Lesson 9

A strict order \(\prec\) can be defined from a non-strict order \(\preceq\) as follows: \[x \prec y \Leftrightarrow (x \preceq y) \land (x \neq y) \ .\] Such a strict order will be transitive (if \(x \prec y\) and \(y \prec z\), then \(x \prec z\)) and antireflexive (\(x \not \prec x\)). Similarly, a non-strict order can be derived from a strict order.