Re: final clubs

[Invent Yourself <xod@sixgirls.org>]

On Fri, 3 Mar 2000, Jorge Llambias wrote:

> From: "Jorge Llambias" <jjllambias@hotmail.com>
> 
> 
> > >        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.





-----
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When they took the sixth amendment, I was quiet because I was innocent.
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