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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: FromTheRafters <FTR@nomail.afraid.org> Newsgroups: sci.math Subject: Re: collective and individual removal Date: Mon, 28 Apr 2025 10:04:02 -0400 Organization: Peripheral Visions Lines: 16 Message-ID: <vuo1sk$3f1rn$1@dont-email.me> References: <vunv23$37o6r$2@dont-email.me> Reply-To: erratic.howard@gmail.com MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-15"; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Mon, 28 Apr 2025 16:04:06 +0200 (CEST) Injection-Info: dont-email.me; posting-host="61b5fa2153ae4dec87da79697fb5fd41"; logging-data="3639159"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+QWbcYjPVhRjZ9s8gWfu9thfifVdla9JE=" Cancel-Lock: sha1:8jjz7T2D57a+W6dmJGqxGnr+EU8= X-ICQ: 1701145376 X-Newsreader: MesNews/1.08.06.00-gb Bytes: 1549 WM explained on 4/28/2025 : > We can remove collectively all terms from the harmonic series. Nothing > remains. > > If we restrict the removal to individually definable terms, then an infinity > remains. > > Is this remainder caused by the impossibility to define infinitely many terms > individually? No! It is sufficient to define one term, namely the last one > definable. But there is no last one definable since they all are. > This is an irrefutable proof of the existence of dark numbers. For some values of irrefutable.