Re: [lojban] Sets etc.

[John Cowan <jcowan@reutershealth.com>]

From: John Cowan <jcowan@reutershealth.com>

Jorge Llambias wrote:

> But is there any reason why masses cannot have a most important
> member?

Sets can be sliced into members in only one way: masses, in many
different ways.

> I'll give it a shot. Let's use {girzu} for "club", and
> {mulgirzu} for "final club". This should work:
> 
>             ca'e ro da poi girzu cu mulgirzu
>             I define: Every club is a final club.
> 
> I think that is the only way that what you called a
> definition can really define final clubs.

This definition is too inclusive.  Here's an example.

Membership in Club A does not preclude membership in any club.
Membership in Club B precludes membership in every other club.
Membership in Club C precludes membership in Club D.
Membership in Club D precludes membership in Club A.
Membership in Club E precludes membership in Clubs A and C.
There are no other clubs.

Then:  Club B is trivially final.  Club A cannot be final
because it is compatible with all other clubs.  Club C is
incompatible with every other club but A, so it is final.
Club D is incompatible with A, B, and C, but not E, so it is
final if E is not final.  The same applies to Club E,
mutatis mutandis.  Therefore neither D nor E is final.

	His visits are occasional to the 'Senior Educational'
	For it is against the rules
	For any one Cat to belong to both that
	And the 'Joint Superior Schools'."
		--T. S. Eliot

-- 

Schlingt dreifach einen Kreis vom dies! || John Cowan <jcowan@reutershealth.com>
Schliesst euer Aug vor heiliger Schau,  || http://www.reutershealth.com
Denn er genoss vom Honig-Tau,           || http://www.ccil.org/~cowan
Und trank die Milch vom Paradies.            -- Coleridge (tr. Politzer)

------------------------------------------------------------------------
GET A NEXTCARD VISA, in 30 seconds!  Get rates as low as 2.9% 
Intro or 9.9% Fixed APR and no hidden fees.  Apply NOW!
http://click.egroups.com/1/915/1/_/17627/_/951944249/
------------------------------------------------------------------------

To unsubscribe, send mail to lojban-unsubscribe@onelist.com