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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) Date: Sat, 18 Jan 2025 08:46:45 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <8abadd80012cca6bf46e6c2610f65d51b9791b4e@i2pn2.org> References: <vg7cp8$9jka$1@dont-email.me> <vlo5f4$39hil$2@dont-email.me> <4c89380adaad983f24d5d6a75842aaabbd1adced@i2pn2.org> <vloule$3eqsr$1@dont-email.me> <ffffed23878945243684de7f2aa9aaaf29564508@i2pn2.org> <vlrej9$2m5k$1@dont-email.me> <d6ed4797-65e8-4004-853c-f07a37af0c11@att.net> <vls4j6$7v2k$3@dont-email.me> <494bfd3b-3c70-4d8d-9c70-ce917c15fc22@att.net> <vm0okb$16cq0$2@dont-email.me> <bff18686-503a-4b7b-9406-b47796f68b47@att.net> <vm15pj$18v7t$1@dont-email.me> <72142d82-0d71-460a-a1be-cadadf78c048@att.net> <vm3hrs$1s9ld$2@dont-email.me> <812e64b1-c85c-48ac-a58c-e8955bc02f8c@att.net> <vm59g4$2b5ib$1@dont-email.me> <aca83786cb60134e106c96414e223bab91d21482@i2pn2.org> <vm8t0f$31v8s$2@dont-email.me> <83b0763709eeeca543bf19d9d08014d75d0e2b78@i2pn2.org> <vmb0vj$3gu90$1@dont-email.me> <06217c76305c8c2a436ee6f75c9162864d97e399@i2pn2.org> <vmdc1r$3vamp$4@dont-email.me> <a0b4f8abd9bae2ea697076033a9c1dbe6af26dac@i2pn2.org> <vmeb6r$3iir$1@solani.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sat, 18 Jan 2025 13:46:45 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="4178783"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US In-Reply-To: <vmeb6r$3iir$1@solani.org> Bytes: 3381 Lines: 41 On 1/17/25 2:31 PM, WM wrote: > Am 17.01.2025 um 15:52 schrieb Richard Damon: >> On 1/17/25 5:39 AM, WM wrote: >>> On 17.01.2025 01:37, Richard Damon wrote: >>>> On 1/16/25 8:18 AM, WM wrote: >>>>> On 15.01.2025 20:54, joes wrote: >>>>>> Am Wed, 15 Jan 2025 18:58:40 +0100 schrieb WM: > >>> Logic says that every FISON which is smaller than another FISON can >>> be dropped. Logic says even more: Every FISON which is smaller than ℕ >>> can be dropped. Therefore all can be dropped. >> >> ANY can be dropped, but not ALL. > > Never more than one mustremain, because the second is smaller and is not > needed, or is greater, then the first can be dropped. Whicj just shows that your logic can't handle the infinite. >> >>> Do you know a FISON that is smaller than ℕ but cannot be dropped?n >> >> No, and all that shows is that there isn't a "largest" FISON that has >> all the Natural Numbers. > > Therefore all are useless and will not produce the actually infinite set > of natural numbers but only the potentially infinite collection of > definable natural numbers. Therefore YOUIR LOGIC is worthless, and can't handle the problem. If you want to say that ALL MATHEMTATICS is worthless, then you are just admitting that you life has been worthless. You are just proving that your "naive mathematics" is worthless, because it NEEDS there to be a bigget value, but can't define one. > > Regards, WM > >