Zorn's theorem

Zorn's theorem is a principle in mathematics that deals with partially ordered sets, which are collections of items where some can be compared to each other. It states that if every chain (a totally ordered subset) within this set has an upper bound (a greater element in the set), then the whole set contains at least one maximal element, which cannot be exceeded by any other element in that set. In simpler terms, if you can find a way to always identify a "ceiling" for groups of items, then there’s at least one item that stands as the highest point in the entire collection.