Path: ...!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: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Fri, 3 Jan 2025 09:47:37 +0100 Organization: A noiseless patient Spider Lines: 17 Message-ID: References: <069069bf23698c157ddfd9b62b9b2f632b484c40@i2pn2.org> <2d3620a6e2a8a57d9db7a33c9d476fe03cac455b@i2pn2.org> <75921cc1f17cdb691969a99e666f237cd09c0b09@i2pn2.org> <25729298b142c60d5b245231984119d42d4ac089@i2pn2.org> <09ef32dfb3944d321e15e1383820166a2082d5cb@i2pn2.org> <6d7fb8f4346eb09ea7ccdff45e8ff3d0c4a45ab0@i2pn2.org> <85c0a8a2a0f1429c0b3c7acc69e659d174710347@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 03 Jan 2025 09:47:38 +0100 (CET) Injection-Info: dont-email.me; posting-host="01d51636a443c1100d6c37c2b77ce98b"; logging-data="4028012"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/oSTY4ws69jBrphkQdiNLerkxcXDJNOyM=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:WWD01UHArulhmDDEBsdKiSp+DMw= In-Reply-To: Content-Language: en-US Bytes: 2591 On 02.01.2025 20:47, Richard Damon wrote: > On 1/2/25 12:28 PM, WM wrote: >> Hint first try to understand 50 %, then 10 %, then 1 %, then 1 ppm, >> then 1 ppb, then 1/10^10^10^10^10. And then go on. Then you understand >> the properties of FISONs. > > And ALL finite fractional ratios of Aleph_0, are Aleph_0, and thus > infinite so the set of FISONs covers less than any fractional ratio of ℕ. This is true for their union too. Otherwise there must be a first FISON going beyond this boundary. Regards, WM