Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: sci.logic Subject: Re: Replacement of Cardinality Date: Tue, 20 Aug 2024 13:36:21 +0300 Organization: - Lines: 29 Message-ID: References: <6c471296-90b8-4cf7-bc9b-480bd34ef190@att.net> <1f25a3d6-7b0e-476d-aa99-ecb003cf763f@att.net> <75e2ce0e-7df8-4266-968b-9c58e4140b03@att.net> <35d8c0a1-dab3-4c15-8f24-068e8200cb07@att.net> <45ad1007-b1a7-49d0-a650-048f02738226@att.net> <9ef8dd8a-69be-44e2-bcf6-ea9c1fb30e21@att.net> <92189533-0c1f-4532-816f-564651cc8bf7@att.net> <155cdc8a628d47be1632791227bccf99425b1d5e@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 20 Aug 2024 12:36:22 +0200 (CEST) Injection-Info: dont-email.me; posting-host="c68d48608550e7e7fabcc3f8200ba7d3"; logging-data="3529403"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/1DAVhhj6v//NAASIgOqIF" User-Agent: Unison/2.2 Cancel-Lock: sha1:rrSagtBC4O3tdI72j70kiAxIH9Q= Bytes: 2802 On 2024-08-19 11:32:44 +0000, WM said: > Le 17/08/2024 à 16:29, Richard Damon a écrit : >> On 8/17/24 9:28 AM, WM wrote: >>> Le 16/08/2024 à 19:39, Jim Burns a écrit : >>> >>>> no element of ℕᵈᵉᶠ is its upper.end, >>>> because >>>> for each diminishable k >>>> diminishable k+1 disproves by counter.example >>>> that k is the upper.end of ℕᵈᵉᶠ >>> >>> SBZ(x) starts with 0 at 0 and increases, but at no point x it increases >>> by more than 1 because of >>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0. Therefore there is a smallest unit fractions >>> and vice versa a greatest natnumber. >>> What can't you understand? > >> But there is no point (>0) where it has a finite value, > > You can't see it and you are unable to derive it from mathematics. But > blindness is not an argument. Blindness is indeed much weeker than a proof but you may use it as an argument as long as you can't find anything better. -- Mikko