Path: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" Newsgroups: sci.math Subject: Re: 2N=E Date: Thu, 24 Oct 2024 12:42:29 -0700 Organization: A noiseless patient Spider Lines: 14 Message-ID: References: <6c56b6df33cedd35cac468735501d2d89ad19048@i2pn2.org> <9e98e573c0368690d336299ab78121c3240aa8e7@i2pn2.org> <6310990a57ee5388e4e3a2c280fde00fc1b142ae@i2pn2.org> <3834533883e5a9dbc8546bf3eb425f762f2d0ab3@i2pn2.org> <6c929080fc639ef2e26217ccd2908b1face54361@i2pn2.org> <272433824a6757890727cb76203777dda01dcf1e@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 24 Oct 2024 21:42:30 +0200 (CEST) Injection-Info: dont-email.me; posting-host="f255236784b0884105f55aca8336b1f6"; logging-data="2917977"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19s5YKnwmjYDdJO80TplvFJjRI/sPjP2nk=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:xpowx7PBVOAQnyPKCRmS0qfpHwU= In-Reply-To: Content-Language: en-US Bytes: 2418 On 10/24/2024 8:27 AM, WM wrote: > On 24.10.2024 16:37, Moebius wrote: > >> Hint: For any nonempty set of natural numbers M: >> >>           M is infinite iff for each and every element m in M there's >> an element m' in M such that m' > m. >> >> (Note that sets don't change.) > > Important! If all those numbers are doubled, then their density is > halved, their number remains constant, and their interval is doubled. Sigh.