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Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: Richard Damon <richard@damon-family.org> Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Wed, 11 Dec 2024 19:32:21 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <4e7901e16785581d0d02a2d6474d7d2615c5fac9@i2pn2.org> References: <vg7cp8$9jka$1@dont-email.me> <viq3i2$105iq$1@dont-email.me> <e055ec41-a98d-4917-802f-169575a5b556@att.net> <virq3t$1gs07$1@dont-email.me> <c8faf784-348a-42e9-a784-b2337f4e8160@att.net> <3af23566-0dfc-4001-b19b-96e5d4110fee@tha.de> <ae606e53-0ded-4101-9685-fa33c9a35cb9@att.net> <viuc2a$27gm1$1@dont-email.me> <8a53c5d4-4afd-4f25-b1da-30d57e7fe91c@att.net> <vj1acu$31atn$3@dont-email.me> <ec451cd6-16ba-463d-8658-8588093e1696@att.net> <vj2f61$3b1no$1@dont-email.me> <10ebeeea-6712-4544-870b-92803ee1e398@att.net> <vj3tl0$3nktg$2@dont-email.me> <1f1a4089-dfeb-45f8-9c48-a36f6a4688fb@att.net> <vj6bqo$b6bt$1@dont-email.me> <b09445be167b757878741be04c87cf76d24d9786@i2pn2.org> <vj6psc$dp01$1@dont-email.me> <84818a4f5d3795b746b017ad0861a3d818c5b053@i2pn2.org> <vj8vd0$stav$1@dont-email.me> <5805ad50ebff3400d1370d8c99790cbc727a340a@i2pn2.org> <e86171d3-e5c1-4725-952d-d4da0f4ded07@tha.de> <1ac93432f1ba567e0f15308b8964bee86b92c706@i2pn2.org> <vjc7q2$1ir2f$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 12 Dec 2024 00:32:21 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2420993"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird X-Spam-Checker-Version: SpamAssassin 4.0.0 In-Reply-To: <vjc7q2$1ir2f$2@dont-email.me> Content-Language: en-US Bytes: 2954 Lines: 28 On 12/11/24 9:32 AM, WM wrote: > On 11.12.2024 03:04, Richard Damon wrote: >> On 12/10/24 12:30 PM, WM wrote: >>> On 10.12.2024 13:17, Richard Damon wrote: >>>> On 12/10/24 3:50 AM, WM wrote: >>> >>>>> Two sequences that are identical term by term cannot have different >>>>> limits. 0^x and x^0 are different term by term. >>>> >>>> Which isn't the part I am talking of, it is that just because each >>>> step of a sequence has a value, doesn't mean the thing that is at >>>> that limit, has the same value. >>> >>> Of course not. But if each step of two sequences has the same value, >>> then the limits are the same too. This is the case for >>> (E(1)∩E(2)∩...∩E(n)) and (E(n)). > >> But the limit of the sequence isn't necessary what is at the "end" of >> the sequence. > > The end of the sequence is defined by ∀k ∈ ℕ : E(k+1) = E(k) \ {k}. > > Regards, WM > None of which are an infinite sets, so trying to take a "limit" of combining them is just improper.