maximal
/ˈmaksɪməl/ · max·i·mal
noun
- The element of a set with the greatest magnitude. In the set {2, 5, 9}, the maximal element is 9.
- Said of an ideal of a ring or a filter of a lattice: that it is as large as it can be without being trivial (improper). The ideal (2) in ℤ is maximal because the only larger proper ideal is the whole ring.
- Said of a set of well‑formed formulas: that it is as large as it can be without being inconsistent; i.e., for any formula φ, the set contains either φ or its negation. A maximal consistent set of sentences in propositional logic contains either P or ¬P for every proposition P.
adjective
- Largest, greatest (in magnitude), highest, most. The maximal height of the mountain range is 4,500 meters.
Synonyms
Antonyms
Did you know? In mathematics, a 'maximal' object is not necessarily the absolute biggest; it is simply one that cannot be enlarged without losing a defining property, a nuance that distinguishes it from the 'maximum' which is the unique greatest element.