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: Sun, 5 Jan 2025 07:47:15 -0500 Organization: i2pn2 (i2pn.org) Message-ID: <09103de9915b5ab3eb2105b832504d41e6119e14@i2pn2.org> References: <98519289-0542-40ce-886e-b50b401ef8cf@att.net> <8e95dfce-05e7-4d31-b8f0-43bede36dc9b@att.net> <53d93728-3442-4198-be92-5c9abe8a0a72@att.net> <9c18a839-9ab4-4778-84f2-481c77444254@att.net> <6db7afa9-f1e1-4d2b-beba-a5fc7a8b8686@att.net> <53806d5c-f456-4c13-8506-24c0b9ab310e@att.net> <545edcf1a7ba488b6324128c9e9ec2bc8be18677@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Sun, 5 Jan 2025 12:47:16 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2128180"; 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: 2697 Lines: 24 On 1/5/25 5:37 AM, WM wrote: > On 04.01.2025 14:17, Richard Damon wrote: >> On 1/4/25 3:42 AM, WM wrote: >>> >>>> On 1/3/2025 2:48 PM, WM wrote: >>>>> On 03.01.2025 19:46, Jim Burns wrote: >>>> >>>> All finite.ordinals removed from >>>> the set of each and only finite.ordinals >>>> leaves the empty set. >>> >>> But removing every ordinal that you can define (and all its >>> predecessors) from ℕ leaves almost all ordinals in ℕ.∀n ∈ ℕ_def: |ℕ \ >>> {1, 2, 3, ..., n}| = ℵo >>> >> And what keep you from "defining" the rest of the Natural Numbers. > > Try it yourself. Then you will see it. > > Regards, WM > But I CAN define any of the Natual Numbers, the whole infinite set of them. Sorry, you are just proving your stupidity.