Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!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: The set of necessary FISONs Date: Sat, 12 Apr 2025 15:20:12 +0200 Organization: A noiseless patient Spider Lines: 15 Message-ID: References: <04dd7515-297c-4e7c-9e6a-a4f43e663552@att.net> <43c020cb-dc8b-4feb-be1d-2a76f02be14e@att.net> <19431656-fb42-4569-9334-b5b7e19c80c6@att.net> <4b45ff34-dc3f-4e32-90a3-237f78fbd321@att.net> <4ed4b6dc-de9b-46f7-b2f8-484557d89281@att.net> <7ac03d2e-5d72-4186-8b33-6fdddb7b83ff@att.net> <7ccdd4c7-d15e-417f-9b85-6f9a790d7d44@att.net> <6b5758dbf7740daac4a44583e187b2cc5863064c@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Sat, 12 Apr 2025 15:20:13 +0200 (CEST) Injection-Info: dont-email.me; posting-host="00f09292e8367fdbc7fc2cb697d174a7"; logging-data="639059"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+Wu3urT2NvdDqLvfW3mebtInIPaYe+moU=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:YSvaLvCMIVso+/5WlMSLsDEDjKA= In-Reply-To: Content-Language: en-US Bytes: 2573 On 11.04.2025 19:59, Richard Damon wrote: > > But the number of Natural Numbers isn't itself a Natural Number, so that > doesn't contradict the statement. The number of definable natural numbers is potentially infinite. All fractions having definable denominators can be removed from the harmonic series. The remaining terms remain infinite nevertheless. The number of all natural numbers is actually infinite. Removing all terms of the harmonic series having natural denominators yields the sum 0. Regards, WM