The ordinal sum

The ordinal sum is a way to combine two ordered sets (like sequences or lists) into one, respecting their original order. Imagine lining up two chains of items: first, all items from the first set, ordered as before, then all items from the second set, also in their original order. Every item in the first set comes before any item in the second set, creating a new, longer sequence that maintains the individual orderings, but now arranged sequentially. This concept helps mathematicians analyze complex ordered structures by building them from simpler components.