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 .
Note about weak < and strict partial order.
totally ordered set linearly ordered set (total order, linear order), chain
Examples: , |
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