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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!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: Fri, 18 Oct 2024 14:22:37 -0700 Organization: A noiseless patient Spider Lines: 51 Message-ID: References: <405557f7289631d63264c712d137244c940b9926@i2pn2.org> <13c08e96ad635f8142b38d89863a80caf17a32a8@i2pn2.org> <4faa63d0ff8c163f01a38736aeb5732184218a29@i2pn2.org> <1aabd037-86bc-47bd-b402-f6b29c5c33e4@att.net> <795ca0f4-114b-4c3a-a4de-7becfa77cd9a@att.net> <15dc80c5-e0be-4e8b-9148-c4a5e0387256@att.net> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Fri, 18 Oct 2024 23:22:38 +0200 (CEST) Injection-Info: dont-email.me; posting-host="f276c36720a0a7a49bc7397de7896a56"; logging-data="3652293"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19lQrWjAuohNnUQyON0PVrkQmNMW9GdFBE=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:oRJtFCnUnGe8CgppWFqG1w7y76I= Content-Language: en-US In-Reply-To: Bytes: 3630 On 10/18/2024 2:15 PM, FromTheRafters wrote: > Chris M. Thomasson presented the following explanation : >> On 10/18/2024 1:55 PM, FromTheRafters wrote: >>> Jim Burns brought next idea : >>>> On 10/18/2024 2:13 PM, Chris M. Thomasson wrote: >>>>> On 9/16/2024 2:38 PM, Jim Burns wrote: >>>>>> On 9/16/2024 4:15 PM, Chris M. Thomasson wrote: >>>> >>>>>>> WM is a strange one. >>>>>>> If no point is between them, >>>>>>> then they are the same. >>>>>> >>>>>> If no point is between different points, >>>>>> then the points aren't in the complete line. >>>>> >>>>> If p0 and p1 are the same point then p1 - p0 is zero. >>>>> >>>>> Say: >>>>> >>>>> p0 = (1, 2, 3) >>>>> p1 = (1, 2, 3) >>>>> >>>>> pdif = p1 - p0 >>>>> >>>>> pdif would be (0, 0, 0) >>>>> >>>>> See? >>>> >>>> I wouldn't choose to say that 0 is between 0 and 0 >>>> If necessary, >>>> I would correct what I'd said so that >>>> it could not be taken to mean that. >>> >>> Yeah, you said different as opposed to unique. I simply took it to >>> mean not the same point. >> [...] >> >> if p0 and p1 are different in my example then pdif will not be all >> components zero. > > For some value of 'different'. > > This is a dot . this is a different dot . but neither dot is unique. Two > different elements from a multiset,each might not be unique (both dots) > but may be distinct (rightmost dot, leftmost dot). Well, I was thinking of p0 and p1 being 3-ary vectors in my example. Three components, x, y and z. So, if p0 and p1 are different, then pdif will not have its x, y and z components all zero.