Exercises
[082] Prerequisites: [07C], [07D], [07N].(Solved on 2023-01-17) Let \(X\) be a well-ordered set. Show that if \(I⊆ X\) is an interval then \(I=[a,b)\) or \(I=[a,b]\) or \(I=[a,∞)\) with \(a,b∈ X\). (The reverse is obviously true).
In particular, an initial segment is \([0_ X,b)\) or \([0_ X,b]\) or all \(X\).
Solution 1