# User:Kompik/sandbox

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## Orderings[edit]

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*

*antichain*

Examples: , |

*minimal element*

*smallest element*

*well-ordering*

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## See also[edit]

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