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Path: ...!news.mixmin.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Moebius <invalid@example.invalid> Newsgroups: sci.logic,sci.math Subject: Re: Replacement of Cardinality Date: Tue, 27 Aug 2024 21:31:00 +0200 Organization: A noiseless patient Spider Lines: 22 Message-ID: <val9hk$33mgs$1@dont-email.me> References: <hsRF8g6ZiIZRPFaWbZaL2jR1IiU@jntp> <va4h96$3r7nv$1@dont-email.me> <H5iV5HXUBwUzWtVKRZj7h4N2LdA@jntp> <va543m$3u6dp$1@dont-email.me> <kN73KZJabPuiasJJ0DR6UOOrMHE@jntp> <d47ad77b3f2bd0bc6280b8eca772b280f3a18dc8@i2pn2.org> <ivRRwss8WgoMTIfJa5g04TJmRxU@jntp> <db885c7c1e1a5bfdf60e90fa9882bfb73b4e6ce7@i2pn2.org> <eY2Memk56jLKsrTeR3kBDQQqfHI@jntp> <bdfbb725-7fc3-4e17-b09b-4d6191d301a5@att.net> <tvUGDEKZBjBIOn4R0HIJvG5es4k@jntp> <val92g$33pkn$1@dont-email.me> Reply-To: invalid@example.invalid MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 27 Aug 2024 21:31:00 +0200 (CEST) Injection-Info: dont-email.me; posting-host="b02d027af6f84bb180cd6049e1baf472"; logging-data="3267100"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19Gu5i2xsDe7weMCGaKkDr8" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:QpCC7n4+3OgIqwT/C2voolumGAk= Content-Language: de-DE In-Reply-To: <val92g$33pkn$1@dont-email.me> Bytes: 2176 Am 27.08.2024 um 21:22 schrieb Chris M. Thomasson: > On 8/27/2024 12:11 PM, WM wrote: >> Le 27/08/2024 à 02:06, Jim Burns a écrit : >>> On 8/25/2024 3:45 PM, WM wrote: >> >>>> This function exists because >>>> nothing contradicts its existence. Right. But the values of the function NUF are: 0 for all real arguments <= 0 and aleph_0 for all real arguments > 0. >> The function exists if actual infinity exists. That's for sure. >> The function does not exist if only potential infinity exists. Right. card(...) can't be aleph_0 in this case. :-) Hence we are glad that in the context of axiomatic set theory the AoI ensures for infinite sets. (Cantor ->transfinite set theory).