Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: WM Newsgroups: sci.math Subject: Re: 2N=E Date: Fri, 25 Oct 2024 18:59:53 +0200 Organization: A noiseless patient Spider Lines: 18 Message-ID: References: <22f95ff7-c361-4d8a-943c-1df76abb98cc@att.net> <9c55eda1-bb24-44ae-9158-2a3b354170cd@att.net> <4ce512c0-8196-4923-9a6b-359c25fdfa3a@att.net> <8418a2e3-bba2-43b4-8c77-3e947a270476@att.net> <6c56b6df33cedd35cac468735501d2d89ad19048@i2pn2.org> <9e98e573c0368690d336299ab78121c3240aa8e7@i2pn2.org> <351593f2-200c-4df5-a93f-9362b8b2bf91@att.net> <5b701e07-18aa-42ab-964b-0ca84e1776ca@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 25 Oct 2024 18:59:54 +0200 (CEST) Injection-Info: dont-email.me; posting-host="8d868b5d34883ac27de334c6e2200e6f"; logging-data="3433227"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+wlQNHsSf1RgIVhm1vtQKKjkndf/fqPbo=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:OQzvJ4AWQWqaUvH6juS6+M4Q96Y= In-Reply-To: Content-Language: en-US Bytes: 2365 On 25.10.2024 18:54, Jim Burns wrote: > On 10/24/2024 10:29 AM, WM wrote: > >> The set, when existing completely, >> covers an interval, namely (0, ω). >> When its density is halved >> while the number of elements is constant, >> then its extension is doubled. > > No. > ⟨0,1,...,n-1,n,n+1,...,n+n-1,n+n⟩ is finite. The extension is doubled in this finite set here as well as in my infinite set. Regards, WM