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1 definition found
 for partial ordering
From The Free On-line Dictionary of Computing (30 December 2018) :

  partial ordering
  
     A relation R is a partial ordering if it is a pre-order
     (i.e. it is reflexive (x R x) and transitive (x R y R z =>
     x R z)) and it is also antisymmetric (x R y R x => x = y).
     The ordering is partial, rather than total, because there may
     exist elements x and y for which neither x R y nor y R x.
  
     In domain theory, if D is a set of values including the
     undefined value ({bottom) then we can define a partial
     ordering relation <= on D by
  
     	x <= y  if  x = bottom or x = y.
  
     The constructed set D x D contains the very undefined element,
     (bottom, bottom) and the not so undefined elements, (x,
     bottom) and (bottom, x).  The partial ordering on D x D is
     then
  
     	(x1,y1) <= (x2,y2)  if  x1 <= x2 and y1 <= y2.
  
     The partial ordering on D -> D is defined by
  
     	f <= g  if  f(x) <= g(x)  for all x in D.
  
     (No f x is more defined than g x.)
  
     A lattice is a partial ordering where all finite subsets
     have a least upper bound and a greatest lower bound.
  
     ("<=" is written in LaTeX as \sqsubseteq).
  
     (1995-02-03)
  

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