Path: ...!eternal-september.org!feeder3.eternal-september.org!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: sci.math Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary) Date: Thu, 2 Jan 2025 08:26:41 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <85c0a8a2a0f1429c0b3c7acc69e659d174710347@i2pn2.org> References: <069069bf23698c157ddfd9b62b9b2f632b484c40@i2pn2.org> <2d3620a6e2a8a57d9db7a33c9d476fe03cac455b@i2pn2.org> <75921cc1f17cdb691969a99e666f237cd09c0b09@i2pn2.org> <25729298b142c60d5b245231984119d42d4ac089@i2pn2.org> <09ef32dfb3944d321e15e1383820166a2082d5cb@i2pn2.org> <6d7fb8f4346eb09ea7ccdff45e8ff3d0c4a45ab0@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Thu, 2 Jan 2025 13:26:41 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="1653393"; 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: Content-Language: en-US Bytes: 2333 Lines: 16 On 1/2/25 6:52 AM, WM wrote: > On 01.01.2025 15:47, FromTheRafters wrote: >> WM wrote : > >>> The collection of definable natural numbers (FISONs) is closed under >>> multiplication >> >> How can that be? > > Potential infinity. > > Regards, WM > Whicn means it never ends, and doesn't have a highest member. IF you limit that "potential" you are no longer closed.