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: The set of necessary FISONs Date: Tue, 18 Feb 2025 16:26:31 +0100 Organization: A noiseless patient Spider Lines: 17 Message-ID: References: <79920977-902d-4f59-a11c-497383221c82@att.net> <468b9c37-ba93-485c-8685-4b320e168251@att.net> <68bab5c2-50d3-43fc-be0d-51e01c5952bb@att.net> <1e5cb0d4-f447-4fa7-b1e9-8056b03d27a2@att.net> <5f7c94ab-c633-40be-a7bc-9ed8c3795501@att.net> <83ca74c3-4714-43a2-afe5-ec9e70a5d828@att.net> <7ab7cbcd-2bcc-45e8-9cec-e97addda22f9@att.net> <4b135882105d3e0445670cc5e4f5cd4540df4c80@i2pn2.org> <6ce2f2978a7afa0e86094debd2e5f1f0eb16f266@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 18 Feb 2025 16:26:31 +0100 (CET) Injection-Info: dont-email.me; posting-host="da03ab08f41375b6d1ffd7b3c68daff2"; logging-data="1837344"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/6VOnHsWQ3PLMAh4nIvU0hxoygns1haJw=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:bbdA9YcvSQxyy2j9AYEbdVFdBH8= Content-Language: en-US In-Reply-To: <6ce2f2978a7afa0e86094debd2e5f1f0eb16f266@i2pn2.org> Bytes: 2563 On 18.02.2025 13:25, Richard Damon wrote: > On 2/18/25 5:02 AM, WM wrote: >> On 18.02.2025 04:02, Richard Damon wrote: >> >>> We can build a sufficent set from non-required FISONs, just like we >>> can factor 36 from non-required factors. >> >> We can go through the factors and find the first required factor 6. > > 6 isn't a required factor, as you can use 4 * 9. We go through the ordinals, with FISONs and with factors. There is a first required factor. There is no first required FISON. All are useless because of ∀n ∈ U(F(n)): |ℕ \ {1, 2, 3, ..., n}| = ℵo. Regards, WM