ConseggioLigure/seed-instruct-eng-lij huggingface dataset:
Translate to Genoese:
The continuum hypothesis, which tries to ascertain the relative cardinality of certain infinite sets, was eventually shown to be independent from the generally accepted set of Zermelo–Fraenkel axioms of set theory.
The Ligurian (Genoese) translation is:
L’ipòtexi do continuum, ch’o çerca d’açertâ a cardinalitæ relativa de çerti insemmi infinii, in sciâ fin a s’é demostrâ comme independente da l’insemme açettou pe commun da-i assiömi de Zermelo-Fraenkel da teoria di insemmi.
Translate to Ligurian:
Few number theorists doubt that the Riemann hypothesis is true.
The Ligurian (Genoese) translation is:
En pöchi i teòrichi che s’indubitan do fæto che l’ipòtexi de Riemann a segge vea.
What’s the Genoese translation of this sentence?
The logistic map is a polynomial mapping, often cited as an archetypal example of how chaotic behaviour can arise from very simple non-linear dynamical equations.
The Ligurian (Genoese) translation is:
A mappa logistica a l’é unna mappatua polinomiale, che tante vòtte a ven mensunâ comme exempio archetipico de comme o comportamento caòtico o òsse nasce da de equaçioin dinamiche no lineare assæ sence.
Translate to Ligurian (Genoese):
Kepler proved that it is the limit of the ratio of consecutive Fibonacci numbers.
The Ligurian (Genoese) translation is:
Keplero o l’à demostrou ch’o l’é o limite do rappòrto di numeri consecutivi di Fibonacci.
Translate from English to Ligurian (Genoese dialect):
For two reasons this representation may cause problems.
The Ligurian (Genoese) translation is:
Sta representaçion a peu portâ à di problemi pe doe raxoin.
Translate to Ligurian (Genoese):
For example, the two representations 0.999... and 1 are equivalent in the sense that they represent the same number.
The Ligurian (Genoese) translation is:
Pe fâ un exempio, e representaçioin 0,999... e 1 en equivalente, into senso che representan o mæximo numero.
What’s the Genoese translation of this sentence?
Using computers and supercomputers, some of the mathematical constants, including π, e, and the square root of 2, have been computed to more than one hundred billion digits.
The Ligurian (Genoese) translation is:
Pe mezo di computer e supercomputer, çerte de constante matematiche, comme π, e, e a reixe quaddrâ de 2, l’é stæto carcolou ciù de çento miliardi de giffre.
Translate from English to Ligurian:
Some constants differ so much from the usual kind that a new notation has been invented to represent them reasonably.
The Ligurian (Genoese) translation is:
Çerte constante en mai tanto despæge a-o tipo commun che l’é stæto inventou unna neuva nottaçion pe representâle de forma raxonâ.
Translate from English to Ligurian (Genoese dialect):
Sometimes, the symbol representing a constant is a whole word.
The Ligurian (Genoese) translation is:
De vòtte o scimbolo ch’o representa unna constante a l’é unna paròlla intrega.
Translate to Ligurian (Genoese):
0 (zero) is a number, and the numerical digit used to represent that number in numerals.
The Ligurian (Genoese) translation is:
0 (zero) o l’é un numero e a giffra numerica deuviâ pe representâ quello mæximo numero.
Translate from English to Genoese:
Names for the number 0 in English include zero, nought (UK), naught (US; ), nil, or—in contexts where at least one adjacent digit distinguishes it from the letter "O"—oh or o.
The Ligurian (Genoese) translation is:
Tra i nommi do 0 in ingleise se peu regordâ zero, nought (into Regno Unio), naught (inti Stati Unii), nil ò – inte quelli contesti donde a-o manco un carattere adiaçente o ô distingue da-a lettia «O» – oh ò o.
Translate this sentence to Ligurian:
For the simple notion of lacking, the words nothing and none are often used.
The Ligurian (Genoese) translation is:
Pe-a noçion de mancansa se deuvia e poule nothing e none.
Can you translate this text to Ligurian?
The symbol nfr, meaning beautiful, was also used to indicate the base level in drawings of tombs and pyramids, and distances were measured relative to the base line as being above or below this line.
The Ligurian (Genoese) translation is:
O scimbolo nfr, ch’o scignifica bello, o vegniva deuviou ascì pe indicâ o ivello de base inti disegni de tombe e piramide e e distanse vegnivan mesuæ respetto a-a linea de base, de d’ato ò de sotta à sta linea.
Translate to Ligurian (Genoese):
The Babylonian placeholder was not a true zero because it was not used alone, nor was it used at the end of a number.
The Ligurian (Genoese) translation is:
O segnapòsto babiloneise o no l’ea un zero veo e pròpio, perché o no vegniva deuviou da solo e manco a-a fin de un numero.
Translate from English to Ligurian:
By AD 150, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero in his work on mathematical astronomy called the Syntaxis Mathematica, also known as the Almagest.
The Ligurian (Genoese) translation is:
Do 150 d.C. Tolomeo, influensou da Ipparco e dai babiloneixi, o deuviava un scimbolo pe-o zero inta seu euvia in scie l’astronomia matematica ciammâ Syntaxis Mathematica, conosciua ascì co-o nomme de Almagesto.
Translate from English to Genoese:
This use was repeated in AD525 in an equivalent table, that was translated via the Latin nulla or "none" by Dionysius Exiguus, alongside Roman numerals.
The Ligurian (Genoese) translation is:
Questa costummansa a l’é stæta repetua do 525 d.C. inte unna tabella equivalente, ch’a l’é stæta traduta da-o latin nulla ‘ninte’ da Dionisio Esiguo, da arente a-i numeri romoen.
Translate this sentence to Genoese:
The Lokavibhāga, a Jain text on cosmology surviving in a medieval Sanskrit translation of the Prakrit original, which is internally dated to AD 458 (Saka era 380), uses a decimal place-value system, including a zero.
The Ligurian (Genoese) translation is:
O Lokavibhāga, un testo giainista in sciâ cosmologia ch’o n’é arrivou pe mezo de unna traduçion in sanscrito de l’etæ de mezo da-a lengua prakrit (co-a dæta interna do 458 d.C., epoca Saka 380), o deuvia un scistema deximale de valoî de pòsto, compreiso un zero.
Translate to Genoese:
In 813, al-Khwarizmi used the Hindu numerals in his astronomical tables."
The Ligurian (Genoese) translation is:
Do 813 al-Khwarizmi o l’à deuviou i numeri indù inte seu tabelle astronòmiche.
What’s the Genoese translation of this sentence?
This book was later translated into Latin in the 12th century under the title Algoritmi de numero Indorum.
The Ligurian (Genoese) translation is:
O libbro, dapeu, o l’é stæto traduto in latin do secolo XII co-o titolo Algoritmi de numero Indorum.
Translate to Ligurian (Genoese):
I pursued my study in depth and learned the give-and-take of disputation.
The Ligurian (Genoese) translation is:
Son anæto avanti in profonditæ co-o mæ studio e ò impreiso o dâ e l’avei da disputaçion.
Translate to Genoese:
I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters.
The Ligurian (Genoese) translation is:
Ò çercou de compoñe sto libbro into mòddo ciù comprenscibile ch’o posciuo, co-o dividdilo inte chinze capitoli.
Translate this sentence to Genoese:
The nine Indian figures are: 9 8 7 6 5 4 3 2 1.
The Ligurian (Genoese) translation is:
E neuve giffre arabe en: 9 8 7 6 5 4 3 2 1.
Translate from English to Genoese:
254–255 include 0 as a natural number, in which case it is the only natural number that is not positive.
The Ligurian (Genoese) translation is:
254-255 comprendan o 0 comme numero naturale; inte sto caxo o l’é l’unico numero naturale no poxitivo.
Translate from English to Ligurian (Genoese dialect):
As a value or a number, zero is not the same as the digit zero, used in numeral systems with positional notation.
The Ligurian (Genoese) translation is:
Comme valô ò numero, o zero o no l’é pægio a-a giffra zero, deuviâ inti scistemi numerichi con nottaçion poxiçionale.
Translate from English to Ligurian:
The number 0 may or may not be considered a natural number, but it is an integer, and hence a rational number and a real number (as well as an algebraic number and a complex number).
The Ligurian (Genoese) translation is:
O numero zero o peu ëse consciderou un numero naturale ò no, ma o l’é un numero intrego, e pe conseguensa un numero raçionale e reale (in azzonta à un numero algebrico e complesso).
Translate from English to Ligurian (Genoese dialect):
It cannot be prime because it has an infinite number of factors, and cannot be composite because it cannot be expressed as a product of prime numbers (as 0 must always be one of the factors).
The Ligurian (Genoese) translation is:
O no peu ëse un numero primmo perché o l’à un numero de fattoî infinio e o no peu ëse compòsto perché o no peu ëse espresso comme produto de numeri primmi (perché o 0 o dev’ëse delongo un di fattoî).
Translate from English to Ligurian:
These rules apply for any real or complex number x, unless otherwise stated.
The Ligurian (Genoese) translation is:
Ste regole peuan vegnî applicæ pe tutti i numeri reali ò complesci x, delongo che no segge indicou unna cösa despægia.
Translate from English to Ligurian:
The cardinality function, applied to the empty set, returns the empty set as a value, thereby assigning it 0 elements.
The Ligurian (Genoese) translation is:
A fonçion cardinalitæ, applicâ à l’insemme veuo, a dà l’insemme veuo comme valô, e pe questo o gh’assegna 0 elementi.
Translate from English to Ligurian:
In abstract algebra, 0 is commonly used to denote a zero element, which is a neutral element for addition (if defined on the structure under consideration) and an absorbing element for multiplication (if defined).
The Ligurian (Genoese) translation is:
Pe commun inte l’algebra astræta se treuva 0 pe indicâ un elemento zero, ch’o l’é un elemento neutro pe l’addiçion (s’o l’é definio in sciâ struttua piggiâ in examme) e un elemento sciorbente pe-a moltiplicaçion (s’o l’é definio).
Can you translate this text to Ligurian?
For some quantities, the zero level is naturally distinguished from all other levels, whereas for others it is more or less arbitrarily chosen.
The Ligurian (Genoese) translation is:
Pe çerte quantitæ, o livello zero o se distingue naturalmente da tutti i atri livelli, mentre pe atre o ven çernuo de forma pöcassæ arbiträia.
Translate this sentence to Ligurian:
It has been shown that a cluster of four neutrons may be stable enough to be considered an atom in its own right.
The Ligurian (Genoese) translation is:
L’é stæto demostrou che un gruppo de quattro neutroin o peu ëse stabile tanto ch’abbasta pe vegnî consciderou comme atomo independente.
What’s the Ligurian translation of this sentence?
For example, the elements of an array are numbered starting from 0 in C, so that for an array of n items the sequence of array indices runs from 0 to .
The Ligurian (Genoese) translation is:
Pe fâ un exempio, i elementi de unna matrixe en numeræ à partî da-o 0 inte C; de conseguensa pe unna matrixe de n elementi a sequensa di indiçi da matrixe a va da-o 0 a-o .
What’s the Genoese translation of this sentence?
In databases, it is possible for a field not to have a value.
The Ligurian (Genoese) translation is:
Inte banche de dæti l’é poscibile che i campi no gh’aggian de valô.
Translate to Genoese:
For text fields this is not blank nor the empty string.
The Ligurian (Genoese) translation is:
Pe-i campi de testo questo o no l’é ni veuo e ni a strinca veua.
Translate to Genoese:
In Formula One, if the reigning World Champion no longer competes in Formula One in the year following their victory in the title race, 0 is given to one of the drivers of the team that the reigning champion won the title with.
The Ligurian (Genoese) translation is:
Inta Formula Uno, se o campion do mondo in carrega o no compete ciù inte l’anno dòppo a seu vittöia inta corsa pe-o titolo, o 0 o ven dæto à un di pilòtti da squaddra co-o quæ o campion in carrega o l’à guägno o titolo.
Translate to Ligurian (Genoese):
Typewriters originally made no distinction in shape between O and 0; some models did not even have a separate key for the digit 0.
The Ligurian (Genoese) translation is:
A-o comenso e machine da scrive no favan de distinçioin tra O e 0; çerti modelli n’aivan manco un tasto indepenendente pe-a giffra 0.
Translate to Ligurian (Genoese):
The digit 0 with a dot in the center seems to have originated as an option on IBM 3270 displays and has continued with some modern computer typefaces such as Andalé Mono, and in some airline reservation systems.
The Ligurian (Genoese) translation is:
O numero 0 con un ponto into mezo pâ ch’o segge nasciuo comme opçion in scî schermi de l’IBM 3270, e o l’à continuou à existe in sce quarche font da computer comme Andalé Mono, coscì comme into scistema de prenottaçion de quarche compagnia area.
Translate this sentence to Genoese:
1 (one, also called unit, and unity) is a number and a numerical digit used to represent that number in numerals.
The Ligurian (Genoese) translation is:
1 (un, ciammou ascì unitæ) o l’é un numero e unna giffra numerica deuviæ pe representâ quello mæximo numero.
Translate from English to Genoese:
In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer.
The Ligurian (Genoese) translation is:
Inte convençioin de segni donde o zero o no l’é consciderou ni poxitivo e ni negativo, 1 o l’é o primmo e ciù piccin intrego poxitivo.
What’s the Genoese translation of this sentence?
Most if not all properties of 1 can be deduced from this.
The Ligurian (Genoese) translation is:
A ciù parte de propietæ do numero 1 peuan vegnî dedòtte da sto fæto.
Translate from English to Ligurian (Genoese dialect):
It is thus the integer after zero.
The Ligurian (Genoese) translation is:
Sto chì o l’é donca o numero intrego dòppo o zero.
Translate this sentence to Genoese:
Styles that do not use the long upstroke on digit 1 usually do not use the horizontal stroke through the vertical of the digit 7 either.
The Ligurian (Genoese) translation is:
I stili che no deuvian o træto longo verso l’erto in sciô numero 1 pe commun no deuvian manco o træto orizzontale atraverso quello verticale in sciô numero 7.
Translate from English to Ligurian:
By definition, 1 is the magnitude, absolute value, or norm of a unit complex number, unit vector, and a unit matrix (more usually called an identity matrix).
The Ligurian (Genoese) translation is:
Pe definiçion, 1 a l’é a grandixe, o valô assoluo ò a nòrma de un numero complesso unitäio, de un vettô unitäio ò de unna matrixe unitäia (ciammâ pe commun matrixe d’identitæ).
Translate from English to Ligurian (Genoese dialect):
In category theory, 1 is sometimes used to denote the terminal object of a category.
The Ligurian (Genoese) translation is:
Inta teoria de categorie, quarche vòtta l’1 o l’é deuviou pe denottâ l’oggetto terminale de unna categoria.
Translate this sentence to Ligurian:
Since the base 1 exponential function (1x) always equals 1, its inverse does not exist (which would be called the logarithm base 1 if it did exist).
The Ligurian (Genoese) translation is:
Da-o momento che a fonçion esponençiale de base 1 (1x) a l’é delongo pægia à l’1, o seu inverso o no l’existe (ch’o se ciammieiva logaritmo de base 1, s’o l’existesse).
What’s the Genoese translation of this sentence?
Likewise, vectors are often normalized into unit vectors (i.e., vectors of magnitude one), because these often have more desirable properties.
The Ligurian (Genoese) translation is:
Da mæxima, de spesso i vettoî vëgnan normalizzæ inte di vettoî unitäi (ò sæ vettoî de magnitudine 1), perché tante vòtte questi an de propietæ ciù boñe.
Translate from English to Ligurian (Genoese dialect):
It is also the first and second number in the Fibonacci sequence (0 being the zeroth) and is the first number in many other mathematical sequences.
The Ligurian (Genoese) translation is:
O l’é ascì o primmo e o segondo numero da sequensa de Fibonacci (o 0 o l’é o zero) e o l’é o primmo numero inte tante atre sequense matematiche.
Translate to Ligurian:
Nevertheless, abstract algebra can consider the field with one element, which is not a singleton and is not a set at all.
The Ligurian (Genoese) translation is:
À tutti i mòddi, l’algebra astræta a peu consciderâ o campo con un elemento, ch’o no l’é un scingoletto e o no l’é pe ninte un insemme.
Translate from English to Ligurian:
A binary code is a sequence of 1 and 0 that is used in computers for representing any kind of data.
The Ligurian (Genoese) translation is:
Un còdixe binäio a l’é unna sequensa de 1 e 0 che se deuvia inti computer pe representâ di dæti de unna qualitæ chesesegge.
Translate this sentence to Ligurian:
We Are Number One is a 2014 song from the children's TV show LazyTown, which gained popularity as a meme.
The Ligurian (Genoese) translation is:
We Are Number One a l’é unna canson do 2014 da-a trasmiscion pe figgeu LazyTown, ch’a l’é vegnua famosa sotta forma de meme.
What’s the Ligurian translation of this sentence?
In association football (soccer) the number 1 is often given to the goalkeeper.
The Ligurian (Genoese) translation is:
Pe-o sòlito into zeugo do ballon o numero 1 o l’é assegnou a-o portê.
Translate to Ligurian (Genoese):
1 is the lowest number permitted for use by players of the National Hockey League (NHL); the league prohibited the use of 00 and 0 in the late 1990s (the highest number permitted being 98).
The Ligurian (Genoese) translation is:
1 o l’é o numero ciù basso consentio pe-i zugoei da National Hockey League (NHL); questa a l’à proibio l’utilizzaçion do 00 e do 0 a-a fin di anni ’90 (o numero ciù erto consentio o l’é o 98).
Translate from English to Ligurian:
Any random sequence of digits contains arbitrarily long subsequences that appear non-random, by the infinite monkey theorem.
The Ligurian (Genoese) translation is:
Unna sequensa casuale chesesegge de giffre a contëgne de sottosequense arbiträiamente longhe che no pan generæ da-o caxo, segondo o teorema de scimie infinie.
Translate to Ligurian (Genoese):
Second, since no transcendental number can be constructed with compass and straightedge, it is not possible to "square the circle".
The Ligurian (Genoese) translation is:
Segondo: dæto che nisciun numero trascendentale o peu vegnî costruto co-a riga e co-o compasso, no l’é poscibile effettuâ a «quaddratua do çercio».
Translate from English to Genoese:
The Indian astronomer Aryabhata used a value of 3.1416 in his Āryabhaṭīya (499 AD).
The Ligurian (Genoese) translation is:
L’astrònomo indian Aryabhata o deuviava un valô de 3,1416 into seu Āryabhaṭīya (499 d.C.).
Translate to Ligurian (Genoese):
The Persian astronomer Jamshīd al-Kāshī produced 9 sexagesimal digits, roughly the equivalent of 16 decimal digits, in 1424 using a polygon with 3×228 sides, which stood as the world record for about 180 years.
The Ligurian (Genoese) translation is:
L’astrònomo persian Jamshīd al-Kāshī do 1424 o l’à produto 9 numeri secsageximæ, pöcassæ equivalenti à 16 numeri deçimæ, deuviando un poligono de dimescion 3x228, ch’o l’é arrestou un record mondiale pe 180 anni pöcassæ.
Translate from English to Ligurian (Genoese dialect):
These avoid reliance on infinite series.
The Ligurian (Genoese) translation is:
Questi fan de mòddo che o recorso à de serie infinie o no segge neçessäio.
Translate from English to Ligurian:
As modified by Salamin and Brent, it is also referred to as the Brent–Salamin algorithm.
The Ligurian (Genoese) translation is:
Dæto ch’o l’é stæto modificou da Salamin e Brent, o l’é conosciuo ascì comme algoritmo Salamin-Brent.
Translate this sentence to Ligurian:
This is in contrast to infinite series or iterative algorithms, which retain and use all intermediate digits until the final result is produced.
The Ligurian (Genoese) translation is:
Questo o l’é in contrasto con e serie infinie ò i algoritmi iterativi, che conservan e deuvian tutte e giffre intermedie fin a-o resultato finale.
What’s the Ligurian translation of this sentence?
Such memorization aids are called mnemonics.
The Ligurian (Genoese) translation is:
Ste mesue de memorizzaçion en dite mnemotecnica.
Translate from English to Genoese:
The digits are large wooden characters attached to the dome-like ceiling.
The Ligurian (Genoese) translation is:
E giffre en di gren caratteri de legno attaccæ a-o soffito à mòddo de copola.
Translate to Genoese:
A numerical digit is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent numbers in a positional numeral system.
The Ligurian (Genoese) translation is:
Unna giffra numerica a l’é un scibolo deuviou da sola (comme o «2») ò inte de combinaçioin (comme inte «25») pe representâ di numeri inte un scistema numerico poxiçionale.
What’s the Genoese translation of this sentence?
A positional number system has one unique digit for each integer from zero up to, but not including, the radix of the number system.
The Ligurian (Genoese) translation is:
Un scistema de numeri poxiçionale o l’à unna giffra unica pe tutti i intreghi da-o zero fin à (ma sensa comprendila) a reixe do scistema di numeri.
What’s the Ligurian translation of this sentence?
The original numerals were very similar to the modern ones, even down to the glyphs used to represent digits.
The Ligurian (Genoese) translation is:
I numeri originali s’assomeggiavan ben ben à quelli moderni, fin a-i glifi deuviæ pe representâ e giffre.
Translate to Ligurian:
The Mayas used a shell symbol to represent zero.
The Ligurian (Genoese) translation is:
I Maya deuviavan un scimbolo à mòddo de scheuggioa pe representâ o zero.
Translate from English to Genoese:
The Thai numeral system is identical to the Hindu–Arabic numeral system except for the symbols used to represent digits.
The Ligurian (Genoese) translation is:
O scistema numerico tailandeise o l’é do tutto pægio a-o scistema numerico indù-arabo, feua che pe-i scimboli deuviæ pe representâ e giffre.
What’s the Genoese translation of this sentence?
They are both base 3 systems.
The Ligurian (Genoese) translation is:
En tutto doî di scistemi à base 3.
Translate from English to Ligurian:
Several authors in the last 300 years have noted a facility of positional notation that amounts to a modified decimal representation.
The Ligurian (Genoese) translation is:
Tanti autoî inti urtimi 300 anni an nottou unna façilitæ de nottaçion poxiçionale ch’a l’à o valô de unna representaçion deximale modificâ.
Translate to Genoese:
For example, 1111 (one thousand, one hundred and eleven) is a repunit.
The Ligurian (Genoese) translation is:
Pe fâ un exempio, 1111 (mille çento unze) a l’é unn’unitæ repetua.
What’s the Genoese translation of this sentence?
Besides counting ten fingers, some cultures have counted knuckles, the space between fingers, and toes as well as fingers.
The Ligurian (Genoese) translation is:
In azzonta a-o carcolo in scê dexe die, çerte coltue contan ascì co-i noetti de die e co-i spaçi de die da man e di pê.
Translate this sentence to Genoese:
Stone age cultures, including ancient indigenous American groups, used tallies for gambling, personal services, and trade-goods.
The Ligurian (Genoese) translation is:
E coltue de l’etæ da pria, compreiso i antighi gruppi indigeni americhen, deuviavan i talli pe-o zeugo d’azzardo, i servixi personæ e o commercio de ben.
Translate this sentence to Ligurian:
Beginning about 3500 BC, clay tokens were gradually replaced by number signs impressed with a round stylus at different angles in clay tablets (originally containers for tokens) which were then baked.
The Ligurian (Genoese) translation is:
À partî da-o 3500 a.C. pöcassæ, e monæe de tæra rossa ean stæte sostituie, pöco à pöco, da di segni numerichi marcæ con un stilo riondo in sce di canti despægi de de töette de pria rossa (che a-o comenso contegnivan de monæe), che dapeu vegnivan cheutte.
Translate this sentence to Ligurian:
These cuneiform number signs resembled the round number signs they replaced and retained the additive sign-value notation of the round number signs.
The Ligurian (Genoese) translation is:
Sti segni cuneiformi deuviæ pe trascrive i numeri s’assomeggiavan a-i segni riondi deuviæ pe-a representaçion di numeri, di quæ piggiavan o pòsto, e mantegnivan a nottaçion additiva segno-valô di segni numerichi riondi.