88=80" and "=E2=88=83" because I saw that it = would be better to start by them and then do "=CE=A3" and "=CE=A0" later. See: https://en.wikipedia.org/wiki/Summation#Capital-sigma_notation By the way: my main objective was to show to the students how definitions work, and how in some cases some definitions can be extended. "=E2=88=80" and "=E2=88=83" were just particular cases of this bi= g idea, and the big idea itself was more important than its particular cases. Cheers, Eduardo