Language/Multiple-languages/Vocabulary/Number-Theory

This is a part of the Sci-Tech Index, a project for science and technology learners.

You can see the titles are a bit of weird. They are going to be read by machine and made use of by other means.

“Prerequisites” for non-English languages are to be generated through programs, so they are kept empty.

In progress.

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Hans-CN: 前提	cmn-Latn.Pinyin-CN: gàiniàn	cmn-Latn.Pinyin-CN: qiántí	deu-Latn-DE: Begriff [m]	deu-Latn-DE: Voraussetzung [f]	fra-Latn-FR: concept [m]	fra-Latn-FR: préalable [m]	jpn-Hrkt-JP: がいねん	jpn-Hrkt-JP: ぜんたい	jpn-Jpan-JP: 概念	jpn-Jpan-JP: 前提	rus-Cyrl-RU: конце́пция	rus-Cyrl-RU: предпосы́лка
number theory		数论		shù lùn		Zahlentheorie [f]		théorie [f] des nombres		すうろん		数論		тео́рия чи́сел
arithmetic		算术		suàn shù		Arithmetik [f]		arithmétique [f]		さんすう		算数		арифме́тика
algebraic number theory		代数数论		dàishù shùlùn		algebraische Zahlentheorie		théorie [f] algébrique des nombres		だいすうてきせいすうろん		代数的整数論		алгебраи́ческая тео́рия чи́сел
analytic number theory		解析数论		jiěxī shùlùn		analytische Zahlentheorie		théorie [f] analytique des nombres		かいせきてきせいすうろん, かいせきすうろん		解析的整数論, 解析数論		аналити́ческая тео́рия чи́сел

Arithmetic

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Hans-CN: 前提	cmn-Latn.Pinyin-CN: gàiniàn	cmn-Latn.Pinyin-CN: qiántí	deu-Latn-DE: Begriff [m]	deu-Latn-DE: Voraussetzung [f]	fra-Latn-FR: concept [m]	fra-Latn-FR: préalable [m]	jpn-Hrkt-JP	jpn-Hrkt-JP:	jpn-Jpan-JP:前提	jpn-Jpan-JP:	rus-Cyrl-RU:	rus-Cyrl-RU:
abacus	basic operations	算盘		suàn pan		Abakus [m]
absolute value, modulus (real number)	real number	绝对值		juéduì zhí		Absolutbetrag [m], absoluter Betrag, Absolutwert [m], absoluter Wert		valeur [f] absolue
addition	number, binary operation	加法		jiā fǎ		Addition [f]		addition [f]
additive inverse, opposite, negation	addition, number	加法逆元, 相反数		jiāfǎ nìyuán, xiāngfǎn shù		Gegenzahl [f]
addend, summand	addition, operand	加数		jiā shù		Summand [m]
analog computer	basic operations, logarithm, exponentiation	模拟计算机		mónǐ jìsuànjī		Analogrechner [m]
anticommutative property, anticommutativity	operation (mathematics)	反交换律		fǎnjiāohuàn lǜ		Antikommutativgesetz [n], Antikommutativität [f]
associative property, associativity	operation (mathematics)	结合律		jiéhé lǜ		Assoziativgesetz [n], Assoziativität [f]
augend	addition, operand	被加数		bèijiā shù		erster Summand
base (exponentiation)	exponentiation	底数（指数）, 基数（指数）		dǐ shù (zhǐ shù), jīshù (zhǐ shù)		Basis [f] (Exponentiation)
base (logarithm)	logarithm	底数（对数）, 基数（对数）		dǐ shù (duì shù), jīshù (duì shù)		Basis [f] (Logarithmus)
basic operations	addition, division, multiplication, subtraction	四则运算		sìzé yùnsuàn		Grundrechnungsarten [f pl], Grundrechenarten [f pl]
binary logarithm	logarithm	以 2 为底的对数		yǐ èr wéi dǐ de duìshù		binärer Logarithmus, dualer Logarithmus		logarithme [m] binaire
binary system	numeral system	二进制		èr jìnzhì		Dualsystem [n], Zweiersystem [n], Binärsystem [n]		système [m] binaire
binary operation, dyadic operation	operation (mathematics)	二元运算		èryuán yùnsuàn		zweistellige Verknüpfung, binäre Verknüpfung
binary relation	relation (mathematics)	二元关系		èryuán guānxi		binäre Relation		relation [f] binaire
chisanbop	addition, subtraction	指算法		zhǐ suànfǎ		Chisanbop
complex number	imaginary number, real number	复数		fù shù		komplexe Zahl		nombre [m] complexe
composite number	division, natural number	合数, 合成数		hé shù, héchéng shù		zusammengesetzte Zahl
constant (mathematics)	number	常数, 定数		cháng shù, dìng shù		Konstante [f], Festwert [m]		constante [f]
counting rods	basic operations	算筹, 算子		suàn chóu, suàn zǐ		Zählstäbe [m pl]
decimal, base-ten	integer	十进制		shíjìn zhì		Dezimalsystem [n], Zehnersystem [n], dekadisches System
decimal logarithm, common logarithm	logarithm	常用对数		chángyòng duìshù		dekadischer Logarithmus, Zehnerlogarithmus [m]
decimal representation	number	小数		xiǎo shù		Dezimaldarstellung [f]
decimal separator	decimal representation, radix character	小数点		xiǎoshù diǎn		Dezimaltrennzeichen [n]
degree (root)	nth root	次方根		cìfāng gēn		Wurzelgrad [m]		degré [m] (racine)
denominator	fraction, operand	分母		fēn mǔ		Nenner [m]		dénominateur [m]
dependent variable	fraction, operand	因变量		yīn biànliàng		abhängige Variable
difference	subtraction	差		chā		Differenz [f]		différence [f]
digit		数字		shù zì		Ziffer [f]		chiffre [m]
distributive property, distributivity	operation (mathematics)	分配律		fēnpèi lǜ		Distributivgesetz [n], Distributivität [f]
dividend	fraction, operand	被除数		bèichú shù		Dividend [m]		dividende [m]
division	number, binary operation	除法		chú fǎ		Division [f]		division [f]
division by zero	division, zero	除以零		chú yǐ líng		Division [f] durch Null		division [f] par zéro
division with remainder, Euclidean division	division	带余除法, 欧几里德除法		dàiyú chúfǎ, Ōujīlǐdé chúfǎ		Division [f] mit Rest
divisor	division, operand	除数		chú shù		Divisor [m]		diviseur [m]
commutative property, commutativity	operation (mathematics)	交换律		jiāohuàn lǜ		Kommutativgesetz [n], Vertauschungsgesetz [n], Kommutativität [f]
Egyptian fraction	unit fraction	埃及分数		Āijí fēnshù		Stammbruchzerlegung [f]
equal sign	equation	等号		děng hào		Gleichheitszeichen [n], Ist-gleich-Zeichen [n]		signe [m] égal
equality		相等		xiāng děng		Gleichheit [f] (Mathematik)		égalité [f]
equation	equality, expression (mathematics)	方程, 等式		fāngchéng, děng shì		Gleichung [f]		équation [f]
Euclid's lemma	prime number	欧几里得引理		Ōujīlǐdé yǐnlǐ		Lemma [n] von Euklid
e (constant), Euler's number	constant (mathematics)	自然常数, 自然底数, 欧拉数		zìrán chángshù, zìrán dǐshù, Ōulā shù		Eulersche Zahl
even number	natural number, division	偶数		ǒu shù		gerade Zahl
exponent	exponentiation	幂, 指数		mì, zhǐ shù		Hochzahl [f], Exponent [m]		exposant [m]
exponentiation	number, binary operation	幂运算, 指数运算		mì yùnsuàn, zhǐshù yùnsuàn		Potenz [f] (Mathematik)
expression (mathematics)	digit, symbol (mathematics)	表达式, 表示式, 运算式		biǎodá shì, biǎoshì shì, yùnsuàn shì		Ausdruck [m] (Mathematik)		expression [f] (mathématique)
finger binary	addition, subtraction, binary system	二进制指算法		èrjìnzhì zhǐsuànfǎ		binär zählen mit Fingern [m pl]
fraction	division, integer	分数		fēn shù		Bruch [m]		fraction [f]
factorization, factoring	object (mathematics)	因式分解		yīnshì fēnjiě		Faktorisierung [f] (Mathematik)		factorisation [f]
function (mathematics)	binary relation, set (mathematics) <set theory>	函数		hán shù		Funktion [f] (Mathematik)		fonction [f]
greater than	inequality (mathematics)	大于		dà yú		größer als		plus grand que
greater than or equal to	inequality (mathematics), equality	大于等于		dàyú děngyú		größer als oder gleich		plus grand ou égal à
hexadecimal, base 16, hex	numeral system	十六进制		shíliù jìnzhì		Hexadezimalsystem [n], Sedezimalsystem [n]
imaginary unit, unit imaginary number	imaginary number	虚数单位		xūshù dānwèi		imaginäre Einheit
imaginary number	negative number, exponentiation	虚数		xū shù		imaginäre Zahl		nombre [m] imaginaire
imaginary axis	imaginary line (mathematics)	虚轴		xū zhóu		imaginäre Achse
imaginary line (mathematics)	line (geometry) <geometry>, point (geometry) <geometry>, imaginary number	虚数线		xūshù xiàn		imaginäre Linie
improper fraction	fraction	假分数		jiǎ fēnshù		unechter Bruch, uneigentlicher Bruch
independent variable, argument of a function	function (mathematics)	自变量		zì biànliàng		unabhängige Variable
inequation	inequality (mathematics)	不等式		bùděng shì		Ungleichung [f]		inéquation [f]
inequality (mathematics)		不等		bù děng		Ungleichheit [f]		inégalité [f]
integer	natural number, negative number	整数		zhěng shù		Ganzzahl [f], ganze Zahl		entier
inverse function, anti-function	function (mathematics)	反函数		fǎn hánshù		Umkehrfunktion [f], inverse Funktion		fonction [f] inverse
irrational number	rational number, real number	无理数		wúlǐ shù		irrationale Zahl
lattice multiplication	multiplication	格子乘法, 铺地锦算法		gézi suànfǎ, pūdìjǐn suànfǎ		Gittermethode [f]
less than	inequality (mathematics)	小于		xiǎo yú		kleiner als		inférieur à
less than or equal to	inequality (mathematics), equality	小于等于		xiǎoyú děngyú		kleiner als oder gleich		inférieur ou égal à
logarithm	number, binary operation	对数		duì shù		Logarithmus [m]		logarithme [m]
long multiplication	multiplication	长乘法		cháng chéngfǎ		Standardmethode [f] der schriftlichen Multiplikation
minuend	subtraction	被减数		bèijiǎn shù		Minuend [m]
minus sign	subtraction, negative number	减号		jiǎn hào		Minuszeichen [n]
mixed number	fraction	带分数		dài fēnshù		gemischte Zahl
modular arithmetic	integer	模算术		mó suànshù		Modulararithmetik [f]
much greater than	inequality (mathematics)	远大于		yuǎn dàyú		viel größer als
much less than	inequality (mathematics)	远小于		yuǎn xiǎoyú		viel weniger als
multiplicand	multiplication, operand	被乘数		bèichéng shù		Multiplikand [m]
multiplication table	multiplication	乘法表		chéngfǎ biǎo		Einmaleins [n]
multiplier	multiplication, operand	乘数		chéng shù		Multiplikator [m]
multiplication	number, binary operation	乘法		chéng fǎ		Multiplikation [f]
multiplicative inverse, reciprocal	multiplication, reciprocation	乘法逆元, 倒数		chéngfǎ nìyuán, dào shù		Kehrwert [m]
natural logarithm	e (constant), logarithm	自然对数		zìrán duìshù		natürlicher Logarithmus
Napier's rods, Napier's bones	lattice multiplication	纳皮尔筹		Nàpí'ěr chóu		Napier'sche Rechenstäbchen, Neper'sche Rechenstäbchen
natural number, counting number	number	自然数		zìrán shù		natürliche Zahl
negative number	number	负数		fù shù		negative Zahl
nomogram, nomograph	analog computer	列线图, 诺谟图		lièxiàn tú, nuòmò tú		Nomogramm [n], Nomographie [f]
notation (mathematics)	numeral, symbol (mathematics)	符号（数学）		fúhào (shùxué)		Notation [f] (Mathematik)
non-negative number	negative number	非负数		fēifù shù		nichtnegative Zahl
non-positive number	positive number	非正数		fēizhèng shù		nichtpositive Zahl
nth root	binary operation	次方根		cìfāng gēn		Wurzel [f] (Mathematik), Radikal [n] (Mathematik)
numeral	digit, symbol (mathematics)	数字		shù zì		Zahl [f], Ziffer [f]
number	numeral, object (mathematics)	数字		shù zì		Zahl [f]
number line	line (geometry) <geometry>	数轴, 数线		shù zhóu, shù xiàn		Zahlengerade [f], Zahlenstrahl [m]
numeral system	notation (mathematics)	数制, 记数系统, 记数法		shù zhì, jìshù xìtǒng, jìshù fǎ		Zahlensystem [n]
numerator	fraction, operand	分子		fēn zǐ		Zähler [m]
object (mathematics)		物体（数学）		wù tǐ (shù xué)		Objekt [n] (Mathematik)
octal, oct	numeral system	八进制		bā jìnzhì		Oktalsystem [n]
odd number	natural number, division	奇数		jī shù		ungerade Zahl
operand	operation (mathematics)	运算数, 运算元		yùnsuàn shù, yùnsuàn yuán		Operand [m]
operation (mathematics)	number	运算		yùnsuàn		Verknüpfung (Mathematik)
operator precedence, order of operations	basic operations, exponentiation, root extraction	运算次序, 运算顺序		yùnsuàn cìxù, yùnsuàn shùnxù		Operatorpräzedenz [f], Operatorrangfolge [f]
parity	natural number	奇偶性		jī'ǒu xìng		Parität [f]
Pascal's triangle, Khayyam triangle, Yang Hui's triangle, Tartaglia's triangle	triangle <geometry>	杨辉三角形, 贾宪三角形, 帕斯卡三角形, 海亚姆三角形		Yáng Huī sānjiǎoxíng, Jiǎ Xiàn sānjiǎoxíng, Pàsīkǎ sānjiǎoxíng, Hǎiyàmǔ sānjiǎoxíng		Pascal'sches Dreieck, Chayyām-Dreieck, Yang-Hui-Dreieck, Tartaglia-Dreieck
peasant multiplication, Egyptian multiplication, Ethiopian multiplication, Russian multiplication	multiplication	农夫算法		nóngfū suànfǎ		russische Bauernmultiplikation
percentage	fraction	百分数		bǎifēn shù		Prozentsatz [m]
percent sign	percentage	百分号		bǎifēn hào		Prozentzeichen [n]
pi, Archimedes' constant	constant (mathematics), ratio, circumstance <geometry>, diameter <geometry>	圆周率		yuánzhōu lǜ		Pi [n], Kreiszahl [f]
plus sign	addition, positive number	加号		jiā hào		Pluszeichen [n]
positional notation, place-value notation, positional numeral system	numeral system	进位制, 进位计数法, 位值计数法		jìnwèi zhì, jìnwèi jìshù fǎ, wèizhí jìshù fǎ		Stellenschreibweise [f]
positive number	number	正数		zhèng shù		positive Zahl
prime number, prime	product (mathematics), natural number	质数, 素数		zhì shù, sù shù		Primzahl [f]
product (mathematics)	multiplication	积		jī		Produkt [n] (Mathematik)
proper fraction	fraction	真分数		zhēn fēnshù		echter Bruch, eigentlicher Bruch
quotient	division	商		shāng		Quotient [f]
radix, base	positional notation	底数（进制）		dǐ shù (jìn zhì)		Basis [f] (Zahlensystem)
radix character	radix	小数点		xiǎoshù diǎn		Radixpunkt [m]
ratio	number	比率, 比值		bǐ lǜ, bǐ zhí		Verhältnis [n]
rational number	fraction, integer	有理数		yǒulǐ shù		rationale Zahl
real axis	real line	实轴		shí zhóu		reelle Achse
real line	line (geometry) <geometry>, point (geometry) <geometry>, real number	实数线		shíshù xiàn		reelle Linie
real number	rational number	实数		shí shù		reelle Zahl
reciprocal function	function, multiplicative inverse	互反函数		hùfǎn hánshù		Reziprokfunktion [f], reziproke Funktion
relation (mathematics)	set (mathematics) <set theory>	关系（数学）		guānxi (shù xué)		Relation [f] (Mathematik)
remainder	division with remainder	余数		yú shù		Rest [m], Teilungsrest [m]
root (mathematics)	nth root	根		gēn		Wurzel [f]
root extraction	nth root	开方		kāi fāng		Radizieren [n]
parentheses	operator precedence	圆括号, 括弧号		yuán kuòhào, kuòhú hào		runde Klammern [f,pl]
simple fraction, common fraction, vulgar fraction	fraction	简分数		jiǎn fēnshù		gemeiner Bruch, gewöhnlicher Bruch
slide rule	analog computer	计算尺		jìsuàn chǐ		Rechenschieber [m], Rechenstab [m]
subtraction	number, binary operation	减法		jiǎn fǎ		Subtraktion [f], Abziehen [n], Abzug [m]
subtrahend	subtraction	被减数		bèijiǎn shù		Subtrahend [m]
sum	addition	和		hé		Summe [f]
symbol (mathematics)		符号（数学）		fúhào (shù xué)		Symbol [n] (Mathematik)
tally marks, hash marks	unary system, addition	计数符号		jìshù fúhào		Strichliste [f]
Trachtenberg system	multiplication	特拉亨伯格速算系統		Tèlāhēngbégé sùsuàn xìtǒng		Trachtenberg-System [n], Trachtenberg-Schnellrechenmethode [f]
unary system	numeral system	一进制		yī jìnzhì		Unärsystem [n]
unit fraction	fraction	单位分数		dānwèi fēnshù		Stammbruch [m]
unique prime factorization theorem, unique factorization theorem, fundamental theorem of arithmetic	prime number	正整数的唯一分解定理, 算术基本定理		zhèng zhěngshù de wéiyī fēnjiě dìnglǐ, suànshù jīběn dìnglǐ		Fundamentalsatz [m] der Arithmetik
zero	number	零		líng		Null [f]

Algebraic Number Theory

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Hans-CN: 前提	cmn-Latn.Pinyin-CN: gàiniàn	cmn-Latn.Pinyin-CN: qiántí	deu-Latn-DE: Begriff [m]	deu-Latn-DE: Voraussetzung [f]	fra-Latn-FR: concept [m]	fra-Latn-FR: préalable [m]	jpn-Hrkt-JP	jpn-Hrkt-JP:	jpn-Jpan-JP:前提	jpn-Jpan-JP:	rus-Cyrl-RU:	rus-Cyrl-RU:

Analytic Number Theory

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Hans-CN: 前提	cmn-Latn.Pinyin-CN: gàiniàn	cmn-Latn.Pinyin-CN: qiántí	deu-Latn-DE: Begriff [m]	deu-Latn-DE: Voraussetzung [f]	fra-Latn-FR: concept [m]	fra-Latn-FR: préalable [m]	jpn-Hrkt-JP	jpn-Hrkt-JP:	jpn-Jpan-JP:前提	jpn-Jpan-JP:	rus-Cyrl-RU:	rus-Cyrl-RU:

* Related Free Educational Resources *

name	link	language	public license
Arithmetic Game	https://arithmetic.zetamac.com/	English	-
Number Empire	https://www.numberempire.com/	Chinese, Dutch, English, French, German, Italian, Japanese, Korean, Polish, Portuguese, Russian, Spanish	-
Wolfram|Alpha	https://www.wolframalpha.com/	English, Japanese	-