maximal
English edit
Etymology edit
Pronunciation edit
Adjective edit
maximal
- Largest, greatest (in magnitude), highest, most.
- (mathematics, of a sequence) Larger 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.
- (mathematics, of an element of a poset) Such 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 has two maximal elements: and
Abbreviations edit
Synonyms edit
- maximum (adj)
Antonyms edit
Derived terms edit
Related terms edit
Translations edit
Largest, greatest, highest, most
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Noun edit
maximal (plural maximals)
- (mathematics) The element of a set with the greatest magnitude.
- (mathematics) 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).
- (logic) 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.
Synonyms edit
References edit
French edit
Etymology edit
Pronunciation edit
Adjective edit
maximal (feminine maximale, masculine plural maximaux, feminine plural maximales)
Related terms edit
Further reading edit
- “maximal”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.
German edit
Pronunciation edit
Adjective edit
maximal (strong nominative masculine singular maximaler, not comparable)
Declension edit
Positive forms of maximal (uncomparable)
number & gender | singular | plural | |||
---|---|---|---|---|---|
masculine | feminine | neuter | |||
predicative | er ist maximal | sie ist maximal | es ist maximal | sie sind maximal | |
strong declension (without article) |
nominative | maximaler | maximale | maximales | maximale |
genitive | maximalen | maximaler | maximalen | maximaler | |
dative | maximalem | maximaler | maximalem | maximalen | |
accusative | maximalen | maximale | maximales | maximale | |
weak declension (with definite article) |
nominative | der maximale | die maximale | das maximale | die maximalen |
genitive | des maximalen | der maximalen | des maximalen | der maximalen | |
dative | dem maximalen | der maximalen | dem maximalen | den maximalen | |
accusative | den maximalen | die maximale | das maximale | die maximalen | |
mixed declension (with indefinite article) |
nominative | ein maximaler | eine maximale | ein maximales | (keine) maximalen |
genitive | eines maximalen | einer maximalen | eines maximalen | (keiner) maximalen | |
dative | einem maximalen | einer maximalen | einem maximalen | (keinen) maximalen | |
accusative | einen maximalen | eine maximale | ein maximales | (keine) maximalen |
Further reading edit
Interlingua edit
Adjective edit
maximal (not comparable)
Portuguese edit
Pronunciation edit
Adjective edit
maximal m or f (plural maximais)
- maximal, maximum
- Synonym: máximo
- (not comparable, relational) of, or pertaining to, the maximum
Derived terms edit
Romanian edit
Etymology edit
Borrowed from French maximal. Equivalent to maxim + -al.
Adjective edit
maximal m or n (feminine singular maximală, masculine plural maximali, feminine and neuter plural maximale)
Declension edit
Declension of maximal
singular | plural | ||||||
---|---|---|---|---|---|---|---|
masculine | neuter | feminine | masculine | neuter | feminine | ||
nominative/ accusative |
indefinite | maximal | maximală | maximali | maximale | ||
definite | maximalul | maximala | maximalii | maximalele | |||
genitive/ dative |
indefinite | maximal | maximale | maximali | maximale | ||
definite | maximalului | maximalei | maximalilor | maximalelor |
Spanish edit
Pronunciation edit
Adjective edit
maximal m or f (masculine and feminine plural maximales)
Derived terms edit
Swedish edit
Adjective edit
maximal (comparative maximalare, superlative maximalast)
Declension edit
Inflection of maximal | |||
---|---|---|---|
Indefinite | Positive | Comparative | Superlative2 |
Common singular | maximal | maximalare | maximalast |
Neuter singular | maximalt | maximalare | maximalast |
Plural | maximala | maximalare | maximalast |
Masculine plural3 | maximale | maximalare | maximalast |
Definite | Positive | Comparative | Superlative |
Masculine singular1 | maximale | maximalare | maximalaste |
All | maximala | maximalare | maximalaste |
1) Only used, optionally, to refer to things whose natural gender is masculine. 2) The indefinite superlative forms are only used in the predicative. 3) Dated or archaic |