Exercises
[080] (Solved on 2023-01-17) If \(S⊆ X\) is an initial segment and \(S≠ X\), show that \(s∈ X⧵ S\) exists and is unique (\(s\) is called the next item to \(S\)) which extends \(S\), i.e. such that \(S ∪ \{ s\} \) is an initial segment.
(Note that there are similarities with the concept of "successor" seen in [1Z0]... We could say that \(s\) is the successor of the segment \(S\)).Solution 1