Lesson 4

Let us give an example. Let \(X=\{2, 3, 4, 5, 6\}\), and the order \(\preceq\) on \(X\) is defined as follows: \(x \preceq y\), if \(x \mid y\) (that is, \(x\) divides \(y\)). In this case \(3 \preceq 3\), \(2 \preceq 4\), \(2 \preceq 6\), and it is not difficult to list all pairs of comparable elements: \[2 \preceq 2, 2 \preceq 4, 2 \preceq 6, 3 \preceq 3, 3 \preceq 6, 4 \preceq 4, 5 \preceq 5, 6 \preceq 6.\]