Lesson 1

There are several natural ways to obtain new orders from existing ones. Let \((X, \preceq_{X})\) and \((Y, \preceq_{Y})\) be partially ordered sets.

One can take a subset \(X' \subseteq X\) and keep the same order on it—this results in a partially ordered set \((X', \preceq_{X})\). Such an order is called induced.