maximal

English

Etymology

From maximum +‎ -al.

Pronunciation

• IPA^(key): /ˈmæksɪməl/

• Audio (Southern England):

  (file)

Adjective

maximal

1. Largest, greatest (in magnitude), highest, most.
2. (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.

3. (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 $\{\{2\},\{1,2\},\{2,3\}\}$ has two maximal elements: $\{1,2\}$ and $\{2,3\}$

Abbreviations

• max.

Synonyms

• maximum (adj)

Antonyms

• minimal

Derived terms

• halfmaximal
• maximal ideal
• maximal munch
• submaximal
• supermaximal

 

Related terms

• maximative

Translations

Largest, greatest, highest, most

• Asturian: máximu
• Belarusian: максіма́льны (maksimálʹny)
• Czech: maximální (cs)
• Danish: maksimal
• Dutch: maximaal (nl)
• Finnish: maksimaalinen (fi), mahdollisimman suuri
• French: maximal (fr) m, maximum (fr)
• German: maximal (de)
• Hungarian: maximális (hu)
• Indonesian: maksimal (id)
• Italian: massimo (it)
• Kazakh: максималды (maksimaldy), ең көп (eñ köp)
• Polish: maksymalny (pl)
• Portuguese: máximo (pt), maximal
• Romanian: maximal (ro)
• Russian: максима́льный (ru) (maksimálʹnyj)
• Spanish: máximo (es)
• Swedish: maximal (sv)
• Turkish: azami (tr), en fazla
• Ukrainian: максима́льний (uk) (maksymálʹnyj)

Noun

maximal (plural maximals)

1. (mathematics) The element of a set with the greatest magnitude.
2. (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).
3. (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

• maximum

References

• maximal on Wikipedia.Wikipedia

French

Etymology

From maximum +‎ -al.

Pronunciation

• IPA^(key): /mak.si.mal/

• Audio:

  (file)

Adjective

maximal (feminine maximale, masculine plural maximaux, feminine plural maximales)

1. maximal

Related terms

• maximum
• max
• maxi

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)

1. maximal

   Antonym: minimal

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

Further reading

• “maximal” in Duden online
• “maximal” in Digitales Wörterbuch der deutschen Sprache

Interlingua

Adjective

maximal (not comparable)

1. maximal

Portuguese

Pronunciation

• (Brazil) IPA^(key): /mak.siˈmaw/ [mak.siˈmaʊ̯], /ma.siˈmaw/ [ma.siˈmaʊ̯]

 

• (Portugal) IPA^(key): /ma.ksiˈmal/ [ma.ksiˈmaɫ], /ma.siˈmal/ [ma.siˈmaɫ]

• (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)

1. maximal, maximum

   Synonym: máximo

2. (not comparable, relational) of, or pertaining to, the maximum

Derived terms

• maximalmente

Romanian

Etymology

Borrowed from French maximal. Equivalent to maxim +‎ -al.

Adjective

maximal m or n (feminine singular maximală, masculine plural maximali, feminine and neuter plural maximale)

1. maximal

Declension

		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

Adjective

maximal m or f (masculine and feminine plural maximales)

1. maximal

Derived terms

• maximalmente

 

Swedish

Adjective

maximal (comparative maximalare, superlative maximalast)

1. maximal; as large as possible

   Antonym: minimal

Declension

Inflection of maximal

Indefinite	positive	comparative	superlative1
common singular	maximal	maximalare	maximalast
neuter singular	maximalt	maximalare	maximalast
plural	maximala	maximalare	maximalast
masculine plural2	maximale	maximalare	maximalast
Definite	positive	comparative	superlative
masculine singular3	maximale	maximalare	maximalaste
all	maximala	maximalare	maximalaste

¹ The indefinite superlative forms are only used in the predicative.
² Dated or archaic.
³ Only used, optionally, to refer to things whose natural gender is masculine.

References

• maximal in Svensk ordbok (SO)
• maximal in Svenska Akademiens ordlista (SAOL)
• maximal in Svenska Akademiens ordbok (SAOB)