X-Digest-Num: 383 Message-ID: <44114.383.2178.959273826@eGroups.com> Date: Fri, 3 Mar 2000 16:52:05 -0500 (EST) From: Invent Yourself Subject: Re: final clubs X-Yahoo-Message-Num: 2178 Content-Length: 1583 Lines: 50 On Fri, 3 Mar 2000, Jorge Llambias wrote: > From: "Jorge Llambias" > > > > > Definition: Every club is a final club. > > > > > > To disprove it all you have to do is find a configuration > > > where some clubs are not final and yet final clubs are > > > well defined. I don't think there is one. > > > >Suppose we have the following situation: > >Club A imposes no conditions on its members > >Club B requires members to swear a loyalty oath, > > and to swear no other oaths > >Club C requires members to swear a loyalty oath, > > and to swear no other oaths > > > >The set of final clubs is well-defined, and is composed of > >clubs B and C (the set of clubs which require loyalty oaths); > >membership in club A neither precludes nor is precluded by > >membership in clubs B or C. This doesn't help us find a > >non-recursive definition of 'final club', but it does > >illustrate that not all clubs are necessarily final. > > > >-- > >Carl Burke > > How can you tell in that example that it is B and C that > are final, and not that A is the only final club? Because you can't be a member of B and C, unless you join them simultaneously. If A was final and {B, C} were not, you could join both B and C. ----- When they took the fourth amendment, I was quiet because I didn't deal drugs. When they took the sixth amendment, I was quiet because I was innocent. When they took the second amendment, I was quiet because I didn't own a gun. Now they've taken the first amendment, and I can say nothing about it.