Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: sci.logic Subject: Re: Simple enough for every reader? Date: Sat, 14 Jun 2025 13:58:06 +0300 Organization: - Lines: 36 Message-ID: <102jkju$52ir$1@dont-email.me> References: <100a8ah$ekoh$1@dont-email.me> <1011qrn$20v83$1@dont-email.me> <10149ic$2jtva$1@dont-email.me> <1014kja$2l9jj$4@dont-email.me> <1016h9p$35it9$1@dont-email.me> <101797i$39rdb$1@dont-email.me> <1019bki$3qe6q$1@dont-email.me> <1019s2k$3sv8u$3@dont-email.me> <101bu77$dqtr$1@dont-email.me> <101cf4h$gl20$2@dont-email.me> <101ejtv$129q7$1@dont-email.me> <101f0rr$14h5f$2@dont-email.me> <101hevt$22j02$1@dont-email.me> <101hn99$25a4g$2@dont-email.me> <101mah1$3t0cq$1@dont-email.me> <101msm5$qln$1@dont-email.me> <101opv8$m16h$1@dont-email.me> <101pvvc$upfh$1@dont-email.me> <101rh76$1djtf$1@dont-email.me> <101sv4s$1o8bc$1@dont-email.me> <101u5sd$24q1b$1@dont-email.me> <101uh03$26rnt$2@dont-email.me> <10235vu$3lmmn$1@dont-email.me> <1029om9$1cir8$2@dont-email.me> <102bcgv$1rtqf$1@dont-email.me> <102bpch$1ud0p$2@dont-email.me> <102e17b$2ijkk$1@dont-email.me> <102e7cv$2jqav$1@dont-email.me> <102gse1$3c4uk$1@dont-email.me> <102ha1f$3f983$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 14 Jun 2025 12:58:07 +0200 (CEST) Injection-Info: dont-email.me; posting-host="305fc436f129229334944ded072371e9"; logging-data="166491"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19SOCKeQWwN5rLidCkvwxic" User-Agent: Unison/2.2 Cancel-Lock: sha1:W0T1I0MapxkmO7cSzTPHycOhbJ4= On 2025-06-13 13:45:20 +0000, WM said: > On 13.06.2025 11:53, Mikko wrote: >> On 2025-06-12 09:41:51 +0000, WM said: >> >>> On 12.06.2025 09:56, Mikko wrote: >>>> On 2025-06-11 11:30:26 +0000, WM said: >>> >>>>> For all natural numbers that can be chosen as individuals: >>>>> |ℕ \ {1, 2, 3, ..., n}| = ℵo. >>>>> The "..." can be removed by the inductive proof >>>>> for all definable n ∈ ℕ: >>>>> |ℕ \ {1}| = ℵo. >>>>> |ℕ \ {m ∈ ℕ | m < n}| = ℵo >>>>> ==> |ℕ \ {m ∈ ℕ | m < n+1}| = ℵo. >>>> >>>> That the set difference of an infinite set and a finite set is infinite >>>> is well understood and therefore an uninteresting result. >>> >>> That is not the only result. >> >> That is the result of your proof. Other results can be discussed in >> other contexts. > > The following result cannot be circumvented: After mankind will have ceased, who will care? > there is a largest natural number ever named. That has no mathematical significance. Whther a number is nambed or not is a featurem of mankind, not of the number. -- Mikko