zero
Translingual
editSignal flag for the digit 0 |
Alternative forms
editEtymology
editPronunciation
editNoun
editzero
- (international standards) NATO & ICAO radiotelephony clear code (spelling-alphabet name) for the digit 0.
- Synonym: nadazero (ITU/IMO)
code | Alfa | Bravo | Charlie | Delta | Echo | Foxtrot | Golf | Hotel | India | Juliett | Kilo | Lima | Mike |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
November | Oscar | Papa | Quebec | Romeo | Sierra | Tango | Uniform | Victor | Whiskey | Xray | Yankee | Zulu | |
zero | one | two | three (tree) | four (fower) | five (fife) | six | seven | eight | nine (niner) | hundred | thousand | decimal |
ICAO/NATO | zero | one | two | three (tree) | four (fower) | five (fife) | six | seven | eight | nine (niner) |
---|---|---|---|---|---|---|---|---|---|---|
ITU/IMO | nadazero | unaone | bissotwo | terrathree | kartefour | pantafive | soxisix | setteseven | oktoeight | novenine |
References
edit- ^ Annex 10 to the Convention on International Civil Aviation: Aeronautical Telecommunications; Volume II Communication Procedures including those with PANS status[1], 6th edition, International Civil Aviation Organization, 2001 October, archived from the original on 31 March 2019, pages §5.2.1.3, Figure 5–1
English
editEtymology
edit0 | 1 → | 10 → | ||
---|---|---|---|---|
Cardinal: zero Ordinal: zeroth Adverbial: never |
From French zéro, from Italian zero, from Medieval Latin zephirum, from Arabic صِفْر (ṣifr, “nothing, cipher”), itself calqued from Sanskrit शून्य (śūnya, “void, nothingness”). Doublet of cipher and chiffre.
Pronunciation
edit- (Received Pronunciation) IPA(key): /ˈzɪə.ɹəʊ/
- (General American) enPR: zîrʹō('), zēʹrō('), IPA(key): /ˈzɪɹ(ˌ)oʊ/, /ˈzi(ˌ)ɹoʊ/
Audio (General American): (file)
- (General Australian) IPA(key): /ˈzɪə.ɹəʉ/
Audio (General Australian): (file)
- (New Zealand) IPA(key): /ˈzɪə.ɹaʉ/
- Hyphenation: ze‧ro
- Rhymes: -ɪəɹəʊ, -iːɹəʊ
Numeral
editzero
- The cardinal number occurring before one and that denotes no quantity or amount at all, represented in Arabic numerals as 0.
- The conductor waited until the passenger count was zero.
- A cheque for zero dollars and zero cents crashed the computers on division by zero.
Usage notes
edit- In an adjectival sense, used with the plural of a countable noun or with an uncountable noun:
- I have zero dollars and zero food.
Synonyms
editDerived terms
edit- alef zero
- big fat zero
- care factor zero
- element zero
- exceptional zero
- ground-zero
- identically zero
- inbox zero
- kilometer zero
- kilometre zero
- Landau-Siegel zero
- myelin protein zero
- non-zero
- ones and zeroes
- patient zero
- semi-zero grazing
- Siegel zero
- status zero
- year zero
- zero article
- zero balancing
- zero-based
- zero blitz
- zero chill
- zero client
- zero conditional
- zero-cool
- zero copula
- zero-coupon note
- zero COVID
- zero dark thirty
- zero day
- zero-derivation
- zero derivation
- zero-derive
- zero derive
- zero divisor
- zero-dose
- zero-edge pool
- zero ending
- zero fighter
- zero fucks given
- zero G
- zero-G
- zero g
- zero-g
- zero-gee
- zero gee
- zero grade
- zero-grazed
- zero-hour contract
- zero-hours
- zero-hours contract
- zero-length
- zero-life
- zero line
- zero lower bound
- zero-marking
- zero matrix
- zero meridian
- zero mode
- zero morph
- zero morpheme
- zero morphism
- zero object
- zero-one law
- zero option
- zero-order design
- zero-order hold
- zero-order logic
- zero period
- zero-point
- zero population growth
- zero prefix
- zero-proof
- zero-rate
- zero-shot
- zero-shot learning
- zero station
- zero suffix
- zero tensor
- zeroth, zeroeth
- zero-turn
- zero-width space
- zero-zero
Descendants
edit- → Tokelauan: helo
Translations
edit
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See also
editNoun
editzero (countable and uncountable, plural zeros or zeroes)
- The numeric symbol that represents the cardinal number zero.
- In unary and k-adic notation in general, zero is the empty string.
- Write 0.0 to indicate a floating point number rather than the integer zero.
- The zero sign in American Sign Language is considered rude in some cultures.
- The digit 0 in the decimal, binary, and all other base numbering systems.
- One million has six zeroes.
- 2024 January 4, Matthew Sparkes, “First working graphene semiconductor could lead to faster computers”, in New Scientist[3], retrieved 2024-01-18:
- This effectively allows switching on and off of the flow of current, so it is either conducting or not conducting, creating the binary system of zeroes and ones used in digital computers.
- (informal, uncountable) Nothing, or none.
- The shipment was lost, so they had zero in stock.
- He knows zero about humour.
- In the end, all of our hard work amounted to zero.
- The value of a magnitude corresponding to the cardinal number zero.
- The electromagnetic field does not drop all of the way to zero before a reversal.
- 2013 July 6, “The rise of smart beta”, in The Economist, volume 408, number 8843, page 68:
- Investors face a quandary. Cash offers a return of virtually zero in many developed countries; government-bond yields may have risen in recent weeks but they are still unattractive. Equities have suffered two big bear markets since 2000 and are wobbling again. It is hardly surprising that pension funds, insurers and endowments are searching for new sources of return.
- The point on a scale at which numbering or measurement originates.
- The temperature outside is ten degrees below zero.
- (mathematics) A value of the independent variables of a function, for which the function is equal to zero.
- The zeroes of a polynomial are its roots by the fundamental theorem of algebra.
- The derivative of a continuous, differentiable function that twice crosses the axis must have a zero.
- The nontrivial zeros of the Riemann zeta function may all lie on the critical line.
- 2006, Ivan Francis Wilde, Lecture Notes on Complex Analysis, Imperial College Press, page 153:
- As the next example shows, the set of zeros may well have a limit point not belonging to the domain.
- (mathematics, algebra) The additive identity element of a monoid or greater algebraic structure, particularly a group or ring.
- Since a commutative zero is the inverse of any additive identity, it must be unique when it exists.
- The zero (of a ring or field) has the property that the product of the zero with any element yields the zero.
- The quotient ring over a maximal ideal is a field with a single zero element.
- (slang) A person of little or no importance.
- They rudely treated him like a zero.
- (military, usually capitalized) A Mitsubishi A6M Zero, a long range fighter aircraft operated by the Imperial Japanese Navy Air Service from 1940 to 1945.
- 1971, Lyndon Johnson, “The New Age of Regionalism”, in The Vantage Point[4], Holt, Reinhart & Winston, →ISBN, →LCCN, →OCLC, page 361:
- The visit to Townsville was filled with nostalgia for me. I remembered very well staying there on June 8, 1942. I shared a room with a brave and friendly officer, Colonel Francis Stevens. Early the next morning we flew to Port Moresby in New Guinea, and from there we took off in separate planes. Colonel Stevens never returned from that flight; his plane was shot down by a Japanese Zero.
- A setting of calibrated instruments such as a firearm, corresponding to a zero value.
- (finance) A security which has a zero coupon (paying no periodic interest).
- The takeovers were financed by issuing zeroes.
Synonyms
edit- (numeric symbol zero): cipher
- (digit zero): slashed zero
- (point of origin on a scale): origin, zero point
- (lowest point): nadir
- (negligible or irrelevant amount): naught, nil, nothing, nought, nowt, null, (informal) bugger all, (informal) fuck all, nada, sod all, sweet FA, sweet Fanny Adams, zilch, zip
- (person of little importance): cipher, nobody, nonentity
- (value of a function’s variables at zero): root
- (identity element of a monoid): additive identity
Antonyms
edit- (antonym(s) of “value of a function's variables at zero”): pole
Hyponyms
editHolonyms
edit- (value of a function's variables at zero): kernel
Derived terms
edit- aleph-zero
- decimal without a zero
- go from zero to hero
- net-zero, net zero
- non-zero
- sub-zero
- zero air
- zero-based budget
- zero coupon bond
- zero-day
- zero deflection
- zero-dimensional
- zero-emission vehicle
- zero-grade
- zero gravity
- zero hour
- zero hundred
- zero ideal
- zeroize, zeroise
- zero-knowledge
- zero-knowledge proof
- zero-length launching
- zero locus
- zero method
- zero one infinity rule
- zero-pass
- zero-point energy
- zero-rated
- zero-sum
- zero-sum game
- zero vector
Translations
edit
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Determiner
editzero
- Synonym of no.
- She showed zero respect.
- 2018 May 4, Tom English, “Steven Gerrard: A 'seriously clever or recklessly stupid' Rangers appointment”, in BBC Sport[5]:
- You have to salute Gerrard's bravery in accepting the challenge of trying to turn Rangers around given that he has zero experience in senior management. Immortality beckons if he does it.
Adjective
editzero (not comparable)
- (meteorology) Of a cloud ceiling, limiting vision to 50 feet (15 meters) or less.
- (meteorology) Of horizontal visibility, limited to 165 feet (50.3 meters) or less.
- (linguistics) Present at an abstract level, but not realized in the surface form.
- The stem of "kobieta" with the zero ending is "kobiet".
Synonyms
edit- (informal: virtually none): no
Derived terms
editTranslations
edit
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Verb
editzero (third-person singular simple present zeroes or zeros, present participle zeroing, simple past and past participle zeroed)
- (transitive) To set some amount to be zero.
- They tried to zero the budget by the end of the quarter.
- The bill was over $400, but the server zeroed it out as a gesture of gratitude.
- Results were inconsistent because an array wasn’t zeroed during initialization.
- Zero the fluorometer with the same solvent used in extraction.
- George parked in space 34, zeroed the trip meter, closed and locked his car, then went back to the guard shack.
- To disappear or make something disappear.
- 1997, Tom Clancy, Executive Orders, page 340:
- Traffic on the encrypted channels used by senior Iraqi generals had peaked and zeroed, then peaked again, and zeroed again.
- 2001, Mark Pesce, “True Magic”, in James Frenkel, editor, True Names by Vernor Vinge and the Opening of the Cyberspace Frontier:
- They discovered the object code for the simulator that was DON, and zeroed it. DON — or his creator — was clever and had planted many copies,
- 2004, Anna Maxted, Being Committed, page 358:
- If I zeroed Jack, I'd get by So I'd erased him, pretended the last few months had never happened.
- To adjust until the variance is reduced to an acceptably low amount.
- The soldier took his gun to the shooting range to zero its aim.
Synonyms
editDerived terms
editTranslations
edit
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Basque
edit0 | 1 → | 10 → | ||
---|---|---|---|---|
Cardinal: zero, huts Ordinal: zerogarren |
Etymology
editFrom Spanish cero, from Medieval Latin zephirum, ultimately from Arabic صِفْر (ṣifr, “zero, nothing, empty, void”).
Pronunciation
edit
Numeral
editzero
Declension
editindefinite | singular | plural | ||
---|---|---|---|---|
absolutive | zero | zeroa | zeroak | |
ergative | zerok | zeroak | zeroek | |
dative | zerori | zeroari | zeroei | |
genitive | zeroren | zeroaren | zeroen | |
comitative | zerorekin | zeroarekin | zeroekin | |
causative | zerorengatik | zeroarengatik | zeroengatik | |
benefactive | zerorentzat | zeroarentzat | zeroentzat | |
instrumental | zeroz | zeroaz | zeroez | |
inessive | anim. | zerorengan | zeroarengan | zeroengan |
inanim. | zerotan | zeroan | zeroetan | |
locative | anim. | — | — | — |
inanim. | zerotako | zeroko | zeroetako | |
allative | anim. | zerorengana | zeroarengana | zeroengana |
inanim. | zerotara | zerora | zeroetara | |
terminative | anim. | zerorenganaino | zeroarenganaino | zeroenganaino |
inanim. | zerotaraino | zeroraino | zeroetaraino | |
directive | anim. | zerorenganantz | zeroarenganantz | zeroenganantz |
inanim. | zerotarantz | zerorantz | zeroetarantz | |
destinative | anim. | zerorenganako | zeroarenganako | zeroenganako |
inanim. | zerotarako | zerorako | zeroetarako | |
ablative | anim. | zerorengandik | zeroarengandik | zeroengandik |
inanim. | zerotatik | zerotik | zeroetatik | |
partitive | zerorik | — | — | |
prolative | zerotzat | — | — |
Further reading
edit- “zero”, in Euskaltzaindiaren Hiztegia [Dictionary of the Basque Academy], Euskaltzaindia
- “zero”, in Orotariko Euskal Hiztegia [General Basque Dictionary], Euskaltzaindia, 1987–2005
Catalan
edit0 | 1 → [a], [b] | 10 → | ||
---|---|---|---|---|
Cardinal: zero | ||||
Catalan Wikipedia article on 0 |
Etymology
editFrom Italian zero, from Medieval Latin zephirum, from Arabic صِفْر (ṣifr, “nothing, cipher”).
Pronunciation
editNumeral
editzero m or f
- (cardinal number) zero
- (metrology) zero; origin point of a scale
Derived terms
editNoun
editzero m (plural zeros)
Ido
edit0 | 1 → | 10 → | ||
---|---|---|---|---|
Cardinal: zero Ordinal: zeresma Adverbial: zerfoye Multiplier: zeropla Fractional: zerima |
Etymology
editBorrowed from English zero, French zéro, Italian zero, Spanish cero.
Pronunciation
editNumeral
editzero
- (temperature) zero
- (arithmetic) cipher, nought
Indonesian
editEtymology
editBorrowed from Dutch zero, from French zéro, from Italian zero, from Medieval Latin zephirum, from Arabic صِفْر (ṣifr, “nothing, cipher”), itself calqued from Sanskrit शून्य (śūnya, “void, nothingness”). Doublet of Safar, sifar, and zero.
Pronunciation
editNumeral
editzero
- zero: the cardinal number occurring before one and that denotes no quantity or amount at all, represented in Arabic numerals as 0.
Noun
editzero (plural zero-zero)
Derived terms
editFurther reading
edit- “zero” in Kamus Besar Bahasa Indonesia, Jakarta: Agency for Language Development and Cultivation – Ministry of Education, Culture, Research, and Technology of the Republic of Indonesia, 2016.
Interlingua
editNumeral
editzero
Italian
edit0 | 1 → [a], [b] | 10 → | ||
---|---|---|---|---|
Cardinal: zero Ordinal: zeresimo Ordinal abbreviation: 0º Adverbial: mai Multiplier: nullo Collective: nessuno | ||||
Italian Wikipedia article on 0 |
Etymology
editFrom New Latin zerum, from Medieval Latin zephirum, from Arabic صِفْر (ṣifr, “nothing”, “cipher”). Doublet of cifra.
Pronunciation
editNumeral
editzero (invariable)
- zero
- 1587, “Cap. IIII: Del multiplicare [Chapter 4: About Multiplication]”, in Cosimo Bartoli, transl., Opere di Orontio Fineo Divise in Cinque Parti: Aritmetica, Geometria, Cosmografia & Oriuoli[6], Venice: Francesco Franceschi Senese, page 10:
- Fatta questa prima mu[l]tiplicatione, va all’altra figura che gl’è à canto del numero Multiplicante che segue, il quale essendo zero, cioè che non significa cosa alcuna, non ti darà ancora cosa alcuna dal suo multiplicarlo
- Having done this first multiplication, go to the figure next to the following multiplying number, which, being zero – that is, it doesn't mean anything – will not give anything when multiplied
Noun
editzero m (plural zeri)
- zero
- 16th c., Vincenzo Borghini, Della moneta fiorentina[7], Florence: Pietro Gaet. Viviani, published 1755, page 175, collected in Discorsi di monsignore D. Vincenzio Borghini - parte seconda:
- aggiugnendo a’ primi numeri un zero, o due, o tre, secondo che è il bisogno nostro, facciam crescere le centinaia in migliaia
- By adding a zero to the first numbers – or two, or three, according to our need – we increase the hundreds to thousands
- nil (football)
Derived terms
editJapanese
editRomanization
editzero
Latin
editNoun
editzerō
Northern Kurdish
editEtymology
editNoun
editzero m
See also
editPolish
edit0 | 1 → | 10 → | ||
---|---|---|---|---|
Cardinal: zero Ordinal: zerowy Adverbial: zerokrotnie Multiplier: zerokrotny Numeral noun: zero Relational adjective: zerowy Related verb: zerować |
Etymology
editBorrowed from French zéro.[1][2] First attested in 1781.[3] Doublet of cyfra and szyfr.
Pronunciation
editNoun
editzero n (related adjective zerowy)
- zero (numeric symbol that represents the cardinal number zero)
- zero (point on a scale at which numbering or measurement originates)
- zero (nothing, or none; lack of something)
- (derogatory) zero (person of little or no importance)
Declension
editCoordinate terms
editDerived terms
edit- zerować impf
- wyjść na zero pf, wychodzić na zero impf
Trivia
editAccording to Słownik frekwencyjny polszczyzny współczesnej (1990), zero is one of the most used words in Polish, appearing 25 times in scientific texts, 43 times in news, 0 times in essays, 3 times in fiction, and 5 times in plays, each out of a corpus of 100,000 words, totaling 76 times, making it the 854th most common word in a corpus of 500,000 words.[4]
References
edit- ^ Mirosław Bańko, Lidia Wiśniakowska (2021) “zero”, in Wielki słownik wyrazów obcych, →ISBN
- ^ Stanisław Dubisz, editor (2003), “zero”, in Uniwersalny słownik języka polskiego [Universal dictionary of the Polish language][2] (in Polish), volumes 1-4, Warsaw: Wydawnictwo Naukowe PWN SA, →ISBN
- ^ Samuel Bogumił Linde (1807–1814) “zero”, in Słownik języka polskiego
- ^ Ida Kurcz (1990) “zero”, in Słownik frekwencyjny polszczyzny współczesnej [Frequency dictionary of the Polish language] (in Polish), volume 2, Kraków, Warszawa: Polska Akademia Nauk. Instytut Języka Polskiego, page 768
Further reading
edit- zero in Wielki słownik języka polskiego, Instytut Języka Polskiego PAN
- zero in Polish dictionaries at PWN
- Aleksander Zdanowicz (1861) “zero”, in Słownik języka polskiego, Wilno 1861
- J. Karłowicz, A. Kryński, W. Niedźwiedzki, editors (1927), “zero”, in Słownik języka polskiego (in Polish), volume 8, Warsaw, page 446
- zero in Narodowy Fotokorpus Języka Polskiego
Portuguese
edit0 | 1 → | 10 → | ||
---|---|---|---|---|
Cardinal: zero Ordinal: zerésimo Ordinal abbreviation: 0.º, 0º | ||||
Portuguese Wikipedia article on 0 |
Pronunciation
edit
- Rhymes: -ɛɾu
- Hyphenation: ze‧ro
Etymology 1
editBorrowed from French zéro, from Italian zero, from Medieval Latin zephirum, from Arabic صِفْر (ṣifr, “nothing, cipher”). Doublet of cifra.
Numeral
editzero m or f
Usage notes
editTakes the plural.
Noun
editzero m (plural zeros)
- zero (name of the digit 0)
- zero (worthless person)
- nothing
- (mathematics) zero (value of a function’s independent variables when the value of the function is zero)
- Synonym: raiz
Derived terms
editEtymology 2
editVerb
editzero
Romanian
editEtymology
editPronunciation
editNumeral
editzero
- Translingual terms borrowed from English
- Translingual terms derived from English
- Translingual terms with IPA pronunciation
- Translingual lemmas
- Translingual nouns
- ICAO spelling alphabet
- English terms borrowed from French
- English terms derived from French
- English terms derived from Italian
- English terms derived from Medieval Latin
- English terms derived from Arabic
- English terms derived from the Arabic root ص ف ر
- English terms derived from Sanskrit
- English doublets
- English 2-syllable words
- English terms with IPA pronunciation
- English terms with audio pronunciation
- English 3-syllable words
- Rhymes:English/ɪəɹəʊ
- Rhymes:English/ɪəɹəʊ/2 syllables
- Rhymes:English/iːɹəʊ
- English lemmas
- English numerals
- English cardinal numbers
- English terms with usage examples
- English nouns
- English uncountable nouns
- English countable nouns
- English nouns with irregular plurals
- English terms with quotations
- English informal terms
- en:Mathematics
- en:Algebra
- English slang
- en:Military
- en:Finance
- English determiners
- English adjectives
- English uncomparable adjectives
- en:Meteorology
- en:Linguistics
- English verbs
- English transitive verbs
- en:Zero
- Basque terms borrowed from Spanish
- Basque terms derived from Spanish
- Basque terms derived from Medieval Latin
- Basque terms derived from Arabic
- Basque terms with IPA pronunciation
- Basque terms with audio pronunciation
- Rhymes:Basque/eɾo
- Rhymes:Basque/eɾo/2 syllables
- Basque lemmas
- Basque numerals
- Basque cardinal numbers
- Catalan terms derived from Italian
- Catalan terms derived from Medieval Latin
- Catalan terms derived from Arabic
- Catalan terms with IPA pronunciation
- Catalan terms with audio pronunciation
- Catalan lemmas
- Catalan numerals
- Catalan cardinal numbers
- ca:Metrology
- Catalan nouns
- Catalan countable nouns
- Catalan masculine nouns
- Ido terms borrowed from English
- Ido terms derived from English
- Ido terms borrowed from French
- Ido terms derived from French
- Ido terms borrowed from Italian
- Ido terms derived from Italian
- Ido terms borrowed from Spanish
- Ido terms derived from Spanish
- Ido terms with IPA pronunciation
- Ido lemmas
- Ido numerals
- io:Arithmetic
- Ido cardinal numbers
- Indonesian terms borrowed from Dutch
- Indonesian terms derived from Dutch
- Indonesian terms derived from French
- Indonesian terms derived from Italian
- Indonesian terms derived from Medieval Latin
- Indonesian terms derived from Arabic
- Indonesian terms derived from the Arabic root ص ف ر
- Indonesian terms derived from Sanskrit
- Indonesian doublets
- Indonesian terms with IPA pronunciation
- Rhymes:Indonesian/ro
- Rhymes:Indonesian/ro/2 syllables
- Indonesian lemmas
- Indonesian numerals
- Indonesian nouns
- Interlingua lemmas
- Interlingua numerals
- Interlingua cardinal numbers
- Italian terms derived from New Latin
- Italian terms derived from Medieval Latin
- Italian terms derived from Arabic
- Italian doublets
- Italian 2-syllable words
- Italian terms with IPA pronunciation
- Italian terms with audio pronunciation
- Rhymes:Italian/ɛro
- Rhymes:Italian/ɛro/2 syllables
- Italian lemmas
- Italian numerals
- Italian cardinal numbers
- Italian indeclinable numerals
- Italian terms with quotations
- Italian nouns
- Italian countable nouns
- Italian masculine nouns
- Japanese non-lemma forms
- Japanese romanizations
- Latin non-lemma forms
- Latin noun forms
- Northern Kurdish terms suffixed with -o
- Northern Kurdish lemmas
- Northern Kurdish nouns
- Northern Kurdish masculine nouns
- Polish terms derived from Italian
- Polish terms derived from Medieval Latin
- Polish terms derived from Arabic
- Polish terms borrowed from French
- Polish terms derived from French
- Polish doublets
- Polish 2-syllable words
- Polish terms with IPA pronunciation
- Polish terms with audio pronunciation
- Rhymes:Polish/ɛrɔ
- Rhymes:Polish/ɛrɔ/2 syllables
- Polish lemmas
- Polish nouns
- Polish neuter nouns
- Polish derogatory terms
- Polish cardinal numbers
- pl:Zero
- Portuguese 2-syllable words
- Portuguese terms with IPA pronunciation
- Rhymes:Portuguese/ɛɾu
- Rhymes:Portuguese/ɛɾu/2 syllables
- Portuguese terms borrowed from French
- Portuguese terms derived from French
- Portuguese terms derived from Italian
- Portuguese terms derived from Medieval Latin
- Portuguese terms derived from Arabic
- Portuguese doublets
- Portuguese lemmas
- Portuguese numerals
- Portuguese cardinal numbers
- Portuguese terms with usage examples
- Portuguese nouns
- Portuguese countable nouns
- Portuguese masculine nouns
- pt:Mathematics
- Portuguese non-lemma forms
- Portuguese verb forms
- Romanian terms borrowed from French
- Romanian terms derived from French
- Romanian terms with IPA pronunciation
- Romanian terms with audio pronunciation
- Romanian lemmas
- Romanian numerals
- Romanian cardinal numbers