Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: The non-existence of "dark numbers" [was: The existence of dark numbers proven by the thinned out harmonic series] Date: Sun, 16 Mar 2025 19:44:10 +0100 Organization: A noiseless patient Spider Lines: 18 Message-ID: References: <163d9b2e-c83f-41d2-a895-65cf4e152a66@att.net> <8e684425-63cb-4d9c-9124-ee07acdd9017@att.net> <73359d09-bf4b-4970-bf4c-133bf2cc6218@att.net> <606abd47-0342-4122-bdd8-239c42beb740@att.net> <5478ed00-1634-433c-a117-a640fcb34069@att.net> <4b6dac29-8143-430d-b234-578200824822@att.net> <49fadcf7-365b-43a6-ad2f-222bd0819758@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sun, 16 Mar 2025 19:44:09 +0100 (CET) Injection-Info: dont-email.me; posting-host="cf4896233970c7bd84555e103c583e26"; logging-data="2431859"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX197toFXwdboTO56azAxeji+efpK4GTJXwc=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:VgLCc67pW0tPufFEfWxFYsG37WI= Content-Language: en-US In-Reply-To: Bytes: 2507 On 16.03.2025 19:14, Jim Burns wrote: > On 3/16/2025 1:20 PM, WM wrote: >> Which index has the first lossless exchange >> where a loss happens? > > A set larger than > each set without same.sized proper.subsets > is not > any set without same.sized proper.subsets: > That set has same.sized proper.subsets. Waffle. All exchanges are indexed. If you claim that the first Bob disappears, then he must disappear at some index. Which is it? Regards, WM