Path: ...!Xl.tags.giganews.com!local-1.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail NNTP-Posting-Date: Sun, 25 Aug 2024 20:31:54 +0000 Subject: Re: Replacement of Cardinality (effective bounds) Newsgroups: sci.math References: <980a0ec7476c9dc5823e59b2969398bd39d9b91d@i2pn2.org> <_lFM72wVqiPQLxO8Gf0IkBJtFhw@jntp> <8bd5624bc47bbca8d04773df845cca2b55435df0@i2pn2.org> <4ef033b9-920b-44d8-8ac7-bc6b587e55bc@att.net> <15471ab0-fb10-45a3-af56-cb631ede8c1c@att.net> From: Ross Finlayson Date: Sun, 25 Aug 2024 13:31:50 -0700 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.6.0 MIME-Version: 1.0 In-Reply-To: <15471ab0-fb10-45a3-af56-cb631ede8c1c@att.net> Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Message-ID: Lines: 101 X-Usenet-Provider: http://www.giganews.com X-Trace: sv3-o12tGAfpOR+JtF2vI/ppY6NElaOLsFFM6oTmY9U8BxJ4Piqk1qPZZ7ntQbIRrbhZfdJLVwg3yIMkyE1!vvvEurBHAHLLOisEBtpZFyUn4OmBIFIY8e/ZRwJxNdf/CbuXD5KOGFzp4BK1hvsbJwptaYbIwrxy X-Complaints-To: abuse@giganews.com X-DMCA-Notifications: http://www.giganews.com/info/dmca.html X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly X-Postfilter: 1.3.40 Bytes: 5060 On 08/25/2024 10:47 AM, Jim Burns wrote: > On 8/24/2024 8:26 PM, Ross Finlayson wrote: >> On 08/24/2024 03:39 PM, Jim Burns wrote: >>> On 8/24/2024 4:50 PM, Ross Finlayson wrote: >>>> On 08/24/2024 11:08 AM, FromTheRafters wrote: >>>>> WM has brought this to us : >>>>>> Le 23/08/2024 à 20:06, joes a écrit : > >>>>>>> The unit fractions don’t reach 0. >>>>>> >>>>>> Of course not. >>>>>> Therefore they must cease before. >>>>> >>>>> Why must they cease at all? >>>> >>>> He can just axiomatize it so, >>>> saying that there's a rule. > >>> Yes, clearly, WM can do it. >>> Much less clear is why WM would do it. >> >> Still, you can just look at it that >> he has a speech impediment, >> and in some generous reading >> he's the only go-between that somehow >> you must explain in his terms, what's in your terms. > > You mean, I must explain like this? > > In a finiteⁿᵒᵗᐧᵂᴹ order ⟨A,<⟩ > each non.empty subset S ⊆ A holds minᑉ.S and maxᑉ.S > > I will consider doing that. > >> So here, it's simplest as >> a system of bounds, modeled in the unbounded, >> instead of just >> a usual system of no bounds, modeled in the unbounded. >> I.e. it's just the sort of opposite that you've chosen >> or have a natural or imposed sort of slur about >> whether they're bounds in the unbounded >> or not-bounds in the un-bounded. > > Huh? > >> Anyways >> you've declared many times that >> you're quite deaf to claims that >> Russell's axiom is in any way false, > > Since I like to know what I'm declaring, > what is Russell's axiom? > > Speaking of axioms in general, > it is a theorem that, > if the axioms do not imply a contradiction, > then they are not false of _everything_ > then a model exists. > > Also, too, > if a model exists, > if the axioms are not false of _everything_ > then the axioms do not imply any contradiction. > >> so, >> I'm not quite sure what it is >> that will make it so that >> anyone who'd care to try and follow your argument >> would have to always insert >> a slate of boilerplate argument > > The usual practice in mathematical argument is > to insert the boilerplate text once, somewhere, > and then pass to the alert reader the job of finding > the relevant previous paragraph or previous chapter > or previous volume or previous school. > > My (questionable) understanding is that it's considered > insulting to always insert the boilerplate. > Perhaps it's seen as tacitly calling the reader > less.than.alert. > > Russell's retro-thesis is that there's an ordinary well-founded inductive set, when already it's shown that Russell's antinomy would affect such a thing, it's an axiom contradicting what would have been. So, yes, your rule number one is considered intrusive as you put it, because, there's already an implicit where it's not so, that the whole "restriction of comprehension" bit is contrived, and that's not that "three-sided polygons are triangles" is anything other than a matter of definition, it's that "three-sided polygons don't exist" is a restriction of comprehension, that thusly is either always intrusive or always capricious. Either way it's not my pick.