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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!weretis.net!feeder9.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: Richard Damon Newsgroups: sci.math Subject: Re: How many different unit fractions are lessorequal than all unit fractions? Date: Wed, 2 Oct 2024 07:17:58 -0400 Organization: i2pn2 (i2pn.org) Message-ID: <461bf21a7f094701b936484f17bd3d68211fcf81@i2pn2.org> References: <890ae313-aa9b-4f49-a53a-2374c9957f01@tha.de> <2555906859e8d5836476a38f4fc437a67872f331@i2pn2.org> <534e5cd6b7a01203c28113337f108c745e57c6ae@i2pn2.org> <380cad54-83a7-4f20-976e-01d810d66c0a@att.net> <841bf27c18dffdc4ce0ea4d6392ccdfea2cef821@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 2 Oct 2024 11:17:58 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="234866"; mail-complaints-to="usenet@i2pn2.org"; posting-account="diqKR1lalukngNWEqoq9/uFtbkm5U+w3w6FQ0yesrXg"; User-Agent: Mozilla Thunderbird In-Reply-To: X-Spam-Checker-Version: SpamAssassin 4.0.0 Content-Language: en-US Bytes: 3045 Lines: 40 On 10/1/24 1:39 PM, WM wrote: > On 01.10.2024 01:14, Richard Damon wrote: >> On 9/30/24 11:15 AM, WM wrote: >>> On 30.09.2024 00:29, FromTheRafters wrote: >>>> WM explained on 9/29/2024 : >>>>> On 28.09.2024 00:08, FromTheRafters wrote: >>>>>  > WM presented the following explanation : >>>>> >>>>>  >> Between two unit fractions there is always a finite gap. >>>>>  > >>>>>  > How big? >>>>> >>>>> In terms of set theory: uncountably many points. >>>> >>>> How wide are these points? >>> >>> More than nothing. >> >> But it must be next to nothing, > > No, between them and nothing there are infinitely many countable sets > and then finite sets of points. So your "smallest" wasn't the smallest, and your set didn't include all the points. You are just admitting you are a liar and don't know what you are talking about. > >> which becomes nothing when we get to the actual infinite set. > > Not in mathematics. Sure it does. Just not in FINTE mathematics, which can't have the full set of the Natural Numbers, which is what breaks yyour logic. > > Regards, WM >