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Path: ...!eternal-september.org!feeder3.eternal-september.org!i2pn.org!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, effectively) Date: Fri, 3 Jan 2025 23:06:11 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <124ce383a23234d762f967a1b32462d68e5a7c03@i2pn2.org> References: <vg7cp8$9jka$1@dont-email.me> <n9CdnR02SsevtPL6nZ2dnZfqnPidnZ2d@giganews.com> <45a632ed-26cc-4730-a8dd-1e504d6df549@att.net> <vkpa98$dofu$2@dont-email.me> <3d2fe306aa299bc78e94c14dadd21645d8db9829@i2pn2.org> <vkr8sq$t59a$2@dont-email.me> <d4669f26483b01c8a43dfd3ac4b61ab4a42bf551@i2pn2.org> <vksikk$17fjt$1@dont-email.me> <aa2941e93e806f1dda55d563dd062db67eb879f1@i2pn2.org> <vktmi3$1ia1u$1@dont-email.me> <c46775b30460bc564b3fe7bd1b838713829024f8@i2pn2.org> <vkv3t1$1qb93$1@dont-email.me> <2163aa0c0efba66c813e8ebda5ef5ece6d19ea34@i2pn2.org> <vl1bp4$2bcos$2@dont-email.me> <ac6061d7f9963a83c7a67f474fe9cb835c98cf5b@i2pn2.org> <vl5tvs$39tus$1@dont-email.me> <9387e323873e24f0a57b8daa49579d9a1c517563@i2pn2.org> <vl6i2u$3ecap$2@dont-email.me> <89598d353b5737d5cbfabd1cde31c797a212e13d@i2pn2.org> <vl7f50$3jdl8$2@dont-email.me> <vl7ftq$3jcou$2@dont-email.me> <vl88fp$3qtjc$2@dont-email.me> <7595ac4af886b0ab3c0f5fe6bcbcbce6103e78aa@i2pn2.org> <vl95se$3vk27$4@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 4 Jan 2025 04:06:11 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1912329"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: <vl95se$3vk27$4@dont-email.me> Content-Language: en-US X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 2738 Lines: 26 On 1/3/25 12:13 PM, WM wrote: > On 03.01.2025 15:50, Richard Damon wrote: >> On 1/3/25 3:52 AM, WM wrote: >>> On 03.01.2025 02:52, Moebius wrote: >>> >>>> Nope. For each and every FISON F: F c IN. >>>> >>>> But UNION(Set_of_FISONs) = IN. >>> >>> Every union of FISONs including them all which stay below a certain >>> threshold stays below that threshold. > >> Which is different from *ALL* of them, > > No. ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo > > Regards, WM > > So, you just confirm your stupidity. You don't seem to know what *ALL* means, and you are unable to define what the difference between N and N_def is. You are just confirming you are nothing but an ignorant liar that doesn't know enough to know he is jsut stupid.