maximal
English
Pronunciation
- IPA(key): /ˈmæksɪməl/
Audio (Southern England) (file)
Adjective
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
Synonyms
- maximum (adj)
Antonyms
Related terms
Translations
Largest, greatest, highest, most
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Noun
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
French
Pronunciation
- IPA(key): /mak.si.mal/
Audio (file)
Further reading
- “maximal”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.
German
Pronunciation
Audio (file) - Rhymes: -aːl
Adjective
maximal (strong nominative masculine singular maximaler, not comparable)
Declension
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 |
Interlingua
Portuguese
Pronunciation
- (Brazil) IPA(key): /mak.siˈmaw/ [mak.siˈmaʊ̯], /ma.siˈmaw/ [ma.siˈmaʊ̯]
- (Portugal) IPA(key): /ma.ksiˈmal/ [ma.ksiˈmaɫ], /ma.siˈmal/ [ma.siˈmaɫ]
- (Southern Portugal) IPA(key): /ma.ksiˈma.li/, /ma.siˈma.li/
- Rhymes: (Portugal) -al, (Brazil) -aw
- Hyphenation: ma‧xi‧mal
Adjective
maximal m or f (plural maximais)
Derived terms
Romanian
Adjective
maximal m or n (feminine singular maximală, masculine plural maximali, feminine and neuter plural maximale)
Declension
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
Pronunciation
- IPA(key): /maɡsiˈmal/ [maɣ̞.siˈmal]
- Rhymes: -al
- Syllabification: ma‧xi‧mal
Derived terms
Swedish
Adjective
maximal (comparative maximalare, superlative maximalast)
Declension
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 |
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