maximal

alternative max.

1. Largest, greatest (in magnitude), highest, most.

   In the dependency graphs above, we can see that the maximal number of incomplete dependencies in each structure is five, while processing the most embedded noun[…].

   2025, Edward A. F. Gibson, “Dependency Locality in Language Processing” (chapter 4), in Syntax: A Cognitive Approach, MIT Press, →DOI, →ISBN, page 120

   1 more example

   The organification of iodide in the thyroid gland was described using a second order rate constant (KthybindC, /nmol/L*hr/kg thyroid weight) fitted to provide thyroidal iodide stores near the maximal value, which increased with age.

   2016 March 2, “Dietary Iodine Sufficiency and Moderate Insufficiency in the Lactating Mother and Nursing Infant: A Computational Perspective”, in PLOS ONE, →DOI

   Synonyms: extreme, maximum, ultimate, extreme, ferocious, exquisite, intense, pluperfect · Antonyms: minimal

2. mathematicsLarger than any previous term in the sequence.

   In the sequence (1, 2, 10, 5, 12, 6), the fifth term, f(5) = 12, is a maximal term, as each of the first 4 terms are smaller than 12.

   Antonyms: minimal

3. mathematicsSuch that no other element is greater (with respect to the given partial order).

   With respect to the ordering induced by set-theoretic inclusion, the set #92;#123;#92;#123;2#92;#125;,#92;#123;1,2#92;#125;,#92;#123;2,3#92;#125;#92;#125; has two maximal elements: #92;#123;1,2#92;#125; and #92;#123;2,3#92;#125;

   Antonyms: minimal

plural maximals · alternative max.

1. mathematicsThe element of a set with the greatest magnitude.
2. mathematicsSaid 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).
3. human sciencesSaid 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.