The Collaborative International Dictionary of English v.0.48:

Order \Or"der\, v. t. [imp. & p. p. Ordered; p. pr. & vb. n.
   Ordering.] [From Order, n.]
   1. To put in order; to reduce to a methodical arrangement; to
      arrange in a series, or with reference to an end. Hence,
      to regulate; to dispose; to direct; to rule.
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            To him that ordereth his conversation aright. --Ps.
                                                  1. 23.
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            Warriors old with ordered spear and shield.
                                                  --Milton.
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   2. To give an order to; to command; as, to order troops to
      advance.
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   3. To give an order for; to secure by an order; as, to order
      a carriage; to order groceries.
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   4. (Eccl.) To admit to holy orders; to ordain; to receive
      into the ranks of the ministry.
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            These ordered folk be especially titled to God.
                                                  --Chaucer.
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            Persons presented to be ordered deacons. --Bk. of
                                                  Com. Prayer.
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   Order arms (Mil.), the command at which a rifle is brought
      to a position with its butt resting on the ground; also,
      the position taken at such a command.
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The Collaborative International Dictionary of English v.0.48:

Ordering \Or"der*ing\, n.
   Disposition; distribution; management. --South.
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WordNet (r) 3.0 (2006):

ordering
    n 1: logical or comprehensible arrangement of separate elements;
         "we shall consider these questions in the inverse order of
         their presentation" [syn: ordering, order,
         ordination]
    2: the act of putting things in a sequential arrangement; "there
       were mistakes in the ordering of items on the list" [syn:
       order, ordering]

The Free On-line Dictionary of Computing (19 January 2023):

partial order
ordering

    (Informally, "order", "ordering") A binary
   relation R that is a pre-order (i.e. it is reflexive (x R
   x) and transitive (x R y R z => x R z)) and antisymmetric
   (x R y R x => x = y).

   The order 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)