ConseggioLigure/seed-instruct-lij-eng huggingface dataset:
Traduxi da-o zeneise à l’ingleise:
Coscì scriveivan i polinòmi, pe fâ un exempio, comme .
A traduçion in ingleise do testo a l’é:
Thus they would write polynomials, for example, as .
Traduxi sto testo da-o ligure à l’ingleise:
O resultato o l’é sempre un numeo poxitivo reale e e identitæ e propietæ illustræ chì de d’ato pe-i esponenti intreghi arrestan vee con ste definiçioin pe-i esponenti reali.
A traduçion in ingleise do testo a l’é:
The result is always a positive real number, and the identities and properties shown above for integer exponents remain true with these definitions for real exponents.
Traduxi da-o zeneise à l’ingleise:
Sta fonçion a l’é pægia a-a reixe de tersa pe-i radicandi reali poxitivi.
A traduçion in ingleise do testo a l’é:
This function equals the usual th root for positive real radicands.
Comm’à l’é a traduçion ingleise de sto testo?
Sto chì o l’é o gruppo de partensa da teoria matematica di semigruppi.
A traduçion in ingleise do testo a l’é:
This is the starting point of the mathematical theory of semigroups.
Quæ a l’é a traduçion ingleise de sto testo?
Poemmo sostituî torna l’insemme N con un numeo cardinale n pe ottegnî Vn; sciben che se no çerne un insemme speçifico standard da-a cardinalitæ n, questo o l’é definio solo fin à l’isomorfismo.
A traduçion in ingleise do testo a l’é:
We can again replace the set N with a cardinal number n to get Vn, although without choosing a specific standard set with cardinality n, this is defined only up to isomorphism.
Traduxi in ingleise:
Nicolas Bourbaki, Elements of Mathematics, Theory of Sets, Springer-Verlag, 2004, III.§3.5.
A traduçion in ingleise do testo a l’é:
Nicolas Bourbaki, Elements of Mathematics, Theory of Sets, Springer-Verlag, 2004, III.§3.5.
Traduxi da-o ligure à l’ingleise:
D’iterâ a tetraçion s’arriva à unn’atra operaçion e coscì avanti; sto conçetto o l’é ciammou iperoperaçion.
A traduçion in ingleise do testo a l’é:
Iterating tetration leads to another operation, and so on, a concept named hyperoperation.
Traduxi sto testo da-o ligure à l’ingleise:
Inte di ambienti applicæ, e fonçioin esponençiale modellan unna relaçion donde un cangio costante inta variabile independente o dà o mæximo cangio proporçionale (saieiva à dî l’aumento ò a diminuçion perçentuale) inta variabile independente.
A traduçion in ingleise do testo a l’é:
In applied settings, exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change (that is, percentage increase or decrease) in the dependent variable.
Ti peu tradue sto testo in ingleise?
Sta propietæ da fonçion a pòrta a-o crescio esponençiale ò a-o descrescio esponençiale.
A traduçion in ingleise do testo a l’é:
This function property leads to exponential growth or exponential decay.
Traduxi da-o zeneise à l’ingleise:
Da mæxima, a compoxiçion de fonçioin onto (surgettive) a l’é sempre onto.
A traduçion in ingleise do testo a l’é:
Similarly, the composition of onto (surjective) functions is always onto.
Traduxi in lengua ingleise:
Dapeu se peu formâ de cadeñe de trasformaçioin compòste insemme, comme .
A traduçion in ingleise do testo a l’é:
Then one can form chains of transformations composed together, such as .
Ti peu tradue sto testo in ingleise?
A categoria di insemmi con de fonçioin comme morfismi a l’é a categoria prototipica.
A traduçion in ingleise do testo a l’é:
The category of sets with functions as morphisms is the prototypical category.
Traduxi da-o zeneise à l’ingleise:
Pe fâ un exempio, o decibel (dB) a l’é unn’unitæ deuviâ pe esprimme o rappòrto pe logaritmi, mascime pe-a potensa e l’ampiessa do segnâ (do quæ a prescion do son o l’é un exempio commun).
A traduçion in ingleise do testo a l’é:
For example, the decibel (dB) is a unit used to express ratio as logarithms, mostly for signal power and amplitude (of which sound pressure is a common example).
Traduxi da-o zeneise à l’ingleise:
Aggiuttan à descrive i rappòrti de frequensa di intervalli de muxica, s’attreuvan inte fòrmole che contan i nummeri primmi ò appròsciman i fattoriali, informan çerti modelli in psicofixica e peuan ëse d’aggiutto inta contabilitæ forense.
A traduçion in ingleise do testo a l’é:
They help to describe frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, and can aid in forensic accounting.
Traduxi da-o ligure à l’ingleise:
O pròscimo integro o l’é 4, ch’o l’é o numeo de giffre de 1430.
A traduçion in ingleise do testo a l’é:
The next integer is 4, which is the number of digits of 1430.
Ti peu tradue sto testo in ingleise?
Primma de l’invençion de Napier gh’ea stæto de atre tecniche de unna portâ scimile, comme a prostaferexi ò l’utilizzaçion de töe de progrescioin, stæte sviluppæ into detaggio da Jost Bürgi verso o 1600.
A traduçion in ingleise do testo a l’é:
Prior to Napier's invention, there had been other techniques of similar scopes, such as the prosthaphaeresis or the use of tables of progressions, extensively developed by Jost Bürgi around 1600.
Comm’à l’é a traduçion ingleise de sto testo?
Parlâ de un numeo comme s’o domandasse tante giffre a l’é unn’alluxon approscimativa a-o logaritmo commun, e o l’ea indicou da Archimede comme «ordine de un numero».
A traduçion in ingleise do testo a l’é:
Speaking of a number as requiring so many figures is a rough allusion to common logarithm, and was referred to by Archimedes as the “order of a number”.
Traduxi in lengua ingleise:
Sti metodi en ciammæ prosthaphaeresis.
A traduçion in ingleise do testo a l’é:
Such methods are called prosthaphaeresis.
Traduxi sto testo in ingleise:
Pe fâ un exempio, tutte e parte da sguscia de un nautilo son unna còpia approscimativa de quella seguente, scallâ da un fattô costante.
A traduçion in ingleise do testo a l’é:
For example, each chamber of the shell of a nautilus is an approximate copy of the next one, scaled by a constant factor.
Traduxi da-o ligure à l’ingleise:
I logaritmi en ligæ ascì à l’autosimilaritæ.
A traduçion in ingleise do testo a l’é:
Logarithms are also linked to self-similarity.
Traduxi in ingleise:
Se deuvian pe quantificâ a perdia di livelli de tenscion inta trasmiscion di segnæ elettrichi, pe descrive i livelli de potensa di soin inte l’acustica e a sciorbensa da luxe inte l’ambito da spettrometria e de l’òttica.
A traduçion in ingleise do testo a l’é:
It is used to quantify the loss of voltage levels in transmitting electrical signals, to describe power levels of sounds in acoustics, and the absorbance of light in the fields of spectrometry and optics.
Traduxi sto testo in ingleise:
Sta «lezze», à tutti i mòddi, a l’é meno realistica de modelli ciù reçenti, comme a lezze da potensa de Stevens.
A traduçion in ingleise do testo a l’é:
This "law", however, is less realistic than more recent models, such as Stevens's power law.)
Comm’à l’é a traduçion ingleise de sto testo?
Quande un logaritmo con unna variabile random o l’à unna distribuçion normale, se dixe che a variabile a l’à unna distrubiçion log-normale.
A traduçion in ingleise do testo a l’é:
When the logarithm of a random variable has a normal distribution, the variable is said to have a log-normal distribution.
Comm’à l’é a traduçion ingleise de sto testo?
Pe un modello comme questo, a fonçion se someggiansa a depende a-o manco da un parametro ch’o l’à da vegnî stimmou.
A traduçion in ingleise do testo a l’é:
For such a model, the likelihood function depends on at least one parameter that must be estimated.
Traduxi sto testo da-o zeneise à l’ingleise:
Do mæximo, l’algoritmo merge sort o crea unna lista no ordenâ co-o dividde a lista à meitæ e ordinando ste chì primma d’azzonze i resultati.
A traduçion in ingleise do testo a l’é:
Similarly, the merge sort algorithm sorts an unsorted list by dividing the list into halves and sorting these first before merging the results.
Traduxi da-o ligure à l’ingleise:
I esponenti de Lyapunov deuvian i logaritmi pe mesuâ o graddo de caotiçitæ de un scistema dinamico.
A traduçion in ingleise do testo a l’é:
Lyapunov exponents use logarithms to gauge the degree of chaoticity of a dynamical system.
Traduxi in ingleise:
O triangolo de Sierpinski (inta figua) o peu vegnî coverto da træ còpie de lê mæximo, ciascheduña co-i loei longhi da meitæ da longhixe de quelli originæ.
A traduçion in ingleise do testo a l’é:
The Sierpinski triangle (pictured) can be covered by three copies of itself, each having sides half the original length.
Traduxi sto testo in ingleise:
Un atro exempio o l’é o logaritmo p-adico, a fonçion inversa de l’esponençiale p-adico.
A traduçion in ingleise do testo a l’é:
Another example is the p-adic logarithm, the inverse function of the p-adic exponential.
Traduxi in lengua ingleise:
L’execuçion de l’esponençiaçion a peu ëse fæta de unna mainea efficaçe, ma o logaritmo discreto, pe çerti gruppi, o l’é tegnuo pe assæ de grammo carcolâ.
A traduçion in ingleise do testo a l’é:
Carrying out the exponentiation can be done efficiently, but the discrete logarithm is believed to be very hard to calculate in some groups.
Traduxi in ingleise:
E reixe quaddræ di numei negativi peuan vegnî discusse inte l’ambito di numei complesci.
A traduçion in ingleise do testo a l’é:
Square roots of negative numbers can be discussed within the framework of complex numbers.
Traduxi sto testo da-o zeneise à l’ingleise:
Inte l’India antiga, a conoscensa di aspetti de teoria e applicaçion do quaddrou e da reixe quaddrâ a l’ea vegia a-o manco quante i Sulba Sutra, che remontan a-o 800-500 a.C. pöcassæ (ma fòscia ancon assæ primma).
A traduçion in ingleise do testo a l’é:
In Ancient India, the knowledge of theoretical and applied aspects of square and square root was at least as old as the Sulba Sutras, dated around 800–500 BC (possibly much earlier).
Traduxi sto testo da-o zeneise à l’ingleise:
A lettia jīm a s’assomeggia a-a forma da reixe quaddrâ che se deuvia ancheu.
A traduçion in ingleise do testo a l’é:
The letter jīm resembles the present square root shape.
Traduxi da-o zeneise à l’ingleise:
O definisce un importante conçetto de deviaçion standard deuviou inta teoria da probabilitæ e inta statistica.
A traduçion in ingleise do testo a l’é:
It defines an important concept of standard deviation used in probability theory and statistics.
Traduxi sto testo da-o ligure à l’ingleise:
A ciù parte de carcolatoe da stacca an un tasto pe-a reixe quaddrâ.
A traduçion in ingleise do testo a l’é:
Most pocket calculators have a square root key.
Traduxi in lengua ingleise:
A complescitæ de tempo pe-o carcolo de unna reixe quaddrâ con n giffre de preçixon a l’é pægia de quella da moltiplicaçion de n giffre.
A traduçion in ingleise do testo a l’é:
The time complexity for computing a square root with n digits of precision is equivalent to that of multiplying two n-digit numbers.
Traduxi sto testo in ingleise:
I problemi de Hilbert en vintitrei problemi d’aritmetica pubricæ da-o matematico todesco David Hilbert do 1900.
A traduçion in ingleise do testo a l’é:
Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.
Traduxi sto testo da-o ligure à l’ingleise:
Pe di atri problemi, comme o chinto, pe tradiçion i esperti s’en missi d’accòrdio in sce unn’interpretaçion univoca e l’é stæto dæto unna soluçion à l’interpretaçion stæta açettâ; à tutti i mòddi exite di problemi, ligæ streitamente à questi, che n’an ancon de soluçion.
A traduçion in ingleise do testo a l’é:
For other problems, such as the 5th, experts have traditionally agreed on a single interpretation, and a solution to the accepted interpretation has been given, but closely related unsolved problems exist.
Traduxi da-o ligure à l’ingleise:
Gh’é doî problemi che no solo no an ancon avuo de soluçion, ma che porrieivan fiña ëse sensa soluçion pe-i standard moderni.
A traduçion in ingleise do testo a l’é:
There are two problems that are not only unresolved but may in fact be unresolvable by modern standards.
Traduxi sto testo da-o zeneise à l’ingleise:
I atri vintun problemi an reçevuo tutti unn’attençion scignificativa, e a-a fin do secolo vintun o travaggio in sce sti problemi o l’ea ancon consciderou da mascima importansa.
A traduçion in ingleise do testo a l’é:
The other twenty-one problems have all received significant attention, and late into the twentieth century work on these problems was still considered to be of the greatest importance.
Traduxi in ingleise:
Hilbert o l’à visciuo pe dozz’anni dòppo che Kurt Gödel o l’aiva pubricou o seu teorema, ma pâ ch’o no l’agge scrito nisciuña respòsta formale a-o travaggio de Gödel.
A traduçion in ingleise do testo a l’é:
Hilbert lived for 12 years after Kurt Gödel published his theorem, but does not seem to have written any formal response to Gödel's work.
Ti peu tradue sto testo in ingleise?
Into discutte a seu opinion che tutti i problemi de matematica dovieivan avei unna soluçion, Hilbert o l’ammette a poscibilitæ che a soluçion a pòsse ëse unna preuva che o problema originâ o l’é imposcibile.
A traduçion in ingleise do testo a l’é:
In discussing his opinion that every mathematical problem should have a solution, Hilbert allows for the possibility that the solution could be a proof that the original problem is impossible.
Traduxi sto testo da-o ligure à l’ingleise:
A primma de queste a l’é stæta demostrâ da Bernard Dwork; unna preuva do tutto despægia da-e primme doe, pe mezo da coomologia l-adica, a l’é stæta fornia da Alexander Grothendieck.
A traduçion in ingleise do testo a l’é:
The first of these was proved by Bernard Dwork; a completely different proof of the first two, via l-adic cohomology, was given by Alexander Grothendieck.
Traduxi sto testo da-o ligure à l’ingleise:
À tutti i mòddi, e ipòtexi de Weil, inta seu portâ, s’assomeggiavan de ciù à un problema sencio de Hilbert, e Weil o no ê à mai inteise comme un programma ch’o l’anesse ben pe tutta a matematica.
A traduçion in ingleise do testo a l’é:
However, the Weil conjectures were, in their scope, more like a single Hilbert problem, and Weil never intended them as a programme for all mathematics.
Traduxi sto testo da-o ligure à l’ingleise:
Erdős de spesso o l’offriva de recompense monetäie; l’entitæ da recompensa a dependeiva da-a difficoltæ perçepia do problema.
A traduçion in ingleise do testo a l’é:
Erdős often offered monetary rewards; the size of the reward depended on the perceived difficulty of the problem.
Traduxi sto testo da-o ligure à l’ingleise:
A-o manco inti media mainstream, l’analogo de facto di problemi de Hilbert do secolo vintun a l’é a lista di sette problemi do Premio do Millennio stæti çernui do 2000 da-o Clay Mathematics Institute.
A traduçion in ingleise do testo a l’é:
At least in the mainstream media, the de facto 21st century analogue of Hilbert's problems is the list of seven Millennium Prize Problems chosen during 2000 by the Clay Mathematics Institute.
Traduxi sto testo da-o ligure à l’ingleise:
L’ipòtexi de Riemann a meita de vegnî nottâ pe-o fæto de figuâ inta lista di problemi de Hilbert, inta lista de Smale, inta lista di problemi do Premio do Millennio e inte ipòtexi de Weil ascì, inta seu forma geometrica.
A traduçion in ingleise do testo a l’é:
The Riemann hypothesis is noteworthy for its appearance on the list of Hilbert problems, Smale's list, the list of Millennium Prize Problems, and even the Weil conjectures, in its geometric guise.
Traduxi da-o ligure à l’ingleise:
1931, 1936 3° Dæto doî poliedri chesegesse con un mæximo volumme, l’é delongo poscibile taggiâ o primmo inte di tòcchi poliedrichi finii che peuan vegnî missi torna insemme pe ottegnî o segondo?
A traduçion in ingleise do testo a l’é:
1931, 1936 3rd Given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces that can be reassembled to yield the second?
Traduxi in ingleise:
1959 15° Fondaçion rigorosa do carcolo enumerativo de Schubert.
A traduçion in ingleise do testo a l’é:
1959 15th Rigorous foundation of Schubert's enumerative calculus.
Quæ a l’é a traduçion ingleise de sto testo?
1927 18 (a) Existe un poliedro ch’o l’ammette solo unna covertua anisoedrica à træ dimenscioin? (b) Quæ o l’é l’imballaggio à sfera ciù denso?
A traduçion in ingleise do testo a l’é:
1927 18th (a) Is there a polyhedron that admits only an anisohedral tiling in three dimensions?(b) What is the densest sphere packing?
Traduxi sto testo in ingleise:
Un numeo o l’é un oggetto matematico deuviou pe contâ, mesuâ e dâ de etichette.
A traduçion in ingleise do testo a l’é:
A number is a mathematical object used to count, measure, and label.
Traduxi sto testo da-o ligure à l’ingleise:
Ciù universalmente, i numei individuali peuan vegnî representæ da di scimboli, diti numerali: pe fâ un exempio, «5» o l’é un numerale ch’o representa o numeo çinque.
A traduçion in ingleise do testo a l’é:
More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five.
Comm’à l’é a traduçion ingleise de sto testo?
I carcoli co-i numei se fan con de operaçioin aritmetiche; e ciù commun en l’addiçion, a sottraçion, a moltiplicaçion, a divixon e l’esponençiaçion.
A traduçion in ingleise do testo a l’é:
Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation.
Comm’à l’é a traduçion ingleise de sto testo?
Gilsdorf, Thomas E. Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas, John Wiley & Sons, 24 frevâ 2012.Restivo, S. Mathematics in Society and History, Springer Science & Business Media, 30 novembre 1992.
A traduçion in ingleise do testo a l’é:
Gilsdorf, Thomas E. Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas, John Wiley & Sons, Feb 24, 2012.Restivo, S. Mathematics in Society and History, Springer Science & Business Media, Nov 30, 1992.
Quæ a l’é a traduçion ingleise de sto testo?
Durante o secolo dixineuve, i studioxi de matematica an comensou à sviluppâ ben ben d’astraçioin despæge che condividdan çerte propietæ di numei e che peua vegnî viste comme unn’estenscion do conçetto.
A traduçion in ingleise do testo a l’é:
During the 19th century, mathematicians began to develop many different abstractions which share certain properties of numbers, and may be seen as extending the concept.
Traduxi sto testo in ingleise:
Un scistema de contezzo o no l’à o conçetto de valô de leugo (comme inta nottaçion deximâ moderna), e pe questo a seu representaçion de numei grendi a l’é limitâ.
A traduçion in ingleise do testo a l’é:
A tallying system has no concept of place value (as in modern decimal notation), which limits its representation of large numbers.
Comm’à l’é a traduçion ingleise de sto testo?
O Brāhmasphuṭasiddhānta de Brahmagupta o l’é o primmo libbro ch’o mensuñe o zero in qualitæ de numeo; pe questo Brahmagupta o l’é consciderou, pe-o sòlito, comme a primma persoña ch’a l’agge formolou o conçetto do zero.
A traduçion in ingleise do testo a l’é:
Brahmagupta's Brāhmasphuṭasiddhānta is the first book that mentions zero as a number, hence Brahmagupta is usually considered the first to formulate the concept of zero.
Traduxi sto testo da-o ligure à l’ingleise:
À un mòddo pægio, Pāṇini (secolo V a.C.) o l’à deuviou l’operatô zero inte l’Ashtadhyayi, un primmo exempio de grammatica algebrica pe-a lengua sanscrita (s’ammie ascì Pingala).
A traduçion in ingleise do testo a l’é:
In a similar vein, Pāṇini (5th century BC) used the null (zero) operator in the Ashtadhyayi, an early example of an algebraic grammar for the Sanskrit language (also see Pingala).
Traduxi sto testo da-o ligure à l’ingleise:
Do 130 d.C. Tolomeo, influensou da Ipparco e da-i babiloneixi, o deuviava un scimbolo pe-o 0 (un çercio piccinetto con unna longa bara in çimma) drento de un scistema numerico sessageximale che pe-o resto o deuviava di numei greghi alfabetichi.
A traduçion in ingleise do testo a l’é:
By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for 0 (a small circle with a long overbar) within a sexagesimal numeral system otherwise using alphabetic Greek numerals.
Traduxi sto testo in ingleise:
A referensa à Diofanto stæta mensunâ a l’é stæta discussa à un mòddo ciù espliçito da-o matematico indian Brahmagupta, inte Brāhmasphuṭasiddhānta do 628, ch’o l’à deuviou i numei negativi pe produe a formola quaddratica de forma generale ch’a se deuvia ancon a-a giornâ d’ancheu.
A traduçion in ingleise do testo a l’é:
Diophantus' previous reference was discussed more explicitly by Indian mathematician Brahmagupta, in Brāhmasphuṭasiddhānta in 628, who used negative numbers to produce the general form quadratic formula that remains in use today.
Traduxi sto testo da-o ligure à l’ingleise:
A-o mæximo tempo i cineixi indicavan i numei negativi con un tratto diagonale atraverso a giffra ch’a no segge zero e ch’a s’attreuva ciù a-a drita do numeo poxitivo correspondente.
A traduçion in ingleise do testo a l’é:
At the same time, the Chinese were indicating negative numbers by drawing a diagonal stroke through the right-most non-zero digit of the corresponding positive number's numeral.
Traduxi da-o zeneise à l’ingleise:
I studioxi de matematica greghi e indien aivan fæto di studdi in sciâ teoria di numei raçionæ, comme parte do studio generale da teoria di numei.
A traduçion in ingleise do testo a l’é:
Classical Greek and Indian mathematicians made studies of the theory of rational numbers, as part of the general study of number theory.
Traduxi in ingleise:
O conçetto de fraçioin deximæ o l’é ligou streitamente a-a nottaçion deximâ do valô de pòsto; pâ che i doî se seggian sviluppæ insemme.
A traduçion in ingleise do testo a l’é:
The concept of decimal fractions is closely linked with decimal place-value notation; the two seem to have developed in tandem.
Traduxi da-o zeneise à l’ingleise:
À tutti i mòddi Pitagora o creddeiva inte l’assolutessa di numei e o no poeiva açettâ l’existensa de numei irraçionali.
A traduçion in ingleise do testo a l’é:
However, Pythagoras believed in the absoluteness of numbers, and could not accept the existence of irrational numbers.
Quæ a l’é a traduçion ingleise de sto testo?
Do secolo dïsette i studioxi de matematica deuviavan, pe commun, de fraçioin deximæ con unna nottaçion moderna.
A traduçion in ingleise do testo a l’é:
By the 17th century, mathematicians generally used decimal fractions with modern notation.
Traduxi sto testo da-o zeneise à l’ingleise:
Do 1872 gh’é stæto a pubricaçion de teorie de Karl Weierstrass (da-o seu allevo E. Kossak), Eduard Heine, Georg Cantor e Richard Dedekind.
A traduçion in ingleise do testo a l’é:
In 1872, the publication of the theories of Karl Weierstrass (by his pupil E. Kossak), Eduard Heine, Georg Cantor, and Richard Dedekind was brought about.
Quæ a l’é a traduçion ingleise de sto testo?
Weierstrass, Cantor e Heine basan e seu teorie in sce de serie infinie, tanto che Dedekind o fonda a seu in sce l’idea de un taggio (Schnitt) into scistema di numei reali, co-o spartî tutti i numei raçionali inte doî gruppi con de propietæ caratteristiche determinæ.
A traduçion in ingleise do testo a l’é:
Weierstrass, Cantor, and Heine base their theories on infinite series, while Dedekind founds his on the idea of a cut (Schnitt) in the system of real numbers, separating all rational numbers into two groups having certain characteristic properties.
Traduxi sto testo in ingleise:
Donca l’ea neçessäio consciderâ l’insemme ciù largo di numei algebrichi (tutte e soluçioin d’equaçioin polinomiali).
A traduçion in ingleise do testo a l’é:
Hence it was necessary to consider the wider set of algebraic numbers (all solutions to polynomial equations).
Ti peu tradue sto testo in ingleise?
Aristotele o l’à definio a noçion tradiçionale de infinio matematico deuviâ in Occidente.
A traduçion in ingleise do testo a l’é:
Aristotle defined the traditional Western notion of mathematical infinity.