Language/Multiple-languages/Vocabulary/Number-Theory

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eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Latn.Pinyin-CN: gàiniàn	deu-Latn-DE: Begriff [m]	fra-Latn-FR: concept [m]	jpn-Jpan-JP: 概念	jpn-Hrkt-JP: が↓いねん	pes-Aran-IR: مَفهوم	rus-Cyrl-RU: конце́пция
number theory		数论	shù lùn	Zahlentheorie [f]	théorie [f] des nombres	数論	す↑うろん	نظریه اعداد	тео́рия чи́сел
arithmetic		算术	suàn shù	Arithmetik [f]	arithmétique [f]	算数	さ↑んす↓う	علم حساب	арифме́тика
algebraic number theory	arithmetic; algebra	代数数论	dàishù shùlùn	algebraische Zahlentheorie	théorie [f] algébrique des nombres	代数的整数論	だ↑いすうてき↓せ↑いす↓うろん	نظریه جبری اعداد	алгебраи́ческая тео́рия чи́сел
analytic number theory	arithmetic; mathematical analysis	解析数论	jiěxī shùlùn	analytische Zahlentheorie	théorie [f] analytique des nombres	解析的整数論, 解析数論	か↑いせきてきせいす↓うろん, か↑いせきす↓うろん	نظریه تحلیل اعداد	аналити́ческая тео́рия чи́сел

Arithmetic

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Latn.Pinyin-CN: gàiniàn	deu-Latn-DE: Begriff [m]	fra-Latn-FR: concept [m]	jpn-Jpan-JP: 概念	jpn-Hrkt-JP: が↓いねん	pes-Aran-IR: مَفهوم	pes-Aran-IR: پیش‌نیاز
abacus	mechanical calculator	算盘	suàn pan	Abakus [m]				چرتکه
absolute value, modulus	real number	绝对值	juéduì zhí	Absolutbetrag [m], absoluter Betrag, Absolutwert [m], absoluter Wert	valeur [f] absolue			قدر مطلق
addition	number (abstract idea); binary operation <mathematical logic>	加法	jiā fǎ	Addition [f]	addition [f]			جمع
additive inverse, opposite, negation	addition; number (abstract idea)	加法逆元, 相反数	jiāfǎ nìyuán, xiāngfǎn shù	Gegenzahl [f]				وارون افزایشی
addend, summand	addition; operand <mathematical logic>	加数	jiā shù	Summand [m]				جمع وند/عامل جمع
analog computer	basic operation; logarithm; exponentiation	模拟计算机	mónǐ jìsuànjī	Analogrechner [m]				رایانه قیاسی
augend	addition; operand <mathematical logic>	被加数	bèijiā shù	erster Summand				مولفه دوم جمع اعداد
base (exponentiation)	exponentiation	底数（指数）, 基数（指数）	dǐ shù (zhǐ shù), jīshù (zhǐ shù)	Basis [f] (Exponentiation)				پایه (عدد نمایی)
base (logarithm)	logarithm	底数（对数）, 基数（对数）	dǐ shù (duì shù), jīshù (duì shù)	Basis [f] (Logarithmus)				پایه (عدد لوگاریتمی)
basic operation	addition; division; multiplication; subtraction	四则运算	sìzé yùnsuàn	Grundrechnungsarten [f pl], Grundrechenarten [f pl]				چهار عمل اصلی
binary logarithm	logarithm	以二为底的对数	yǐ èr wéi dǐ de duìshù	binärer Logarithmus, dualer Logarithmus	logarithme [m] binaire			لوگاریتم باینری (دو دویی)
binary system	numeral system	二进制	èr jìnzhì	Dualsystem [n], Zweiersystem [n], Binärsystem [n]	système [m] binaire			سیستم باینری
chisanbop	addition; subtraction	指算法	zhǐsuàn fǎ	Chisanbop [n]				محاسبه انگشتی
complex number	imaginary number; real number	复数	fù shù	komplexe Zahl	nombre [m] complexe			اعداد مختلط
composite number	division; natural number	合数, 合成数	hé shù, héchéng shù	zusammengesetzte Zahl				عدد مرکب/عدد غیر اول
constant	number (abstract idea)	常数, 定数	cháng shù, dìng shù	Konstante [f], Festwert [m]	constante [f]			ثابت
counting rods	basic operation	算筹, 算子	suàn chóu, suàn zǐ	Zählstäbe [m pl]				میله های شمارش
decimal, base-ten	integer	十进制	shíjìn zhì	Dezimalsystem [n], Zehnersystem [n], dekadisches System				دسیمال/ اعداد بر پایه ده
decimal logarithm, common logarithm	logarithm	常用对数	chángyòng duìshù	dekadischer Logarithmus, Zehnerlogarithmus [m]				لگاریم بر پایه ده
decimal representation	number (symbol)	小数	xiǎo shù	Dezimaldarstellung [f]				نمایش اعشاری/نمایش دهدهی
decimal separator	decimal representation; radix character	小数点	xiǎoshù diǎn	Dezimaltrennzeichen [n]				ممیز
degree	nth root	次方根	cìfāng gēn	Wurzelgrad [m]	degré [m]			درجه
denominator	fraction; operand <mathematical logic>	分母	fēn mǔ	Nenner [m]	dénominateur [m]			مخرج کسر
difference	subtraction	差	chā	Differenz [f]	différence [f]			تفاضل
digit	number (abstract idea); symbol	数字（单个符号）	shù zì (dāngè fúhào)	Ziffer [f]	chiffre [m]			رقم
direct rounding	rounding up; rounding down; rounding towards zero; rounding away from zero	无条件简化	wútiáojiàn jiǎnhuà					رُند کردن
dividend	fraction; operand <mathematical logic>	被除数	bèichú shù	Dividend [m]	dividende [m]			مقسوم
division	number (abstract idea); binary operation <mathematical logic>	除法	chú fǎ	Division [f]	division [f]			تقسیم
division by zero	division; zero	除以零	chú yǐ líng	Division [f] durch Null	division [f] par zéro			تقسیم بر صفر
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 <mathematical logic>	除数	chú shù	Divisor [m]	diviseur [m]
Egyptian fraction	unit fraction	埃及分数	Āijí fēnshù	Stammbruchzerlegung [f]
engineering notation	scientific notation	工程计数法	gōngchéng jìshù fǎ	technische Notation [f]
equal sign	equality <mathmatical logic>	等号	děng hào	Gleichheitszeichen [n], Ist-gleich-Zeichen [n]	signe [m] égal
Euclid's lemma	prime number	欧几里得引理	Ōujīlǐdé yǐnlǐ	Lemma [n] von Euklid
Euler's number, e	constant	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 (abstract idea); binary operation <mathematical logic>	幂运算, 指数运算	mì yùnsuàn, zhǐshù yùnsuàn	Potenz [f]
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	因式分解	yīnshì fēnjiě	Faktorisierung [f]	factorisation [f]
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
improper fraction	fraction	假分数	jiǎ fēnshù	unechter Bruch, uneigentlicher Bruch
infinity	number (abstract idea)	无穷	wú qióng	Unendlichkeit [f]
integer	natural number; negative number	整数	zhěng shù	Ganzzahl [f], ganze Zahl	entier
inverse function, anti-function	function <mathematical logic>	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]
logarithm	number (abstract idea); binary operation <mathematical logic>	对数	duì shù	Logarithmus [m]	logarithme [m]
long division	division	长除法	cháng chúfǎ	Standardmethode [f] der schriftlichen Division
long multiplication	multiplication	长乘法	cháng chéngfǎ	Standardmethode [f] der schriftlichen Multiplikation
mechanical calculator, calculating machine	basic operation	机械计算器	jīxiè jìsuànqì	Rechenmaschine [f]	calculatrice [f] mécanique, machine [f] à calculer, machine [f] arithmétique	機械式計算機	き↓かいしきけ↑いさ↓んき		вычисли́тельная маши́на, счётная маши́на
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]
multiplicand	multiplication; operand <mathematical logic>	被乘数	bèichéng shù	Multiplikand [m]
multiplication table	multiplication	乘法表	chéngfǎ biǎo	Einmaleins [n]
multiplier	multiplication; operand <mathematical logic>	乘数	chéng shù	Multiplikator [m]
multiplication	number (abstract idea); binary operation <mathematical logic>	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	Euler's number; 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 (abstract idea)	自然数	zìrán shù	natürliche Zahl
negative number	number (abstract idea)	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	numeral; symbol	符号	fúhào	Notation [f]
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 <mathematical logic>	次方根	cìfāng gēn	Wurzel [f] , Radikal [n]
number (abstract idea)	object	数	shù zì (chōuxiàng gàiniàn)	Zahl [f] (abstrakte Idee)
number (symbol), numeral	digit	数字（整个符号）	shù zì (zhěnggè fúhào)	Zahl [f] (Symbol)
number line	line <geometry>	数轴, 数线	shù zhóu, shù xiàn	Zahlengerade [f], Zahlenstrahl [m]
numeral system	notation	数制, 记数系统, 记数法	shù zhì, jìshù xìtǒng, jìshù fǎ	Zahlensystem [n]
numerator	fraction; operand <mathematical logic>	分子	fēn zǐ	Zähler [m]
object		物体	wù tǐ	Objekt [n]
octal, oct	numeral system	八进制	bā jìnzhì	Oktalsystem [n]
odd number	natural number; division	奇数	jī shù	ungerade Zahl
operator precedence, order of operation <mathematical logic>	basic operation; 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	number (symbol); 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
Pascal's calculator, arithmetic machine, Pascaline	machine calculator	滚轮式加法器, 帕斯卡计算器	gǔnlúnshì jiāfǎqì, Pàsīkǎ jìsuànqì	Pascaline [f]	pascaline [f], machine [f] d’arithmétique, roue pascaline	パスカリン	パ↑スカ↓リン		суммирующая машина Паска́ля, Паскали́на
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]
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 (abstract idea)	正数	zhèng shù	positive Zahl
prime number, prime	product; natural number	质数, 素数	zhì shù, sù shù	Primzahl [f]
product	multiplication	积	jī	Produkt [n]
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 (abstract idea)	比率, 比值	bǐ lǜ, bǐ zhí	Verhältnis [n]
rational number	fraction; integer	有理数	yǒulǐ shù	rationale Zahl
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
remainder	division with remainder	余数	yú shù	Rest [m], Teilungsrest [m]
root	nth root	根	gēn	Wurzel [f]
root extraction	nth root	开方	kāi fāng	Radizieren [n]
rounding	decimal representation	数值修约	shùzhí xiūyuē	Rundung [f], Runden [n]
round away from zero, round towards infinity	rounding	向无穷取整	xiàng wúqióng qǔzhěng	von Null wegrunden
round down, round towards negative infinity	rounding	向下取整	xiàng xià qǔzhěng	abrunden
round towards zero, round away from infinity	rounding	向零取整	xiàng líng qǔzhěng	gegen Null runden
round up, round towards positive infinity	rounding	向上取整	xiàng shàng qǔzhěng	aufrunden
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
scientific notation	significant figures	科学计数法	kēxué jìshù fǎ	wissenschaftliche Notation [f]
significant figures, significant digits	rounding	有效数字, 有效数位	yǒuxiào shùzì, yǒuxiào shùwèi	signifikante Stellen [f pl], signifikante Ziffern [f pl]
slide rule	analog computer	计算尺	jìsuàn chǐ	Rechenschieber [m], Rechenstab [m]
subtraction	number (abstract idea); binary operation <mathematical logic>	减法	jiǎn fǎ	Subtraktion [f], Abziehen [n], Abzug [m]
subtrahend	subtraction	减数	jiǎn shù	Subtrahend [m]
sum	addition	和	hé	Summe [f]
symbol		符号	fúhào	Symbol [n]
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	zhèngzhěngshù de wéiyī fēnjiě dìnglǐ, suànshù jīběn dìnglǐ	Fundamentalsatz [m] der Arithmetik
zero	number (abstract idea)	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-Jpan-JP: 概念	jpn-Jpan-JP: 前提	jpn-Hrkt-JP: が↓いねん	jpn-Hrkt-JP: ぜ↑んてい	rus-Cyrl-RU: конце́пция	rus-Cyrl-RU: предпосы́лка

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-Jpan-JP: 概念	jpn-Jpan-JP: 前提	jpn-Hrkt-JP: が↓いねん	jpn-Hrkt-JP: ぜ↑んてい	rus-Cyrl-RU: конце́пция	rus-Cyrl-RU: предпосы́лка

* Appendix *

Adjective & Adjective Phrase; Verb & Verb Phrase

eng-Latn-US: concept	eng-Latn-US: prerequisite	cmn-Hans-CN: 概念	cmn-Latn.Pinyin-CN: gàiniàn	deu-Latn-DE: Begriff [m]	fra-Latn-FR: concept [m]
add
divide by
greater than	inequality <mathematical logic>	大于	dà yú	größer als	plus grand que
greater than or equal to	inequality <mathematical logic>	大于等于	dàyú děngyú	größer als oder gleich	plus grand ou égal à
multiply
subtract
extract the root, radicate
less than	inequality <mathematical logic>	小于	xiǎo yú	kleiner als	inférieur à
less than or equal to	inequality <mathematical logic>	小于等于	xiǎoyú děngyú	kleiner als oder gleich	inférieur ou égal à
much greater than	inequality <mathematical logic>	远大于	yuǎn dàyú	viel größer als
much less than	inequality <mathematical logic>	远小于	yuǎn xiǎoyú	viel weniger als

Symbol

symbol	eng-Latn-US: concept	cmn-Hans-CN: 概念	cmn-Latn.Pinyin-CN: gàiniàn	deu-Latn-DE: Begriff [m]	fra-Latn-FR: concept [m]	jpn-Jpan-JP: 概念	jpn-Hrkt-JP: が↓いねん	rus-Cyrl-RU: конце́пция
+	addition; positive number
-	subtraction; negative number
×	multiplication
÷	division
%	percent
√	root
=	equal to
≠	not equal to
<	less than
>	greater than
≤	less than or equal to
≥	greater than or equal to
∞	infinity
E, e	E notation
e	Euler's number
lg	decimal logarithm
log	logarithm
ln	natural logarithm

Process

eng-Latn-US: process	eng-Latn-US: constituent	cmn-Hans-CN: 过程	cmn-Hans-CN: 构件	cmn-Latn.Pinyin-CN: guòchéng	cmn-Latn.Pinyin-CN: gòujiàn	deu-Latn-DE: Prozess [m]	deu-Latn-DE: Bestandteil [m]	fra-Latn-FR: procès [m]	fra-Latn-FR: composant [m]	jpn-Jpan-JP: 過程	jpn-Jpan-JP: 構材	jpn-Hrkt-JP: か↑てい	jpn-Hrkt-JP: こ↑うざい	rus-Cyrl-RU: проце́сс	rus-Cyrl-RU: соста́вная часть
addition	augend, addend, sum
division	dividend, divisor, quotient
multiplication	multiplicand, multiplier, product
subtraction	minuend, subtrahend, difference
division with remainder	dividend, divisor → quotient, remainder

Related Free Educational Resources

branch	name	link	language	public license
Arithmetic	Arithmetic Game	https://arithmetic.zetamac.com/	English	-
Arithmetic	gbrainy	https://wiki.gnome.org/Apps/gbrainy	English	GNU GPL 2.0
Arithmetic	Number Empire	https://www.numberempire.com/	Multiple languages	-
Arithmetic	Wolfram\|Alpha	https://www.wolframalpha.com/	English, Japanese	-