Warning: mysqli::__construct(): (HY000/1203): User howardkn already has more than 'max_user_connections' active connections in D:\Inetpub\vhosts\howardknight.net\al.howardknight.net\includes\artfuncs.php on line 21
Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!eternal-september.org!feeder2.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: "Chris M. Thomasson" Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Date: Thu, 7 Nov 2024 13:18:56 -0800 Organization: A noiseless patient Spider Lines: 39 Message-ID: References: <30dffbdf129483f7b61e3284d1e7bf2ad2e5ea16@i2pn2.org> <9ca97f4a24ae1e3041583265125cf860d2fada11@i2pn2.org> <6ed3abd1b4d30ed6db4b9152f7a0ad5da583f147@i2pn2.org> <9a16dc217c4a1833dd297216773623a70ad06a10@i2pn2.org> <9aee86160da6eb1d047509ca9f0a82344039a4e9@i2pn2.org> <33a111f2689b5530ef63e6b112435a22054d0109@i2pn2.org> <36c22325d16774d5ccda6eaecf07b5b33409d33b@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Thu, 07 Nov 2024 22:18:56 +0100 (CET) Injection-Info: dont-email.me; posting-host="0717cb24f79abe485311c08787b6fcd4"; logging-data="2956680"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19rnQPVRCxkIgPwALaz3enV87U78mnUAk0=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:DgZEr8eEpT/GFJA4H37NiZRUH1k= Content-Language: en-US In-Reply-To: Bytes: 3180 On 11/6/2024 6:27 PM, Richard Damon wrote: > On 11/6/24 10:15 AM, WM wrote: >> On 06.11.2024 12:46, Richard Damon wrote: >>> On 11/5/24 11:45 AM, WM wrote: >>>> On 05.11.2024 04:08, Richard Damon wrote: >>>>> On 11/4/24 12:11 PM, WM wrote: >>>>>> On 04.11.2024 13:14, Richard Damon wrote: >>>>>>> On 11/4/24 6:07 AM, WM wrote: >>>>>> >>>>>>>> By induction you can prove the sum n(n+1)/2 for every initial >>>>>>>> segment 1+2+3+...+n. But not for all natural numbers. >>>>>> >>>>>>> But all Natural Numbers can be defined. >>>>>> >>>>>> All defined numbers can be summed. Not all natural numbers can be >>>>>> summed. >>>>> >>>>> Why not? >>>> >>>> because most cannot be defined. >>> >>> But they ARE defined. >> >> Then sum all of them. >> >> Regards, WM > > They will sum to Aleph_0, since there is a countable infinite number of > them. The will sum, but they will never sum to a so-called largest natural number... Right? > > Note, Addition on Natural Numbers is closed for FINITE sums (the sum of > a finite number of numbers), not necessarily for infinite series of them.