(a) Let A1 and A2 be disjoint sets, well-ordered by <1 and <2, respectively. Define an order relation on A1 ∪ A2 by letting a<b either if a, b ∈ A1 and a <1 b, or if a, b ∈ A2 and a <2 b, or if a ∈ A1 and b ∈ A2. Show that this is a well-ordering.
(b) Generalize (a) to an arbitrary family of disjoint well-ordered sets, indexed by a well-ordered set.
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