From mboxrd@z Thu Jan 1 00:00:00 1970 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Yuri Khan Newsgroups: gmane.emacs.help Subject: Re: [External] : Re: How to make M-x TAB not work on (interactive) declaration? Date: Mon, 16 Jan 2023 14:55:06 +0700 Message-ID: References: <61c2cc81db661e2624771a06a1274eac.support1@rcdrun.com> <87y1qdct5m.fsf@gnu.org> <874jt0imh0.fsf@dataswamp.org> 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="15013"; mail-complaints-to="usenet@ciao.gmane.io" To: =?UTF-8?Q?Rudolf_Adamkovi=C4=8D?= , help-gnu-emacs@gnu.org Original-X-From: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane-mx.org@gnu.org Mon Jan 16 08:56:09 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 1pHKLh-0003h9-20 for geh-help-gnu-emacs@m.gmane-mx.org; Mon, 16 Jan 2023 08:56:09 +0100 Original-Received: from localhost ([::1] helo=lists1p.gnu.org) by lists.gnu.org with esmtp (Exim 4.90_1) (envelope-from ) id 1pHKLA-0004Sk-Df; Mon, 16 Jan 2023 02:55:36 -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 1pHKKx-0004SL-VO for help-gnu-emacs@gnu.org; Mon, 16 Jan 2023 02:55:24 -0500 Original-Received: from mail-wm1-x330.google.com ([2a00:1450:4864:20::330]) by eggs.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_128_GCM_SHA256:128) (Exim 4.90_1) (envelope-from ) id 1pHKKv-00028c-Ja for help-gnu-emacs@gnu.org; Mon, 16 Jan 2023 02:55:22 -0500 Original-Received: by mail-wm1-x330.google.com with SMTP id g10so19339704wmo.1 for ; Sun, 15 Jan 2023 23:55:19 -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=DvoptjXhDxcRRsHlgSQfGSnScpD1l6bIi9ZubQi8iAA=; b=qM9DChtiJJF2Bt6ve2KL8I19LWbanbvTnWqfgEmIwV1Y0hRozHeBa+XDzwt/iFH0D1 hVxX9QZrnTZu01DlUM3FNJ9jQ0xhd5p2IGY/xRn1gTYpwzqxfWmud1zXUPN0o4OO3ukz Uhy5pVOs7QZZPrm1vaaPvEabAJRoc9agsamIzkKhHVprBGplbiGQfuGDnhgSqislD6+A Wiz0FRpztYdXWov0u9GrjKcXCb3TwTZT/vjHEsJ9c2N0qZw3x444tKi+8C+MmqAVU77q ZEL5NzvSXpkLzB0+pYErSOrYb7wYJm/e42/0ELG2uN9TJ0jtdWB1gz+eUW4243eSv19s +qHA== 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=DvoptjXhDxcRRsHlgSQfGSnScpD1l6bIi9ZubQi8iAA=; b=cMcdSzl5k4C116+eY4iTKqjBWcVqSEkCLFVq9NIvmrvdsUEPyxH2Yp01nYcQSkjz8d paXiNUK1bXDIEvoHxOI/OjTalmfyGznTQ5ouk+LWO8Mog0Oq3BH6i9/7MyIW7SwUPv7h XtI/HcOq9iE1HTOtGTeNbAg2eEZtAyfn8CtGm0CxJHHhPGjRNlHP4WfQbr/PKRPPTB8q PCCszqNWmAv2x4Qszbs1GecfQ/H8U6xisRizmh+LzQs+8DFOBR4GXhFM0wE0j2fJPTt9 nNB44Co8ZmJ1bjbgQy2zu1/HcDN2jR7NClPDQwbk0mdED6v5YTaDTquQQ5m1VzUy13Je YRWQ== X-Gm-Message-State: AFqh2kov6eUSlwvEI8E2Ef5p2ELDwjF4ZQPUXXCY7Mnq5G4BFRqVdBa8 4sao9w8l4yY3hx9mDqDl9p1saQ559MpgK3beLFY= X-Google-Smtp-Source: AMrXdXuuUuXZaM6BHdiZh1whck4571hOKiSJrNsM9aPnm5AahPFM8CLlteKJ2LPuyF4M9U4Xea3POFPmdeqFqIgDNus= X-Received: by 2002:a05:600c:3ac8:b0:3d8:e0d3:ee0e with SMTP id d8-20020a05600c3ac800b003d8e0d3ee0emr4680743wms.144.1673855717823; Sun, 15 Jan 2023 23:55:17 -0800 (PST) In-Reply-To: Received-SPF: pass client-ip=2a00:1450:4864:20::330; envelope-from=yurivkhan@gmail.com; helo=mail-wm1-x330.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:142263 Archived-At: On Mon, 16 Jan 2023 at 11:44, Jean Louis wrote: > > >> (+) =E2=9E=9C 0 > > > > Send me references on what is additive identity. > > Though that it is so, it does not answer why is it so. Consider a sum of n elements: S =3D (+ x_1 =E2=80=A6 x_{n-1} x_n). By definition, it is equal to the sum of the first n-1 elements, plus the nth element: S =3D (+ x_1 =E2=80=A6 x_{n-1}) + x_n. No problem this far= ? (except for me mixing prefix and infix notation) Now, plug n=3D1 into this general formula. S =3D x_1 =3D (+) + x_1. Therefore, the sum of an empty list (+) has to be 0. In the same vein, a product of n elements: P =3D (* x_1 =E2=80=A6 x_{n-1} x= _n) =3D (* x_1 =E2=80=A6 x_{n-1}) * x_n, which in the case of n=3D1 becomes P =3D x= _1 =3D (*) * x_1. Therefore, the product of the empty list (*) has to be 1.