Path: ...!2.eu.feeder.erje.net!3.eu.feeder.erje.net!feeder.erje.net!news.szaf.org!news.karotte.org!news.space.net!news.muc.de!.POSTED.news.muc.de!not-for-mail From: Alan Mackenzie Newsgroups: sci.math Subject: Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"] Date: Fri, 28 Mar 2025 15:45:47 -0000 (UTC) Organization: muc.de e.V. Message-ID: References: <9e0c7e728f7de44e13450d7401fe65d36c5638f3@i2pn2.org> <3449b34c60603bf59f694df42857003d0bda7ab5@i2pn2.org> Injection-Date: Fri, 28 Mar 2025 15:45:47 -0000 (UTC) Injection-Info: news.muc.de; posting-host="news.muc.de:2001:608:1000::2"; logging-data="88869"; mail-complaints-to="news-admin@muc.de" User-Agent: tin/2.6.4-20241224 ("Helmsdale") (FreeBSD/14.2-RELEASE-p1 (amd64)) Bytes: 3129 Lines: 51 WM wrote: > Am 26.03.2025 um 22:38 schrieb Alan Mackenzie: >> WM wrote: >>> On 26.03.2025 21:06, joes wrote: >>>> Am Wed, 26 Mar 2025 20:36:40 +0100 schrieb WM: >>>>> The potential infinite is a variable finite. Cantor's actual infinity is >>>>> not variable but fixed. (Therefore Hilbert's hotel is potential >>>>> infinity.) >>>> What we refer to as infinite isn't variable. >>> The number of guests/rooms in Hilbert's hotel is infinite but can >>> grow. That is variable infinity. >> You are mistaken. (Countable) infinity stays the same when you add >> finite and countably infinite numbers to it. > That proves that cardinality is nonsense. When a new guest arrives, > then the number of guests grows by 1. Yes indeed. There were aleph-0 guests beforehand, the new guest arrives growing that number by 1, giving aleph-0. Why do you find this so difficult to understand? >> Thus in Hilbert's hotel, although all the rooms are occupied, one of >> these rooms can be vacated to make room for a new guest without >> expelling an existing guest. > Real fools are really delighted by counterintuitive results. You've run out of mathematics, so you resort to ad hominem. Not very good. Hint: the person who devised "Hilbert's hotel" was in no sense a fool. >> Adding that new guest doesn't change the number of guests in the >> hotel, or the number of rooms required. > Real fools are really delighted by counterintuitive results. >> See many of Jim's posts over the last few days for details. > There is only one important detail, namely that lossless exchanges > cause losses. It is sufficient to reject every intelligent being. An infinite process of lossless exchanges can cause loss, as we have seen. > Regards, WM -- Alan Mackenzie (Nuremberg, Germany).