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Path: eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> Newsgroups: sci.logic,sci.math Subject: Re: Replacement of Cardinality Date: Sun, 4 Aug 2024 16:07:37 -0700 Organization: A noiseless patient Spider Lines: 23 Message-ID: <v8p1jp$9gvr$1@dont-email.me> References: <hsRF8g6ZiIZRPFaWbZaL2jR1IiU@jntp> <-qUZ96ARwcjh9QPfyWRnijjNwoY@jntp> <6b837540-3d9a-4b8e-9a70-88d52e81a1a4@att.net> <xQQT0K_Q_k2FbMcCUXF8j3CEg84@jntp> <9822f5da-d61e-44ba-9d70-2850da971b42@att.net> <p36L63dXamDAkHDhkZhDKqx-h-o@jntp> <d8bbe664-a601-4590-9a7f-d5312b4dae54@att.net> <F6pqEi9Vg1YMcYTcIPQNs6NU_vI@jntp> <4f606ef2-ef6c-487b-b959-d109e374929f@att.net> <v8mh6f$3mmj9$2@dont-email.me> <I2JWgvxiRMkr8F2KSK6i7i5b1n0@jntp> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 05 Aug 2024 01:07:38 +0200 (CEST) Injection-Info: dont-email.me; posting-host="8fb2bf3bc0b69bac1b2db0bf88076279"; logging-data="312315"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19FX3kZjFxAlyR2jR1/vZLnbhQcBnoJTkY=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:I+MCHXDlDBhKI3vFdeA8RbkmIQ4= In-Reply-To: <I2JWgvxiRMkr8F2KSK6i7i5b1n0@jntp> Content-Language: en-US On 8/4/2024 8:35 AM, WM wrote: > Le 04/08/2024 à 02:15, Moebius a écrit : >> Am 03.08.2024 um 21:54 schrieb Jim Burns: >>> On 8/3/2024 10:23 AM, WM wrote: >> >>>> NUF(x) = ℵ₀ for all x > 0 is wrong. >> >> Nonsense. >> >> Actually, Ax > 0: NUF(x) = ℵ₀. > > You mean that there are ℵ₀ unit fractions smaller than all positive x? > Impossible. ℵ₀ unit fractions occupy ℵ₀*2^ℵ₀ points. Not even one unit > fraction cann be smaller than all positive x. Huh? Say x = 1/2, there are infinite smaller unit fractions, say, 1/4, 1/5, 1/6, ect... However there is only one larger one, 1/1. See? No smallest one for 1/0 is not a unit fraction! There is a largest one, 1/1... They tend to zero, but there is no smallest one... See?