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partial_order [2008/04/28 16:33] vkuncak |
partial_order [2008/04/29 22:29] vkuncak |
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| * **minimal element** of $S$ if $a \in S$ and there is no element $a' \in S$ such that $a' < a$ | * **minimal element** of $S$ if $a \in S$ and there is no element $a' \in S$ such that $a' < a$ | ||
| * **maximal element** of $S$ if $a \in S$ and there is no element $a' \in S$ such that $a < a'$ | * **maximal element** of $S$ if $a \in S$ and there is no element $a' \in S$ such that $a < a'$ | ||
| - | * **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, $\sqcup$) 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, $\sqcap$) of $S$ if $a$ is the least element in the set of all upper bounds of $S$ | ||