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Thinking about MINUS

From: Walt <wamitty_at_verizon.net>
Date: Sat, 06 Jan 2007 20:29:07 GMT
Message-ID: <nETnh.1011$us1.760_at_trndny04> 





The discussion over in "Curious SQL question"  started me thinking (after I
got over my embarassment at posting a wrong solution).



Suppose you started with these two primitive concepts:



A universal set,  called U  (whatever that is)



and



MINUS(A,B),  a function that removes from set A any elements common to A and
B.



Can you derive the rest of it?  Here's my first attempt:



Infix notation:    A MINUS B = MINUS (A,B).  Just a notational convenience
for me.  This should be trivial. I apologize to any readers who find this
inconvenient.



Empty Set:  PHI = U MINUS U.   Note that PHI is somehow "bound" to U.
Whether the PHIs of different universes are or are not the same PHI is
something I'll let the rest of you discuss.



NOT operator.    NOT(A) = U MINUS A.



Left association.   (A MINUS B) MINUS C = (A MINUS C) MINUS B (proof
omitted)



INTERSECTION.   A INTERSECT B   =   A MINUS (A MINUS B)



    
  
  •   B MINUS

(B MINUS A)





UNION.  A UNION B =   NOT (NOT (A) INTERSECT NOT (B))


From here,  it looks like we can bootstrap our way up to the rest of set
theory and Boolean algebra.


Or am I seeing something wrong  (again)?
Received on Sat Jan 06 2007 - 21:29:07 CET












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