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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: 2N=E Date: Mon, 4 Nov 2024 22:08:46 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <55737882c19ea6d576a04e71473a1cd87a15bb7b@i2pn2.org> References: <vb4rde$22fb4$2@solani.org> <vftj9t$26ql2$1@dont-email.me> <8b31df46-1361-4dd1-aed3-1f42039af960@att.net> <vfu2qi$29m4j$2@dont-email.me> <84c1bb5d-67db-4d21-918a-f86cd1f815c5@att.net> <vfvefj$9264$2@solani.org> <ca84d22c-3684-4744-a145-a941bac4651f@att.net> <vg0iba$2q8fo$1@dont-email.me> <c2087013-5e5c-4e01-b356-29ffa484bfc2@att.net> <vg0p6j$2ra8e$1@dont-email.me> <vg0u81$2s8he$1@dont-email.me> <vg29sb$36ojr$3@dont-email.me> <vg2cb1$379th$1@dont-email.me> <vg2eqf$36ojq$9@dont-email.me> <vg2i33$38a2j$1@dont-email.me> <vg31uv$3b2rd$1@dont-email.me> <a3f1a8c045d260ea779c538c2f5a360631cb7d64@i2pn2.org> <vg5n8t$3sb7d$4@dont-email.me> <a4609d595975de654c01758fba3906e7cea16285@i2pn2.org> <vg7oe0$9ma8$7@dont-email.me> <ded233b7dedcb4e18af9f7f60e5c45c1a510bd44@i2pn2.org> <vg80mc$d2am$1@dont-email.me> <b429867dd2a0a5ebdcfdb71a2eaf7457bacfd879@i2pn2.org> <vgaa1n$t046$5@dont-email.me> <282974aaed1fcb8eae0c5d69ffb6ba39a1909b64@i2pn2.org> <vgb00p$11df6$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Tue, 5 Nov 2024 03:08:47 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="999091"; 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: <vgb00p$11df6$2@dont-email.me> Content-Language: en-US Bytes: 2944 Lines: 27 On 11/4/24 12:24 PM, WM wrote: > On 04.11.2024 13:26, Richard Damon wrote: > >> Yes, we know if you will double them again, as we started with the >> assumption that we double ALL the number, and any even number will be >> reached from doubling the number that is one half of it and will be >> doubled again. > > Please mark the sentence which you suspect to be wrong: > > - All natural numbers exist. > - The even numbers have only half of the substance(*) of the integers. Not a valid statement, as half of infinity is still infinity. > - Multiplication of all elements of a set does not change the substance. > > (*) For every interval (0, 2n] the number E of even natnumbers is half > of the number N of natnumbers: E/N = 1/2. For (0, oo] we obtain the > limit of the sequence 1/2, 1/2, 1/2, ... which is 1/2. This is the ratio > of the substances or, as Cantor called it, the reality. In other words, your logic can only deal with finite subsets of the infinite set, and thus isn't a system that can handle actual infinity. > > Regards, WM