Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | Next revision Both sides next revision | ||
|
partial_order [2008/04/30 10:00] vkuncak |
partial_order [2008/04/30 15:20] vkuncak |
||
|---|---|---|---|
| Line 31: | Line 31: | ||
| Given a partial order $(A,\le)$ and a set $S \subseteq A$, we call an element $a \in A$ | Given a partial order $(A,\le)$ and a set $S \subseteq A$, we call an element $a \in A$ | ||
| - | * **upper bound** of $S$ if for all $a' \in S$ we have $a \le a'$ | + | * **upper bound** of $S$ if for all $a' \in S$ we have $a' \le a$ |
| * **lower bound** of $S$ if for all $a' \in S$ we have $a \le a'$ | * **lower bound** of $S$ if for all $a' \in S$ we have $a \le a'$ | ||
| * **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 $a' < a$ | ||