Exercise
124
[206]Prerequisites:[07C],[07D],[07F].Difficulty:*.
At the beginning of the section we assumed that the ordering \(≤\) on \(X\) be total. The definitions of interval in [07C] and [07D] however, they can also be given for an order that is not (necessarily) total. What happens in exercise [07F] when the order is not total? Which result is true, which is false, and if so what counterexample can we give?