Path: ...!eternal-september.org!feeder3.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? Date: Mon, 21 Oct 2024 00:46:33 -0700 Organization: A noiseless patient Spider Lines: 42 Message-ID: References: <405557f7289631d63264c712d137244c940b9926@i2pn2.org> <13c08e96ad635f8142b38d89863a80caf17a32a8@i2pn2.org> <4faa63d0ff8c163f01a38736aeb5732184218a29@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Mon, 21 Oct 2024 09:46:34 +0200 (CEST) Injection-Info: dont-email.me; posting-host="c770b3133348e91147f2be2370fb578a"; logging-data="919258"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19Z0lIA+1Ora8xQitdsexibHE0xFnx7b0k=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:bep+p5hG63TlX2gC40iZUD86Z+8= In-Reply-To: Content-Language: en-US Bytes: 3286 On 9/14/2024 9:35 PM, Chris M. Thomasson wrote: > On 9/14/2024 7:23 PM, Moebius wrote: >> Am 15.09.2024 um 02:18 schrieb Chris M. Thomasson: >>> On 9/14/2024 5:07 PM, Moebius wrote: >>>> Am 15.09.2024 um 01:54 schrieb Chris M. Thomasson: >>>>> On 9/14/2024 10:30 AM, FromTheRafters wrote: >>>>>> WM presented the following explanation : >>>>>>> On 14.09.2024 01:05, FromTheRafters wrote: >>>>>>>> WM explained : >>>>>>> >>>>>>>>> No, that is your big mistake. In the interval [0, 1] there is a >>>>>>>>> point next to 0 and a point next to 1, and infinitely many are >>>>>>>>> beteen them. >>>>>>>> >>>>>>>> Define 'next [to]' in this context. >>>>>>> >>>>>>> Two points are next to each other means that no point is between >>>>>>> them. >>>>>> >>>>>> So which point is next to zero. Is it rational, or is it >>>>>> irrational? In either case it is greater than zero and there is >>>>>> again more room for an even closer number. >>>> >>>> If r e IR, r > 0, then 0 < r/2 < r. >>>> >>>> Hence there is no real number > 0 "next to 0". >>>> >>>>> WM says .00001 is next to zero... Ahhh shit, what about .000001? >>> >>> .(0)1 is close to zero? ;^D >> >> Close, but no cigar. >> >> After all, 0.(0)01 is closer. :-P > > Indeed! ;^D ..(0)1 says its the closest to zero. ..(0)01 says that little shit is all hype! ;^) Like a comic strip.