LARA

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partial_order [2008/04/29 22:29]
vkuncak
partial_order [2008/04/30 09:15]
vkuncak
Line 31: Line 31:
   * **greatest element** of $S$ if $a \in S$ and for all $a' \in S$ we have $a' \le a$   * **greatest element** of $S$ if $a \in S$ and for all $a' \in S$ we have $a' \le a$
   * **least element** of $S$ if $a \in S$ and for all $a' \in S$ we have $a \le a'$   * **least element** of $S$ if $a \in S$ and for all $a' \in S$ we have $a \le a'$
-  * **least upper bound** (lub, supremum, $\sqcup$) of $S$ if $a$ is the least element in the set of all upper bounds of $S$ +  * **least upper bound** (lub, supremum, meet, $\sqcup$) of $S$ if $a$ is the least element in the set of all upper bounds of $S$ 
-  * **greatest lower bound** (glb, infimum, $\sqcap$) of $S$ if $a$ is the least element in the set of all upper bounds of $S$+  * **greatest lower bound** (glb, infimum, join, $\sqcap$) of $S$ if $a$ is the least element in the set of all upper bounds of $S$
  
 Taking $S=A$ we obtain minimal, maximal, greatest, least elements for the entire partial order. Taking $S=A$ we obtain minimal, maximal, greatest, least elements for the entire partial order.