Path: ...!weretis.net!feeder6.news.weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: FromTheRafters Newsgroups: sci.math Subject: Re: Contradiction of bijections as a measure for infinite sets Date: Fri, 05 Apr 2024 08:57:27 -0400 Organization: Peripheral Visions Lines: 25 Message-ID: References: <5fxRDo_iHMUImphe8RGVplmYuCQ@jntp> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-15"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 05 Apr 2024 12:57:33 +0200 (CEST) Injection-Info: dont-email.me; posting-host="508690cf842d01bdae3a61b7f054180f"; logging-data="1468515"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+p+5lGpBRaVUpZ+DZTSWIQf4JS8GHgT2I=" Cancel-Lock: sha1:56habYGomvWQuL3hMt7Nc3uscyY= X-ICQ: 1701145376 X-Newsreader: MesNews/1.08.06.00-gb Bytes: 2474 WM explained on 4/4/2024 : > Le 03/04/2024 à 15:59, FromTheRafters a écrit : >> WM presented the following explanation : >>> Le 02/04/2024 à 17:51, Jim Burns a écrit : >>>> On 4/2/2024 3:36 AM, WM wrote: >>> >>>> If your assumption leads to "no bijection", >>>> but there is a bijection, >>>> then your assumption is wrong. >>> >>> My trick proves that there is no bijection. >>> Or could you explain why first bijecting n and n/1 should destroy an >>> existing bijection? >> >> Your 'trick' only fails to demonstrate a bijection. Failing to demonstrate >> a bijection does not mean that there is no bijection, only that your >> 'trick' doesn't work to that end. > > Explain why first bijecting n and n/1 should destroy an existing bijection! You still seem to think that sets change. If you mean 'n' is an element of the naturals then of course N bijects with the naturals as embedded in Q. Also, the complement of the naturals over one in Q is the same size as the proper subset you created. No sets (read also functions) were destroyed.