maximal

Plural: maximals

Adjective

• the greatest or most complete or best possible
  • "maximal expansion"

Adj

• 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).

Noun

• 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.

Examples

• "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."
• "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;"

Synonyms

maximum

Antonyms

minimal, minimum

Related Words

maximative