To be pedantic, the definition is wrong too. His definition is not the max but the supremum: - max: largest element that is in the set, if it exists - sup: sm

To be pedantic, the definition is wrong too. His definition is not the max but the supremum: - max: largest element that is in the set, if it exists - sup: smallest element larger than all elements in the set But he doesn't really use the definition he gives anyways, his invariant to prove correctness does not rely on it.