X-Received: by 2002:ac8:5803:0:b0:400:8f80:8dbd with SMTP id g3-20020ac85803000000b004008f808dbdmr31705qtg.3.1687702051550; Sun, 25 Jun 2023 07:07:31 -0700 (PDT) X-Received: by 2002:a25:d347:0:b0:bb3:8f5d:240b with SMTP id e68-20020a25d347000000b00bb38f5d240bmr10918491ybf.10.1687702051340; Sun, 25 Jun 2023 07:07:31 -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: Sun, 25 Jun 2023 07:07:31 -0700 (PDT) In-Reply-To: <1b79c668-4caf-5149-02f0-095368f87ba1@att.net> Injection-Info: google-groups.googlegroups.com; posting-host=2003:e4:7747:4aa7:f8d5:fdaf:1840:5b11; posting-account=jn1PxAoAAAD-XIFhTFFaTyGmTiEGt0_b NNTP-Posting-Host: 2003:e4:7747:4aa7:f8d5:fdaf:1840:5b11 References: <5ecf2c26-d125-4ba6-ac58-55acd906e111n@googlegroups.com> <7c5b1af0-08cd-4289-be3f-0bc57e199e30n@googlegroups.com> <7332a9ff-5d3f-bbe8-99f1-a7763c8a4cee@att.net> <4b598837-4840-4932-9944-0b16d264c43bn@googlegroups.com> <4ec24863-35b9-fc54-7e96-23f2677e1c2c@att.net> <4ddad321-cb5c-467f-a59e-f4d624eb4a61n@googlegroups.com> <2fb4c5a1-3d9d-9b02-f6f8-8e800f2f8ea3@att.net> <8363ca78-8496-8d6d-765e-50d4854bfd4c@att.net> <6115c3b7-20f0-49f2-a676-03adb4b8eb5cn@googlegroups.com> <456c8e66-730b-ce76-fe7a-1927dbf6fa85@att.net> <173f0674-3927-4d71-8392-db499056a751n@googlegroups.com> <935029c9-dd60-d452-e73b-c9bda9a95516@att.net> <90f5d0bc-5c3a-416a-8ca0-860a05f719e0n@googlegroups.com> <364a6a02-ecd1-5dbc-3bd3-e4564453d69d@att.net> <33b8c197-a026-4076-bb5d-d2dc3126fd0bn@googlegroups.com> <1b79c668-4caf-5149-02f0-095368f87ba1@att.net> User-Agent: G2/1.0 MIME-Version: 1.0 Message-ID: Subject: Re: Some results about unit fractions From: WM Injection-Date: Sun, 25 Jun 2023 14:07:31 +0000 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable X-Received-Bytes: 3527 Xref: csiph.com sci.logic:254962 Jim Burns schrieb am Samstag, 24. Juni 2023 um 16:22:12 UTC+2: > On 6/24/2023 8:43 AM, WM wrote:=20 > > Show one *infinite* successor that has=20 > > no element in common with some predecessor. > That is not your claim.=20 No, it would be sufficient to show one *infinite* successor that has at lea= st one element not in common with at least one predecessor. > This is your claim. > | Every infinite endsegment has=20 > | an infinite set in common with=20 > | every predecessor and=20 > | every infinite successor. Of course. > =E2=9F=A86.02214076=C3=9710=C2=B2=C2=B3=E2=80=A6=E2=9F=A9 does not have > an infinite set in common with=20 > every predecessor and=20 > every infinite successor. It is not an endsegment. =E2=9F=A86.02214076=C3=9710=C2=B2=C2=B3, 6.0221407= 6=C3=9710=C2=B2=C2=B3 + 1, =E2=80=A6=E2=9F=A9 is an endsegment and obeys my= claim. > The argument is how we know that=20 > =E2=9F=A86.02214076=C3=9710=C2=B2=C2=B3=E2=80=A6=E2=9F=A9 is a counter-ex= ample=20 > to your claim. It is not an endsegment and hence not a counter-example. > Each element is not common to=20 > all infinite end segments.=20 What is the infinite contents? No unjustified "therefore" please, but an example. That is an infinite ends= egment that has at least one element not in common with at least one predec= essor, Regards, WM