maximal elements

A maximal element in a set is one that cannot be improved or increased in a specific comparison way within that set. Imagine a list of options where each option can be ranked based on certain criteria, like quality or size. A maximal element is one that isn't "dominated" or surpassed by any other option in the list — meaning no other option is strictly better in all relevant aspects. It's important to note: a maximal element doesn't have to be the absolute best overall, just one that isn't clearly outperformed by another within the set.