From mboxrd@z Thu Jan 1 00:00:00 1970 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Michael Heerdegen Newsgroups: gmane.emacs.help Subject: Re: (*)->1 Date: Sat, 14 Jan 2023 13:33:30 +0100 Message-ID: <87lem5jnxh.fsf@web.de> References: <61c2cc81db661e2624771a06a1274eac.support1@rcdrun.com> <87y1qdct5m.fsf@gnu.org> <874jt0imh0.fsf@dataswamp.org> <875ydeas0w.fsf@dataswamp.org> <87tu0tjpbe.fsf@web.de> Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="2170"; mail-complaints-to="usenet@ciao.gmane.io" User-Agent: Gnus/5.13 (Gnus v5.13) To: help-gnu-emacs@gnu.org Cancel-Lock: sha1:drK2ErKeznK6mp3nVvNsB2jwpYg= Original-X-From: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane-mx.org@gnu.org Sat Jan 14 13:34:11 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 1pGfjf-0000OK-67 for geh-help-gnu-emacs@m.gmane-mx.org; Sat, 14 Jan 2023 13:34:11 +0100 Original-Received: from localhost ([::1] helo=lists1p.gnu.org) by lists.gnu.org with esmtp (Exim 4.90_1) (envelope-from ) id 1pGfjC-0001Wa-Rf; Sat, 14 Jan 2023 07:33:42 -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 1pGfj9-0001WS-Uy for help-gnu-emacs@gnu.org; Sat, 14 Jan 2023 07:33:39 -0500 Original-Received: from ciao.gmane.io ([116.202.254.214]) by eggs.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.90_1) (envelope-from ) id 1pGfj8-00025m-E7 for help-gnu-emacs@gnu.org; Sat, 14 Jan 2023 07:33:39 -0500 Original-Received: from list by ciao.gmane.io with local (Exim 4.92) (envelope-from ) id 1pGfj6-000ADa-Lh for help-gnu-emacs@gnu.org; Sat, 14 Jan 2023 13:33:36 +0100 X-Injected-Via-Gmane: http://gmane.org/ Received-SPF: pass client-ip=116.202.254.214; envelope-from=geh-help-gnu-emacs@m.gmane-mx.org; helo=ciao.gmane.io X-Spam_score_int: -15 X-Spam_score: -1.6 X-Spam_bar: - X-Spam_report: (-1.6 / 5.0 requ) BAYES_00=-1.9, FREEMAIL_FORGED_FROMDOMAIN=0.001, FREEMAIL_FROM=0.001, HEADER_FROM_DIFFERENT_DOMAINS=0.25, SPF_HELO_NONE=0.001, SPF_PASS=-0.001 autolearn=no 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:142236 Archived-At: Michael Heerdegen writes: > Jean Louis writes: > > > Thus (+) ➜ 0 without value result should not be zero. If no values > > where given to addition, no addition has taken place. Value of zero > > should not get out of nothing. > > Mathematically it is neither right nor wrong. It is a convention to > assign 0 to an empty sum. This is for convenience, and it doesn't lead > to contradictions. Some more comments: 1. The mathematical background is the associative property in monoids: https://en.wikipedia.org/wiki/Monoid 2. You surely never complained about a^0 = 1 although "it's an empty product". You surely used that often because it's convenient. 3. Similar things in Lisp are (append) ==> () (concat) ==> "" (or) ==> nil (and) ==> t The result is always the neutral element of the associative operation. Michael.