Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" Newsgroups: sci.math Subject: Re: The non-existence of "dark numbers" Date: Wed, 2 Apr 2025 13:02:01 -0700 Organization: A noiseless patient Spider Lines: 21 Message-ID: References: <555d7095-81a0-4576-adac-f2aa8327f4df@att.net> <8397e10f-36cb-43c6-8d2b-e4d20809ee83@att.net> <4b83f1c2-c16f-40b4-a5b6-68991e3c230c@att.net> <440ff556-a769-482e-ad2a-064af14c5781@att.net> <369e62e9-93e6-4256-96ed-f9d8489aa017@att.net> <5004d400-7c2e-4d59-ad66-5986a416ef89@att.net> <411d5c64-ddb6-4655-a264-2149d054ff7d@att.net> <94fa0364396567adcb4e87213ba7392c45ed8a1d@i2pn2.org> <5355732a3f22baa4483b5718dd1c74f90362f653@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Wed, 02 Apr 2025 22:02:03 +0200 (CEST) Injection-Info: dont-email.me; posting-host="acd139d64ffb874fa50402f6e491198c"; logging-data="2778479"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19pU/qF6nuHbmwa37RgXGTlZnlh+fI+wmY=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:DcVmKzrMwSL0AqpSLqmSlyLseMQ= Content-Language: en-US In-Reply-To: Bytes: 2740 On 4/2/2025 7:10 AM, WM wrote: > On 27.03.2025 22:34, joes wrote: >> Am Thu, 27 Mar 2025 20:50:00 +0100 schrieb WM: >>> Am 27.03.2025 um 15:58 schrieb joes: >>>> Am Wed, 26 Mar 2025 21:09:03 +0100 schrieb WM: >>> >>>>>> At finite steps, but not in the limit. >>>>> Countability is proved without limits. Bijections are one-to-one >>>>> without limit. >>>> I have no idea what you are talking about. What can be proved to be >>>> countable without resorting to limits? >>> Limits deviate from countability. >> You are writing way too short. There are countable infinities, >> whether you like that word or not. > > Countable infinities are claimed by Cantor, but no limits. [...] There is no largest natural number.