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Sometimes we will write, for a relation , instead of . In this chapter we will deal with ordering -- relations with special properties and we will denote these relations usally . In fact, the definition of ordering reminds properties of the usual relation on numbers.

A relation R on set A is called

  • reflexive iff aRa for any ;
  • antisymmetric iff if aRb and bRa implies a = b for any ;
  • transitive iff aRb and bRc implies aRc for any .

partial order

Note about weak < and strict partial order.

totally ordered set linearly ordered set (total order, linear order), chain


Examples: , |

minimal element

smallest element


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