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Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM <wolfgang.mueckenheim@tha.de> Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers Date: Mon, 18 Nov 2024 19:20:24 +0100 Organization: A noiseless patient Spider Lines: 15 Message-ID: <vhg0h8$1adlc$4@dont-email.me> References: <vg7cp8$9jka$1@dont-email.me> <vh00jj$1m6co$1@dont-email.me> <97304048-24f5-4625-82a7-d17427f2f6e3@att.net> <vh0hta$1pmql$1@dont-email.me> <65febd06-662b-4fa4-9aa8-f7353a79a110@att.net> <vh2k9p$29cql$1@dont-email.me> <157a949d-6c19-4693-8cee-9e067268ae45@att.net> <vh35nd$2d81g$1@dont-email.me> <cb0c9917-09a9-45f0-8fe9-cd059fa82dde@att.net> <vh4itg$2o3vu$1@dont-email.me> <8165b44b-1ba5-429d-8317-0b043b214b53@att.net> <vh76bi$3bnde$1@dont-email.me> <d90452a5-965b-443f-9146-96cdf9b3906c@att.net> <vh8ft0$3jqb5$3@dont-email.me> <vh8g5e$3juug$1@dont-email.me> <vh8otd$3lhlt$2@dont-email.me> <vhb1is$6hbv$2@dont-email.me> <vhb1mu$6hbv$4@dont-email.me> <vhb32t$7ese$1@dont-email.me> <vhch7n$hge9$2@dont-email.me> <vhcieh$jjk5$1@dont-email.me> <vhcjg5$hdd4$3@dont-email.me> <vhckkh$k32g$1@dont-email.me> <vhcp0r$hge9$6@dont-email.me> <vhd7d7$nt37$1@dont-email.me> <vhd9lq$obb0$1@dont-email.me> <vhdl0k$qltl$1@dont-email.me> <vhfqcv$1adld$1@dont-email.me> <vhfso7$1bik6$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 18 Nov 2024 19:20:25 +0100 (CET) Injection-Info: dont-email.me; posting-host="4277cd5398b33328aee403404fb6cf14"; logging-data="1390252"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX193HTDWI2FxMAin+PXClEVxXjvhgjMLHE0=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:8RAP7WYnKXfCyGx5ztUmQOrXXWk= Content-Language: en-US In-Reply-To: <vhfso7$1bik6$1@dont-email.me> Bytes: 2553 On 18.11.2024 18:15, FromTheRafters wrote: > WM brought next idea : >>> |ℕ| - |ℕ| = 0 because if you subtract one element from ℕ then you have >> no longer ℕ and therefore no longer |ℕ| describing it. > > Still wrong. If you remove one element from ℕ, then you have still ℵo but no longer all elements of ℕ. If |ℕ| describes the number of elements, then it has changed to |ℕ| - 1. If you don't like |ℕ| then call this number the number of natural numbers. Regards, WM