From: DRAGONFLY           
To: THE SPECIALIST      
Subject: Relationships  
Date & Time: 05/06/91 18:40:11
Message Number 16590

Let me take these out of order:
   
TS> What's a poset?
   
   A poset is a "partially ordered set," and it's a part of lattice
theory.  Basically, if you take a set (say, the set of all living 
people), and you take an "ordering relation" on the set (say, X is
a parent or an ancestor of B) that does NOT need to operate on all
possible pairs (that is, we don't need to assume that Jimmy Smith,
in Sarasota is either an ancestor or descendent of Hoo Wang Chao,
in Beijing.)  Does that make sense?
    
   You might consider all the words or phrases in English for the 
best one to call your father at a certain time, as an "ordering
relation."  You'd probably rather call him "elderly gentleman" than
"old man" when he's around.  (Take the nnext sentence seriously.)
But would you rather call him "blue suede shoes" or "Altoids 
peppermints"?  Neither, of course. 
    
   Going on to your second example of numbers, sure: you can impose
an ordering relation that makes it into a "completely ordered set."
But there are other relations that don't.  (For example, let a < b
if a factors into fewer primes than b does.)
      
   What does all this have to do with our topic of conversation?
Continued, next message.
                        //Dragonfly//