From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: from mp10.migadu.com ([2001:41d0:8:6d80::]) (using TLSv1.3 with cipher TLS_AES_256_GCM_SHA384 (256/256 bits)) by ms5.migadu.com with LMTPS id SG7vNp6OwmIwAAEAbAwnHQ (envelope-from ) for ; Mon, 04 Jul 2022 08:54:23 +0200 Received: from aspmx1.migadu.com ([2001:41d0:8:6d80::]) (using TLSv1.3 with cipher TLS_AES_256_GCM_SHA384 (256/256 bits)) by mp10.migadu.com with LMTPS id ILz3NZ6OwmI5PgAAG6o9tA (envelope-from ) for ; Mon, 04 Jul 2022 08:54:22 +0200 Received: from lists.gnu.org (lists.gnu.org [209.51.188.17]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by aspmx1.migadu.com (Postfix) with ESMTPS id 532922FC13 for ; Mon, 4 Jul 2022 08:54:22 +0200 (CEST) Received: from localhost ([::1]:39732 helo=lists1p.gnu.org) by lists.gnu.org with esmtp (Exim 4.90_1) (envelope-from ) id 1o8FyN-0001vM-W0 for larch@yhetil.org; Mon, 04 Jul 2022 02:54:20 -0400 Received: from eggs.gnu.org ([2001:470:142:3::10]:43204) by lists.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.90_1) (envelope-from ) id 1o8Fql-0003jg-Hu for emacs-orgmode@gnu.org; Mon, 04 Jul 2022 02:46:27 -0400 Received: from mail-out01.uio.no ([2001:700:100:10::50]:56885) by eggs.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.90_1) (envelope-from ) id 1o8Fqi-00063q-M6 for emacs-orgmode@gnu.org; Mon, 04 Jul 2022 02:46:26 -0400 Received: from mail-mx12.uio.no ([129.240.10.84]) by mail-out01.uio.no with esmtps (TLS1.2) tls TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384 (Exim 4.94.2) (envelope-from ) id 1o8Fqc-007ZSb-5z for emacs-orgmode@gnu.org; Mon, 04 Jul 2022 08:46:18 +0200 Received: from [84.209.16.135] (helo=fedora.shmi.ifi.uio.no) by mail-mx12.uio.no with esmtpsa (TLS1.2:ECDHE-RSA-AES256-GCM-SHA384:256) user msteffen (Exim 4.94.2) (envelope-from ) id 1o8Fqb-0006t9-JD; Mon, 04 Jul 2022 08:46:18 +0200 From: Martin Steffen To: emacs-orgmode@gnu.org Subject: Re: [more absurd] Organization: IFI UiO Norway References: <87zghtv1o1.fsf@mat.ucm.es> <87o7y6aw8l.fsf@mat.ucm.es> <87iloeatbo.fsf@mat.ucm.es> <87bku6arzq.fsf@mat.ucm.es> <875ykeaqrh.fsf@mat.ucm.es> <87zghpa2f0.fsf@mat.ucm.es> Date: Mon, 04 Jul 2022 08:46:11 +0200 In-Reply-To: (tomas@tuxteam.de's message of "Mon, 4 Jul 2022 08:23:54 +0200") Message-ID: <86o7y5ide4.fsf@login.ifi.uio.no> User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/27.2 (gnu/linux) MIME-Version: 1.0 Content-Type: text/plain X-UiO-SPF-Received: Received-SPF: neutral (mail-mx12.uio.no: 84.209.16.135 is neither permitted nor denied by domain of ifi.uio.no) client-ip=84.209.16.135; envelope-from=msteffen@ifi.uio.no; helo=fedora.shmi.ifi.uio.no; X-UiO-Spam-info: not spam, SpamAssassin (score=-5.0, required=5.0, autolearn=disabled, T_SCC_BODY_TEXT_LINE=-0.01, UIO_MAIL_IS_INTERNAL=-5) X-UiO-Scanned: 97A84F59E6D7B69BD417C2B82CFD9F7207C4A7A3 X-UiOonly: 972A3285AA18E872C711129DEB67ECDBAD112C35 Received-SPF: pass client-ip=2001:700:100:10::50; envelope-from=msteffen@ifi.uio.no; helo=mail-out01.uio.no X-Spam_score_int: -18 X-Spam_score: -1.9 X-Spam_bar: - X-Spam_report: (-1.9 / 5.0 requ) BAYES_00=-1.9, SPF_HELO_PASS=-0.001, SPF_PASS=-0.001, T_SCC_BODY_TEXT_LINE=-0.01 autolearn=ham autolearn_force=no X-Spam_action: no action X-BeenThere: emacs-orgmode@gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: "General discussions about Org-mode." List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: emacs-orgmode-bounces+larch=yhetil.org@gnu.org Sender: "Emacs-orgmode" X-Migadu-Flow: FLOW_IN X-Migadu-To: larch@yhetil.org X-Migadu-Country: US ARC-Message-Signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=yhetil.org; s=key1; t=1656917662; h=from:from:sender:sender:reply-to:subject:subject:date:date: message-id:message-id:to:to:cc:mime-version:mime-version: content-type:content-type:in-reply-to:in-reply-to: references:references:list-id:list-help:list-unsubscribe: list-subscribe:list-post; bh=ojpyOQQi2inLeWbT5BudoxWruxCy9Cow498j8wbhSus=; b=pdSoApUWHx3OobtnBBcWa+mRLMCOMwRoE8huHG9SQ4sT4q8HFdIvZGm0PnrPc0WJNyNE8+ gjTyiPSovusF3UzkQX6s+zag0FjA1h9z8DLjHGZZFy5ojN9DE1m1FDn1VVPd6b7/GMQ0My 8UhGe+5Q9TThoYNFKUi59gzy6GEOAFP/o6s3T7Gsh19nqU4uzaGNuWAsYOOzNh+rfg98IE bbNQJGXXl0X9LVBAAEpE9npKZMPp7Czut9ho9KtLc1KSrdONDChEEFwdTYDjXL69/BNxJo modX6W7kIRXguO97agyUQ4Hio6YxO1jgINh3WX4KOFngTHpo57rcZZRac9mc8w== ARC-Seal: i=1; s=key1; d=yhetil.org; t=1656917662; a=rsa-sha256; cv=none; b=Jf36uWQ8AIcci1HXu6QpajY6P7GKu8UDF/bXR1BSBuZjxozGDb0ccQqrk8OYYVTnH7onD1 R8Jihu3JklT5W6JPIgjeXrp09DhtZYSc8mIFi5VBcf0t6IbX73cBFVpTtIFqFz9ExXx47g weizO2t9iI1ff6MY46pUNX9o6UQm2EnyInwssbUTM16Qu/ir7V404MJc9RrtQF9sdmY4Zv TrNRV2trVU02t8QXos/letObG2kBdSLTyrIkdyTLXQ7pattP7NhniEUTLgYd7vO6ptLljU gOmtHjRpBEQMi0HBkLQ35rPExgJ8mnaQ/Tdvi09hvKxAb69oKPTGEMoJSb/iBg== ARC-Authentication-Results: i=1; aspmx1.migadu.com; dkim=none; dmarc=none; spf=pass (aspmx1.migadu.com: domain of "emacs-orgmode-bounces+larch=yhetil.org@gnu.org" designates 209.51.188.17 as permitted sender) smtp.mailfrom="emacs-orgmode-bounces+larch=yhetil.org@gnu.org" X-Migadu-Spam-Score: -1.24 Authentication-Results: aspmx1.migadu.com; dkim=none; dmarc=none; spf=pass (aspmx1.migadu.com: domain of "emacs-orgmode-bounces+larch=yhetil.org@gnu.org" designates 209.51.188.17 as permitted sender) smtp.mailfrom="emacs-orgmode-bounces+larch=yhetil.org@gnu.org" X-Migadu-Queue-Id: 532922FC13 X-Spam-Score: -1.24 X-Migadu-Scanner: scn0.migadu.com X-TUID: ar+pp3PsaRMJ >>>>> writes: > On Mon, Jul 04, 2022 at 07:10:27AM +0200, Uwe Brauer wrote: > [...] >> That really su... (My use case only concerned numbers from 0-10). >> >> So it boils down to the question: why isn't 0 considered as >> natural numbers, as, according to the Peano axioms, it is? > I don't know whether you're serious or making fun (Poe's Law and > all that), but actually, Peano's axioms couldn't care less: as far > as they are concerned, natural numbers could well start at 23 or > something. > Actually it seems to be some kind of "cultural question" whether > mathematicians start counting at 0 or at 1; my observation is that > they tend to agree across one faculty at one university. I know > positively one that tends to count from 1 (HU Berlin), another > that counts from 0 (Freiburg), both in Germany. In some sense that's defendable (that what could call natural numbers is a cultural question or historical, like looking at what Peano did nor did not define). On the other hand, one normally does not just deals with the numbers as such, one does something with it (like comparing them or calculating with them). If one takes the reservoir of numbers (in decimal notation, {0,1,2,3 .....} indeed it is irrelelvant where to start, 0,1, or 23. Also if one does nothing else than comparing them (that would be considering them as "ordinals", one has one single smallest number, and again it's it's irrelevant if that's ``called'' nor notated $0$, "zero" or "1", or "23". Now, if one starts doing simple calculations (addition, multiplication), the natural numbers including 0 is simply more "elegant" or ``richer'' than without. One has laws like n+0 = n, n*0=0 (one then says, 0 is a neutral element wrt. +, there is terminology for all than, and it's simply that N with 0 has nicer ``algebraic'' characteristics than without. It's quite analogous to the choice between defining lists as to include the empty list '() as a ``natural'' list, or insist on that ``natural'' lists must have 1 or more elements. > I once asked a maths prof and he said foundational folks (set > theorists, math logicians -- that's the typical environment where > you'd tend to stumble upon Peano) tend to favour starting at 0. Foundational folks can elaborate on that analogy between lists and nats, but as you say, in both cases they favor to include 0 to nats and the empty list to lists (and there are more examples) and it's favored for good reasons (at least to them). best, Martin > Historically, Peano himself seems to have been a one-counter: > "Peano's original formulation of the axioms used 1 instead of 0 > as the "first" natural number,[6] while the axioms in Formulario > mathematico include zero." as quoted in [1]. > Cheers > [1] https://en.wikipedia.org/wiki/Peano_axioms -- t