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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Julio Di Egidio Newsgroups: sci.math Subject: Re: All infinities are countable in ordinary mathematics Date: Sun, 4 May 2025 18:54:35 +0200 Organization: A noiseless patient Spider Lines: 38 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 04 May 2025 18:54:37 +0200 (CEST) Injection-Info: dont-email.me; posting-host="452704407c9a0d26017a3a7940bd6c99"; logging-data="1954706"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+Tw48eXdbtsGjAOWk0fYKgwOx0KcXvPC4=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:pINAcPtGwotXuveLZ2SVfDhYHso= Content-Language: en-GB, it In-Reply-To: Bytes: 2685 On 04/05/2025 17:17, Ross Finlayson wrote: > On 05/04/2025 06:27 AM, Julio Di Egidio wrote: >> If there exist definite transfinite numbers, then their >> reciprocals must be infinitesimals, not zero.  Which is >> good, as infinitesimals necessitate specific additional >> laws, reciprocally making the transfinite sharper.  And >> one issue is immediately apparent: infinitesimals are >> not compatible with the Archimedean principle.  Ergo, >> all infinities are countable in ordinary mathematics. > > Pythagorean Archimedean [bollocks] > > A usual account of infinity has that it's not ordinary, > rather, per Mirimanoff, extra-ordinary, then that it's > fragments or extensions, the model of integers. Are you aware of the fact that the least upper-bound property, which is an axiom of the standard theory of real numbers, and a formalisation of the notion of continuum with it, *implies the Archimedean property*? Indeed, there is ordinary and there is extra-ordinary, and *invalidly* then *inconsistently* mixing results is the problem there. (But already the prefix "extra", which is necessarily extra-to given something, here the "ordinary", should at least make *you* pause, and rather warn you that you have it upside-down, what "ordinary mathematics" even is, as per the usual inversion of all that counts. Conversely, your balderdash, here as elsewhere, always eventually back to your blind take-everything and fully prosaic Platonism, remains the other side of the very same mangled/fraudulent coin. Strictly speaking.) Julio