maximal

Pronunciation: /ˈmæksɪməl/

The English word “maximal” has 6 meanings listed here.

adjective

Largest, greatest (in magnitude), highest, most.
Larger than any previous term in the sequence.
Such that no other element is greater (with respect to the given partial order).

The element of a set with the greatest magnitude.
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).
Said of a set of well-formed formulas: that it is as large as it can be without being inconsistent; i.e. that for any well-formed formula φ, the set contains either φ or ~φ.

From maximum + -al.

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Definitions are from Wiktionary, extracted by Kaikki.org, and are available under the CC BY-SA 4.0 licence.