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Path: ...!3.eu.feeder.erje.net!2.eu.feeder.erje.net!feeder.erje.net!proxad.net!feeder1-2.proxad.net!usenet-fr.net!pasdenom.info!from-devjntp Message-ID: <EWjydktrw41PByy85crvGiL8Ai8@jntp> JNTP-Route: news2.nemoweb.net JNTP-DataType: Article Subject: Re: because =?UTF-8?Q?g=E2=A4=A8=28g=E2=81=BB=C2=B9=28x=29=29=20=3D=20g?= =?UTF-8?Q?=28y=29=20=5B=31/=32=5D=20Re=3A=20how?= References: <qHqKnNhkFFpow5Tl3Eiz12-8JEI@jntp> <0682ec96-856f-4659-918d-f4f08edada3e@att.net> <IzQUzuTPV4P3XMbkfmQrEzl_xMs@jntp> <e261dbb5-4d89-4753-aee0-db91a1924356@att.net> <6xC7D4OsaY-Dbt6UCvgZwElFXdY@jntp> <ff51fcc9-94ac-4c33-afd8-21c01cd7bb03@att.net> <sdM6tt0a2wvVmLtfLrvf50vhr-o@jntp> <ec1c7139-44dc-43da-a81b-a788524ec0fa@att.net> <9XyUBE0IPOJTIEc95u0LtlnjWsI@jntp> <1f4bd9ca-5ade-43c0-a50d-927ce267d059@att.net> Newsgroups: sci.math JNTP-HashClient: nUBgbovQ7TxmRuoM2Kkv_gNQo3o JNTP-ThreadID: 4YLc1knY-8u5i_KQ0oWqy89D7aY JNTP-Uri: http://news2.nemoweb.net/?DataID=EWjydktrw41PByy85crvGiL8Ai8@jntp User-Agent: Nemo/0.999a JNTP-OriginServer: news2.nemoweb.net Date: Mon, 13 May 24 20:27:54 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/124.0.0.0 Safari/537.36 Injection-Info: news2.nemoweb.net; posting-host="7a19405b4245f47946ffce65063ceb09f86be43b"; logging-data="2024-05-13T20:27:54Z/8856103"; posting-account="217@news2.nemoweb.net"; mail-complaints-to="julien.arlandis@gmail.com" JNTP-ProtocolVersion: 0.21.1 JNTP-Server: PhpNemoServer/0.94.5 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-JNTP-JsonNewsGateway: 0.96 From: WM <wolfgang.mueckenheim@tha.de> Bytes: 2784 Lines: 33 Le 10/05/2024 à 20:56, Jim Burns a écrit : > On 5/10/2024 8:18 AM, WM wrote: >> Le 08/05/2024 à 23:55, Jim Burns a écrit : >>> On 5/8/2024 3:55 PM, WM wrote: >>>> Le 07/05/2024 à 00:11, Jim Burns a écrit : > >>>>> All which canNOT be counted.to are not.in ℕ >>>> >>>> All which canNOT be counted.to are not.in ℕ_def. >>> >>> And all which CAN be counted.to are in ℕ_def. >> >> Yes. > > Thank you. > > ℕ_def is the set of all and only > numbers which CAN be counted.to. > ℕ_def is what everyone else calls ℕ Yes, most are too stupid to see the difference: ℕ contains numbers which never can be counted to. >> ℕ_def is a potentially infinite collection >> and as such has no fxed number of elements. >> We use the indefinite oo in this case. > > Weⁿᵒᵗᐧᵂᴹ use ℵ₀ to refer to |ℕ_def| ℕ_def contains only numbers which can be counted to and which have ℵ₀ successors. f |ℕ_def| = ℵ₀ would be succeeded by ℵ₀. Regards, WM