X-Received: by 2002:a05:620a:1a02:b0:757:8569:7a3c with SMTP id bk2-20020a05620a1a0200b0075785697a3cmr2881693qkb.1.1683724051049; Wed, 10 May 2023 06:07:31 -0700 (PDT) X-Received: by 2002:a25:6741:0:b0:b9d:52cf:4a6b with SMTP id b62-20020a256741000000b00b9d52cf4a6bmr7690870ybc.1.1683724050825; Wed, 10 May 2023 06:07:30 -0700 (PDT) Path: csiph.com!tncsrv06.tnetconsulting.net!usenet.blueworldhosting.com!diablo1.usenet.blueworldhosting.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail Newsgroups: sci.logic Date: Wed, 10 May 2023 06:07:30 -0700 (PDT) In-Reply-To: <1e6007a4-f550-284a-7327-9d516080277e@att.net> Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7701:33eb:18d3:a63c:516e:dbf9; posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b NNTP-Posting-Host: 2003:e4:7701:33eb:18d3:a63c:516e:dbf9 References: <5ecf2c26-d125-4ba6-ac58-55acd906e111n@googlegroups.com> <4a001624-8eb3-414a-8499-edc6f9ca1b3an@googlegroups.com> <9e201575-3f2e-4392-a7fb-8076d48c932en@googlegroups.com> <9e18c025-fa83-39b4-60ca-7e31862de5df@att.net> <7f09fd94-ca64-412c-b340-d4dcb4d0b02an@googlegroups.com> <5cd36fbd-d283-8ac3-cbc8-8253341f40cb@att.net> <50edea23-3037-6676-7660-81e27579c86f@att.net> <257f187d-704f-5622-cf9f-a87ac2b0d751@att.net> <94666d79-7fcd-4303-a40a-4efa0db8a258n@googlegroups.com> <7ac1db2d-7847-db0b-85b7-9e97abbb5c33@att.net> <7e44eba1-911f-423f-8c68-09d4793b1843n@googlegroups.com> <022caa28-9bac-573b-3ca3-5123b8db042f@att.net> <63329f5f-724b-4d9b-bccd-5805141befa4n@googlegroups.com> <1e6007a4-f550-284a-7327-9d516080277e@att.net> User-Agent: G2/1.0 MIME-Version: 1.0 Message-ID: <168681c7-3ea4-4843-a2cc-e4e2d4efe445n@googlegroups.com> Subject: Re: Some results about unit fractions From: WM Injection-Date: Wed, 10 May 2023 13:07:31 +0000 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable X-Received-Bytes: 2853 Xref: csiph.com sci.logic:252955 Jim Burns schrieb am Mittwoch, 10. Mai 2023 um 14:47:53 UTC+2: > On 5/9/2023 4:53 PM, WM wrote:=20 > > Jim Burns schrieb am Dienstag,=20 > > 9. Mai 2023 um 17:48:22 UTC+2:=20 >=20 > >> A 1=C3=971 1-ended set of swaps=20 > >> is not defined to be=20 > >> a 1=C3=971 2-ended set of swaps.=20 > >=20 > > Lossless exchanges are lossless exchanges=20 > > in every environment. > > > Every swap takes place in a finite set,=20 > > namely between sender and receiver.=20 > > This does not change when=20 > > repeated without end. > =20 >=20 > No.=20 Your world is strange and without interest to me. In my world lossless exchanges remain lossless in every case. Regards, WM