dict_data.json

{"bg" : {"ro" : {"disjoint" : ["disjuncte"], "mutually disjoint" : ["familie de mulţimi disjuncte ", "familie de mulţimi disjuncte "], "power set" : ["mulţimea tuturor submulţimilor"], "pairwise disjoint" : ["familie de mulţimi disjuncte ", "familie de mulţimi disjuncte "]}, "tr" : {"disjoint" : ["ayrık"], "mutually disjoint" : ["çift olarak ayrık", "karşılıklı olarak ayrık"], "power set" : ["üssü küme"], "pairwise disjoint" : ["çift olarak ayrık", "karşılıklı olarak ayrık"]}, "de" : {"disjoint" : ["disjunkt"], "mutually disjoint" : ["paarweise disjunkt"], "power set" : ["Potenzmenge"], "pairwise disjoint" : ["paarweise disjunkt"]}}, "de" : {"bg" : {"disjunkt" : ["disjoint"], "Potenzmenge" : ["power set"], "paarweise disjunkt" : ["pairwise disjoint", "mutually disjoint"]}, "ru" : {"Differenz" : ["set difference"], "gleich" : ["equal"], "leere Menge" : ["empty set"], "Vereinigung" : ["union", "union"]}, "tr" : {"Obermenge" : ["üst küme"], "echte Teilmenge" : ["düzgün alt küme"], "Potenzmenge" : ["üssü küme"], "Durchschnitt" : ["kesişim"], "leere Menge" : ["Boş küme"], "Differenz" : ["fark kümesi"], "disjunkt" : ["ayrık"], "echte Obermenge" : ["düzgün alt küme"], "Schnitt" : ["kesişim"], "gleich" : ["eşit"], "Paare" : ["çift"], "Teilmenge" : ["alt"], "paarweise disjunkt" : ["çift olarak ayrık", "karşılıklı olarak ayrık"], "Paar" : ["çift"], "Vereinigung" : ["birleşim", "birleşim"]}, "en" : {"Selbst-Primzahl" : ["self prime"], "konverse Relation" : ["converse relation"], "Monoid" : ["monoid"], "Riemannsche Zetafunction" : ["Riemann zeta function"], "Googol" : ["googol"], "Primorial-Primzahlen" : ["Primorial primes"], "Elternknoten" : ["parent"], "Projektion" : ["projection", "projection"], "magisches Quadrat aus Primzahlen" : ["magic square of prime"], "reellwertige Funktion" : ["real-valued function", "real function"], "Semi-magische Quadrate" : ["Semimagic square"], "glückliche Zahl" : ["lucky numbers", "lucky number"], "1 -dimenionale Cartesische Raum" : ["1 -dim Cartesian space"], "Ramanujan-Konstante" : ["Ramanujan’s constant"], "schwachbesetztes Antimagisches Quadrat" : ["sparse antimagic square"], "Baxter-Hickerson-Funktion" : ["Baxter-Hickerson function"], "Eulersche Zahl" : ["Napier’s constant", "Euler’s constant", "1"], "Fortunate-Zahl" : ["Fortunate number"], "totale Ordnung" : ["simple order", "total ordering"], "Wurzel" : ["root", "root", "root"], "totale Funktion" : ["total function"], "stetig" : ["continuous"], "Obermenge" : ["superset"], "Riemann’sche Vermutung" : ["Riemann hypothesis"], "geordnete Menge" : ["ordered set"], "aufspannt" : ["span"], "triviale Untergruppe" : ["trivial subgroup"], "vollständiger Graph" : ["complete graph"], "sublime Zahl" : ["sublime number"], "konvergiert" : ["converges", "converges"], "Googolplexplex" : ["googolplexplex"], "Motzkin-Primzahl" : ["Motzkin prime"], "Brunsche Konstante für Cousin-Primzahlen" : ["Brun’s constant for cousin primes"], "erhabene Zahl" : ["sublime number"], "absolut unnormal" : ["absolutely abnormal", "absolutely non-normal"], "Primorial" : ["primorial"], "teilt" : ["divides", "divisor"], "defizient" : ["deficient number"], "Untergruppe" : ["subgroup"], "Panmagischen Quadrat" : ["panmagic square"], "Summe" : ["sum", "sum", "sum", "sum"], "Maximalgrad" : ["maximum degree"], "Wilson-Zahl" : ["Wilson number"], "Wilbraham-Gibbs-Konstante" : ["Wilbraham-Gibbs constant"], "irreflexiv" : ["irreflexive", "anti-reflexive"], "multiplikative Struktur" : ["multiplicative structure"], "dritte Ableitung" : ["third derivative"], "Primitivwurzel" : ["primitive root"], "einfache Ordnung" : ["simple order", "total ordering"], "Newman-Shanks-Williams-Primzahl" : ["NSW prime", "Newman-Shanks-Williams prime"], "Abundanz" : ["abundance"], "unendliche Summe" : ["infinite sum"], "Companion Pell-Zahlen" : ["companion Pell number", "Pell-Lucas number"], "Leyland-Zahl" : ["Leyland number"], "Taillenweite" : ["girth"], "Barriere" : ["barrier"], "Mersenne-Zahl" : ["Mersenne number"], "Kantenanzahl" : ["number of edges"], "negativen reellen Zahlen" : ["negative real number"], "Mills-Primzahl" : ["Mills prime"], "praktische Zahl" : ["panarithmic number", "practical number"], "Innere" : ["interior"], "Lebesgue-Identität" : ["Lebesgue identity"], "Eulersche Phi-Funktion" : ["phi function"], "permutierbare Primzahl" : ["permutable prime"], "Cahen-Konstante i" : ["Cahen’s constant"], "Fermatsche Pseudoprimzahl" : ["Fermat pseudoprime"], "kleinste gemeinsame Vielfache" : ["smallest common multiple", "lowest common multiple", "least common multiple", "smallest common multiple", "lowest common multiple", "least common multiple"], "Cullen-Zahl" : ["Cullen number"], "zwölften Smarandache-Konstanten" : ["twelfth Smarandache constant", "twelfth Smarandache constants"], "Endecke" : ["endvertices"], "super-Catalan-Zahlen )" : ["super-Catalan number", "Schröder-Hipparchus number"], "Quotientenmenge" : ["quotient space"], "perfekte Zahl" : ["perfect number"], "quadratfrei" : ["square-free"], "Hausdorff-Grenzwert" : ["Hausdorff limit"], "Stern-Primzahl" : ["Stern prime"], "kubikfreie Taxicab-Zahl" : ["cubefree taxicab number"], "fröhliche Primzahlen" : ["happy prime"], "Partialsumme" : ["partial sum"], "Newton" : ["Newton’s"], "echte Teilmenge" : ["proper subset"], "Relation auf" : ["relation on"], "Zentrale Delannoy-Zahlen" : ["central Delannoy number"], "Fermatsche Primzahl" : ["Fermat prime"], "Teilersumme" : ["aliquot sum"], "Stoneham-Zahlen" : ["Stoneham number"], "Lucas-Zahlen" : ["Lucas numbers"], "Halbprimzahl" : ["2-almost prime", "pq number", "biprime", "semiprime", "2-almost prime"], "vollständiger Raum" : ["complete space"], "Zykel" : ["cycle"], "Loop" : ["loop"], "Pell-Zahlen 2. Art" : ["companion Pell number", "Pell-Lucas number"], "Gruppoid" : ["magma", "groupoid"], "Uban-Zahlen" : ["Uban number"], "Soziale Zahlen" : ["Sociable number"], "rechtes Ideal" : ["right ideal"], "Franel-Zahlen" : ["Franel number", "Franel number"], "zyklische Zahl" : ["cyclic number"], "Pierpont-Primzahl" : ["Pierpont prime"], "Euklid-Mullin-Folge" : ["Euclid-Mullin sequence", "Euclid Mullin sequence"], "Googolplexian" : ["googolplexian"], "untere" : ["lower"], "fünfzehnte Smarandache-Konstante" : ["fifteenth Smarandache constant"], "initial" : ["source"], "Googolminex" : ["googolminex"], "quadratischer Nichtrest" : ["quadratic nonresidue"], "antisymmetrisch" : ["antisymmetric"], "inverse Function" : ["inverse function"], "Linien" : ["arc", "branch", "line", "edge"], "Nullstelle" : ["zero"], "zweite Skewes-Zahl" : ["second Skewes number"], "Valenz" : ["valency"], "Durchschnitt" : ["intersection"], "arithmetische Funktion" : ["number-theoretic function", "arithmetical", "arithmetic"], "echter Teilgraph" : ["proper subgraph"], "Ultramagisches Quadrat" : ["ultramagic square"], "vierzehnte Smarandache-Konstante" : ["fourteenth Smarandache constant"], "Woodall-Zahl" : ["Woodall number", "Cullen numbers of the second kind"], "symmetrisches magisches Quadrat" : ["associative magic square"], "Gelfond’s Konstante" : ["Gelfond’s constant"], "Komponenten" : ["component"], "azyklisch" : ["DAG", "acyclic"], "1 -Tupel" : ["1 -tuple"], "hochzusammengesetzte Zahl" : ["highly composite number"], "undefiniert auf" : ["undefined at", "undefined at"], "Zehnerlogarithmus" : ["common logarithm", "decadic logarithm", "decimal logarithm", "Briggsian logarithm"], "zyklische Gruppe" : ["cyclic group"], "zweite Tschebyschow-Funktion" : ["second Chebyshev"], "abgeschlossen o" : ["closed"], "Punkte" : ["junction", "point", "node", "vertices"], "small-set" : ["small set"], "Länge" : ["length", "length", "length"], "Modulus" : ["modulus", "modulus", "modulus"], "Doppel-Mersenne-Zahl" : ["double Mersenne number"], "Brücke" : ["bridge"], "Quotienten" : ["quotient"], "Schröder-Hipparchus-Zahl" : ["super-Catalan number", "Schröder-Hipparchus number", "super-Catalan number", "Schröder-Hipparchus number"], "Kanten" : ["arc", "branch", "line", "edge", "edge"], "ganze Teil" : ["greatest integer function", "floor"], "abzählbar" : ["countable"], "Ausgangsgrad" : ["outdegree"], "Wolstenholme-Primzahl" : ["Wolstenholme prime"], "Addition" : ["Additon"], "offene Kugel" : ["open ball"], "Exponentiation" : ["exponentiation"], "Differenz" : ["difference", "difference", "difference", "difference"], "Ordnung" : ["separation", "proper", "order", "order"], "Moufang Eigenschaft" : ["Moufang Identity"], "zehnten Smarandache-Konstanten" : ["tenth Smarandache constants", "tenth smarandache constants"], "alternierende harmonische Serie" : ["alternating harmonic series"], "untere Grenze" : ["lower bound"], "spezielle lineare Gruppe" : ["special linear group"], "Kuchen-Zahl" : ["cake number"], "Primzahllücke" : ["prime gap"], "potente Zahl" : ["2-full numbers", "square-full number", "squareful number", "powerful number"], "Wilson-Quotient" : ["Wilson quotient"], "maximaler" : ["maximal connected subgraph"], "Linkstrunkierbare Primzahlen" : ["left-truncatable prime"], "1 -perfekt" : ["multiperfect", "1 -perfect"], "Imaginärteil" : ["real part"], "Brunsche Konstante" : ["Brun’s constant"], "Plastic-Konstante" : ["plastic constant", "plastic number"], "geschlossene Kugel" : ["closed ball"], "Kreuzprodukt" : ["cross product"], "Aufrundung" : ["least integer function", "ceiling"], "stückweise definiert" : ["defined piecewise"], "Schwache Primzahlen" : ["weakly prime"], "Padovan-Zahlen" : ["Padovan number"], "Abschluss" : ["closure"], "quadratischer Rest" : ["quadratic residue"], "Harshad-Zahl" : ["Niven number", "Harshad number"], "iterierte Querprodukt" : ["multiplicative digital root"], "harmonische Zahl" : ["harmonic number"], "Gelfond-Schneider Konstante" : ["Hilbert number", "Gelfond-Schneider constant"], "distributiv" : ["distributive"], "Perrin-Pseudoprimzahl" : ["Perrin pseudoprime"], "Beidseitig trunkierbare Primzahlen" : ["two-sided prime"], "Cousin-Primzahlen" : ["Cousin prime"], "orthogonal" : ["orthogonal array representation"], "Bailey-Borwein-Plouffe-Formel" : ["Bailey-Borwein-Plouffe formula", "BBP formula"], "Graph" : ["graph", "graph"], "Definiens" : ["definiens"], "asymmetrisch" : ["asymmetric"], "echte Obermenge" : ["proper subset"], "magische Serie" : ["magic series"], "multiperfekte Zahl" : ["multiperfect", "1 -perfect"], "pythagoreisches Zahlentripel" : ["Pythagorean triple"], "linksseitige Grenzwert" : ["leftsided limit"], "Ganzzahlige Division" : ["Integer division", "Integer division"], "Aliquot-Folge" : ["aliquot sequence"], "Hetero-Quadrat" : ["heterosquare"], "reelle Funktion" : ["real-valued function", "real function"], "symmetrisch" : ["symmetric"], "Mercator-Reihe" : ["Newton-Mercator series", "Mercator series"], "Querprodukt" : ["digit product"], "Standardform" : ["standard form"], "adjazent" : ["neighbour", "adjacent"], "Devlali-Zahl" : ["Devlali number", "Colombian number", "self number"], "Ramanujan-6-10-8-Identität" : ["Ramanujan 6-10-8 identity"], "Blatt" : ["leaf"], "Smarandache-Funktion" : ["Smarandache function"], "1  mal differeinzierbar" : ["1 times differentiable", "1  times differentiable"], "Grad" : ["degree"], "Schleife" : ["cycle"], "Division" : ["division"], "verallgemeinerte Taxicab-Zahl" : ["generalized taxicab number"], "Nivenmorphic-Zahl" : ["Nivenmorphic number"], "nichttrivialen Teiler" : ["non-trivial divisor", "proper"], "additive Struktur" : ["additive structure"], "Ideal" : ["ideal", "two-sided ideal"], "leere" : ["empty graph"], "ganzzahlige Intervall" : ["integer interval"], "Ring" : ["ring", "ring"], "Nah-Wilson-Primzahl" : ["near Wilson prime"], "minimale Länge" : ["minimum length"], "reduziert" : ["reduced"], "Beschränkung" : ["restriction"], "Zwischenprimzahl" : ["interprime"], "n-Fastprimzahl" : ["almost prime"], "Schröder-Zahl" : ["Schröder number"], "Jacobsthal-Zahlen" : ["Jacobsthal numbers"], "Cahen-Konstante" : ["Cahen’s constant"], "Liouvillesche Zahl" : ["Liouville number"], "Proth-Zahlen" : ["Proth number"], "positiven reellen Zahlen" : ["positive real number", "positive real number"], "fünfte Smarandache-Konstante" : ["fifth Smarandache constant"], "Lobb-Zahl" : ["Lobb number"], "leicht abundant" : ["quasiperfect number"], "iterierte Quersumme" : ["digital root", "repeated digital sum"], "goldene Schnitt" : ["golden ratio"], "geometrische Mittel" : ["geometric mean"], "magische Summe" : ["magic sum"], "Knödel-Zahlen" : ["Knoedel number"], "schwachbesetztes totales antimagisches Quadrat" : ["sparse totally antimagic square"], "pronische Zahl" : ["rectangular number", "oblong number", "pronic number"], "ehrgeizige Zahl" : ["aspiring number"], "Metrik" : ["distance function", "metric"], "Binar" : ["magma", "groupoid"], "Primzahl" : ["prime number"], "Proth-Zahl" : ["Proth number"], "kongruent modulo" : ["congruent modulo"], "induziert" : ["induce"], "Rest" : ["remainder"], "Primär-Pseudoperfekte-Zahl" : ["primary pseudoperfect number"], "Relation" : ["relation"], "Vielfaches" : ["multiple"], "zyklisch" : ["cyclic"], "Häufungspunkt" : ["limit point"], "Higgs-Primzahl" : ["Higgs prime"], "Endknoten" : ["end"], "Mirpzahlen" : ["emirp"], "Produkt" : ["product", "product", "product"], "Wall-Sun-Sun-Primzahl" : ["Fibonacci-Wieferich prime", "Wall-Sun-Sun prime"], "zahlentheoretische" : ["number-theoretic function", "arithmetical", "arithmetic"], "Sophie-Germain-Primzahl" : ["Sophie Germain prime"], "arithmetische Mittel" : ["arithmetic mean"], "Startwert" : ["lower", "lower bound"], "natürliche Dichte" : ["natural density"], "Sphenische Zahlen" : ["sphenic number"], "1 -regulär" : ["regular", "1 -regular"], "freundliches Paar" : ["friendly pair"], "Jacobi-Symbol" : ["Jacobi symbol"], "Primfaktor" : ["prime factor"], "natürlichen Zahlen" : ["natural number"], "abzählbar unendlich" : ["countably infinite"], "sehnenlos" : ["chordless"], "gleichmäßig konvergent" : ["uniformly convergent"], "generierten Subring" : ["subring generated"], "Schnapszahl" : ["repdigit"], "maximale Läenge" : ["maximum length"], "Abstandsfunktion" : ["distance function", "metric"], "normales magisches Quadrat" : ["normal magic square"], "partielle Ordnung" : ["partial order", "partial ordering"], "Vektor" : ["vector"], "echte Untergruppe" : ["proper subgroup"], "Binomialkoeffizient" : ["binomial coefficient"], "glückliche Primzahlen" : ["lucky prime"], "Sarrus-Zahlen" : ["Sarrus number"], "Äquivalenzklasse" : ["equivalence class"], "Eulersche 1 -Funktion" : ["phi function"], "Fakultät" : ["factorial"], "punktweise konvergent" : ["pointwise convergent"], "normale Zahl zur Basis 1" : ["normal in base 1"], "Teilüberdeckung" : ["subcover"], "harmonische Mittel" : ["harmonic mean"], "Frugal-Zahl" : ["frugal number"], "zweite Ableitung" : ["second derivative"], "Ringoid" : ["ringoid"], "injektiv" : ["injective"], "multirelationionaler Ausdruck" : ["multi-relation expression"], "griechisch-lateinisches Quadrat" : ["Euler square", "Greco-Latin square"], "Multiplikation" : ["multiplication", "Multiplication", "Multiplication"], "Sexy-Primzahlen" : ["Sexy primes"], "all-Harshad-Zahl" : ["all-Niven number", "all-Harshad number"], "Überdeckung" : ["cover"], "vierten Smarandache-Konstanten" : ["fourth Smarandache constant"], "abundant" : ["abundant number"], "induzierter Teilgraph" : ["induced subgraph"], "Zahlenpalindrome" : ["palindromic number"], "Lychrel-Zahl" : ["Lychrel number"], "trivialen Teiler" : ["divides", "divisor"], "Quasiordnung " : ["quasiorder", "preorder"], "Ende" : ["end", "end", "endvertices"], "Raum der Funktionen" : ["function space"], "Rechtstrunkierbare Primzahlen" : ["right-truncatable prime"], "konvexes Polytop" : ["convex polytope"], "quasiperfekte Zahl" : ["quasiperfect number"], "Skewes-Zahl" : ["first Skewes number", "Skewes number"], "Motzkin Zahlen" : ["Motzkin number"], "sechste Smarandache-Konstante" : ["sixth Smarandache constant"], "nicht" : ["not connected", "disconnected"], "unzusammenhängend" : ["not connected", "disconnected"], "achte Smarandache-Konstante" : ["eighth Smarandache constant"], "eulersche Funktion" : ["phi function"], "trennt" : ["separate"], "Schröder-Hipparchus-Zahlen" : ["super-Catalan number", "Schröder-Hipparchus number"], "binäre Logarithmus" : ["binary logarithm"], "Sehne" : ["chord"], "Monstergruppe" : ["Friendly Giant", "Fischer–Griess monster", "monster group"], "geschlossen ." : ["closed"], "Liouville-Konstante" : ["Liouville constant"], "Ecken" : ["junction", "point", "node", "vertices"], "Eingangsgrad" : ["indegree"], "Summationsbereich" : ["range of summation"], "Endecken" : ["end", "endvertices"], "Definiendum" : ["definiendum"], "bijektiv" : ["bijective"], "1 -Simplex" : ["1 -simplex"], "Unendlichkeit" : ["Infinity"], "Gregory-Zahl" : ["Gregory number"], "differenzierbar" : ["differentiable"], "antireflexiv" : ["irreflexive", "anti-reflexive"], "Quersumme" : ["digit sum"], "Eban-Zahlen" : ["Eban number"], "Abrundung" : ["greatest integer function", "floor"], "Woodall-Zahlen" : ["Woodall number", "Cullen numbers of the second kind"], "nullfrei" : ["zerofree"], "Hurwitzsche Zetafunction" : ["Hurwitz zeta function"], "Körper" : ["field"], "Cauchyfolge" : ["Cauchy sequence"], "Mills-Konstante" : ["Mills’ constant"], "Struktur" : ["structure"], "strikte Ordnung" : ["strict ordering"], "Freundliche Zahlen" : ["Friendly number"], "reverse Keith-Zahl" : ["reverse Keith number"], "offene Menge" : ["open"], "elitär" : ["elite"], "Hilbert-Zahl" : ["Hilbert number", "Gelfond-Schneider constant", "Hilbert number"], "Bild" : ["image", "image"], "1 -potenzglatt" : ["1 -powersmooth"], "konvexe Hülle e" : ["convex hull"], "1 -fache Cartesische Product" : ["1 -fold Cartesian product"], "zusammengesetzte Zahl" : ["composite number"], "Automorphismus" : ["automorphism"], "Diophantische Gleichung" : ["Diophantine equation"], "Schnitt" : ["intersection"], "quadratische Mittel" : ["root mean square"], "Umkehrung" : ["reversal"], "Niven-Zahl" : ["Niven number", "Harshad number"], "zweite Smarandache-Konstante" : ["second Smarandache constant", "second smarandache constant"], "Pfad" : ["path"], "Gaussklammer" : ["greatest integer function", "floor"], "1 -Ulam-Zahlen" : ["1 -Ulam number"], "gleich" : ["equal"], "einfach" : ["simple", "simple"], "unendlich differenzierbar" : ["infinitely differentiable", "smooth"], "echten" : ["non-trivial divisor", "proper"], "BBP-Formel" : ["Bailey-Borwein-Plouffe formula", "BBP formula"], "obere" : ["upper bound", "upper bound"], "Urbild" : ["pre-image"], "Wertebereich" : ["codomain"], "gute Primzahl" : ["good prime"], "Euklid-Zahlen" : ["Euclid number"], "lineare Ordnung" : ["linear order"], "Abundancy" : ["abundancy"], "Prothsche Primzahl" : ["Proth prime"], "Suptraktion" : ["Subtraction"], "Äquivalenzrelation" : ["equivalence relation"], "Reguläre Zahlen" : ["Regular number"], "fröhlich" : ["happy", "happy number"], "Pfeile" : ["arc", "branch", "line", "edge"], "vollkommene Zahl" : ["perfect number"], "Limes inferior" : ["limit inferior", "infimum limit", "inferior limit", "lower limit", "inner limit"], "Paare" : ["pairs"], "isomorph" : ["isomorphic"], "unabhängig" : ["independent"], "Verkettung" : ["composition"], "Quelle" : ["source"], "pythagoräische Primzahl" : ["Pythagorean prime"], "linker Nullteiler" : ["left zero divisor"], "inneren Ecken" : ["inner vertices"], "Sierpinski-Zahl" : ["Sierpinski number"], "erste Tschebyschow-Funktion" : ["first Chebyshev function"], "Motzkin-Zahl" : ["Motzkin number"], "Eckenanzahl" : ["number of vertices"], "stabile Mengen" : ["stable set"], "Faktorielle" : ["factorial"], "teilerfremd" : ["mutually prime", "relatively prime", "co-prime", "coprime"], "Aban-Zahlen" : ["Aban number"], "Fermatsche Zahl" : ["Fermat number"], "Leibniz Notation" : ["Leibniz’s notation"], "1 mal differenzierbar" : ["1 times differentiable", "1  times differentiable"], "Abelsch" : ["Abelian"], "Kynea-Zahl" : ["Kynea number"], "Narayana-Zahlen" : ["Narayana number"], "verallgemeinerte Woodall-Zahl" : ["generalized Woodall number"], "normalisierte sinc-Funktion" : ["normalized sinc function"], "Factorion" : ["factorion"], "verbunden" : ["linked"], "kompakt" : ["compact"], "Teilmenge" : ["subset"], "Stammbruch" : ["unit fraction"], "Komponente" : ["component"], "Pythagoräisches Quadrupel" : ["Pythagorean quadruple"], "Riesel-Zahl" : ["Riesel number"], "magisches Quadrat" : ["magic square"], "Endwert" : ["lower", "lower bound"], "Sylvester-Folge" : ["Sylvester sequence"], "total geordnete Menge" : ["totally ordered set"], "1 mal differeinzierbar" : ["1 times differentiable", "1  times differentiable"], "leere Summe" : ["nullary sum", "empty sum"], "Operativ" : ["magma", "groupoid"], "Mangoldt-Funktion" : ["von Mangoldt function"], "lateinisches Quadrat" : ["Latin square"], "1 -potente Zahl" : ["1 -full number", "1 -ful number", "1 -powerful number"], "zirkulare Primzahl" : ["circular prime"], "dritte Smarandache-Konstante" : ["third Smarandache constant"], "1 -additiv" : ["1 -additive"], "harmonische-Teiler-Zahl" : ["Ore number", "harmonic divisor number"], "Teiler" : ["divides", "divisor"], "transitiv" : ["transitive"], "1 -Abschluss" : ["1 -closure"], "natürliche Logarithmus" : ["natural logarithm"], "1 te Ableitung" : ["1 th derivative", "1 th derivative"], "vielfache Harshad-Zahl" : ["multiple Harshad number"], "gerichteter Graph" : ["oriented graph", "digraph", "directed graph"], "regulär" : ["regular", "1 -regular", "regular"], "Absolutbetrag" : ["absolute value"], "Hilbert-Primzahl" : ["Hilbert prime"], "Perrin-Zahlen" : ["Perrin number"], "Integralkosinus" : ["cosine integral", "cosine integral", "cosine integral"], "Potenz" : ["power", "power", "power", "power"], "kubischer Graph" : ["cubic graph"], "topologischer Raum" : ["topological space"], "Beraha-Konstante" : ["Beraha constant"], "dekadische Logarithmus" : ["common logarithm", "decadic logarithm", "decimal logarithm", "Briggsian logarithm"], "surjektiv" : ["surjective"], "super-Catalan-Zahl" : ["super-Catalan number", "Schröder-Hipparchus number", "super-Catalan number", "Schröder-Hipparchus number"], "abgeschloffen" : ["clopen"], "Pell-Lucas-Zahlen" : ["companion Pell number", "Pell-Lucas number"], "erste Skewes-Zahl" : ["first Skewes number", "Skewes number"], "Meertens-Zahl" : ["Meertens number"], "affin unabhängig" : ["affinely independent"], "1 -Ulam-Folge" : ["1 -Ulam sequence"], "asymptotische Dichte" : ["asymptotic density"], "Fischer–Griess Monster" : ["Friendly Giant", "Fischer–Griess monster", "monster group"], "reellen Zahlen reelle" : ["real number"], "1 – 2 -Weg" : ["1 – 2 path", "1 – 2  path"], "Giuga-Zahl" : ["Giuga number"], "Silberne Schnitt" : ["silver ratio"], "Knoten" : ["node", "vertices", "junction", "point", "node", "vertices"], "verallgemeinerte Woodall-Primzahl" : ["generalized Woodall prime"], "sechzehnte Smarandache-Konstante" : ["sixteenth smarandache constant", "sixteenth Smarandache constant"], "Erdös-Borwein-Konstante" : ["Erdös-Borwein constant"], "Googolplexplexplex" : ["googolplexplexplex"], "Teilerfunktion" : ["divisor function"], "Hardy-Ramanujan-Zahl" : ["Hardy-Ramanujan number"], "Palindromzahlen" : ["palindromic number"], "Lagrange Notation" : ["Lagrange’s notation"], "Ore-Zahl" : ["Ore number", "harmonic divisor number"], "Teilersummenfunktion" : ["sum-of-divisors function"], "Mantisse" : ["mantissa", "significand"], "Idoneal-Zahl" : ["idoneal number"], "Kubikzahl" : ["cube"], "Rechteckzahl" : ["rectangular number", "oblong number", "pronic number"], "Kolumbianische Zahl" : ["Devlali number", "Colombian number", "self number"], "Null" : ["zero"], "Moufang Loop" : ["Moufang loop"], "Primzahlvierling" : ["prime quadruple", "prime quadruplet"], "Nachbar" : ["neighbour", "adjacent"], "Weg" : ["path"], "Smarandache-Wellin-Zahl" : ["Smarandache-Wellin number"], "Wilson-Primzahl" : ["Wilson prime"], "Ableitungsfunktion" : ["derivative function"], "komplexen Zahlen b" : ["complex number"], "generiert" : ["generated"], "Paar" : ["pair"], "Integralsinus" : ["sine integral", "sine integral"], "Laufindex" : ["index of summation", "index of multiplication"], "Topologie" : ["topology", "open set topology"], "Fastprimzahl n-ter Ordnung" : ["almost prime"], "teilbar" : ["divides", "divisor"], "ganzzahligen Quotienten" : ["integer quotient", "integer quotient"], "Eulers Notation" : ["Euler’s notation"], "beidseitiges Ideal" : ["ideal", "two-sided ideal"], "Vektorprodukt" : ["vector product"], "Senke" : ["sink"], "quasigeordnete Menge" : ["proset", "preordered set"], "Carmichael-Zahl" : ["Carmichael number"], "glücklichen Zahlen von Euler" : ["lucky numbers of Euler"], "nicht-normalisierte sinc-Funktion" : ["unnormalized sinc function"], "sichere Primzahl" : ["safe prime"], "Extravagante-Zahl" : ["extravagant number"], "erste Ableitung" : ["first derivative"], "dreizehnte Smarandache-Konstante" : ["thirteenth smarandache constant", "thirteenth Smarandache constant"], "Umfang" : ["circumference"], "Silver-Konstante" : ["Silver constant"], "Nicht-Hypotenuse-Zahl" : ["nonhypotenuse number"], "Copeland-Erdös-Zahl" : ["Copeland-Erdös constant"], "Taylorreihe" : ["Mclaurin series", "Taylor series"], "Achilles Zahl" : ["Achilles number"], "Primfaktorzerlegung" : ["Prime factorization"], "Modul" : ["modulus"], "Äquidigital-Zahl" : ["equidigital number"], "Subtraktion" : ["subtraction", "Subtraction", "Subtraction"], "linkes Ideal" : ["left ideal"], "Kardinalität" : ["size", "cardinality"], "starke Primzahl" : ["strong prime"], "Carol-Zahl" : ["Carol number"], "glatte Zahl" : ["1 -smooth"], "summierte Mangoldt-Funktion" : ["summatory von Mangoldt function", "Chebyshev function"], "neunte Smarandache-Konstante" : ["ninth Smarandache constant"], "Euclidische Raum" : ["Euclidean space"], "echter Teiler" : ["non-trivial divisor", "proper"], "hyperbolische Integralkosinus" : ["hyperbolic cosine integral"], "Nullteiler" : ["zero divisor"], "Keith-cluster i" : ["Keith cluster"], "definitionale Gleichung" : ["definitional equation"], "1 -glatt" : ["1 -smooth"], "Googolplex" : ["googolplex"], "Radikal einer ganzen Zahl" : ["radical of an integer"], "Magma" : ["magma", "groupoid"], "endlich" : ["finite"], "normalisiert" : ["normalized"], "imaginäre Einheit" : ["imaginary unit"], "Catalan-Mersenne-Zahlen" : ["Catalan-Mersenne number"], "assoziativ" : ["associative"], "Rechteckszahl" : ["rectangular number", "oblong number", "pronic number"], "Isomorphismus" : ["isomorphism"], "Teilung" : ["separation", "proper", "order"], "Repunit-Primzahl" : ["repunit prime"], "Wagstaff-Primzahl" : ["Wagstaff prime"], "1  mal differenzierbar" : ["1 times differentiable", "1  times differentiable"], "Kind" : ["child"], "Zahlentheorie" : ["Number theory"], "normale" : ["normal"], "Baum" : ["tree"], "terminal" : ["sink"], "verallgemeinerte Cullen-Zahl" : ["generalized Cullen number"], "Lucas-Polynome" : ["Lucas polynomials"], "Maximum" : ["maximum"], "relativ prim" : ["mutually prime", "relatively prime", "co-prime", "coprime"], "Knödel-Zahl" : ["Knoedel number"], "Minimalgrad" : ["minimum degree"], "annährend gleich" : ["approximately equal"], "Fakultäts-Primzahlen" : ["Factorial primes"], "konvergent" : ["convergent"], "Identitätsfunktion" : ["identity function"], "triviale divisor" : ["trivial divisor"], "Fortunate-Primzahl" : ["Fortunate prime"], "Reihe" : ["series"], "Standard-Ulam-Folge" : ["standard Ulam sequence"], "Fastprimzahl" : ["2-almost prime", "pq number", "biprime", "semiprime", "2-almost prime"], "Summationsindex" : ["index of summation"], "höfliche Zahl" : ["polite number"], "Gruppe" : ["group", "group"], "Eulersches Quadrat" : ["Euler square", "Greco-Latin square"], "Ramanujan-Soldner-Konstante" : ["Ramanujan-Soldner constant"], "Harshadmorphic-Zahl f" : ["Nivenmorphic number"], "Sierpinski-Konstante w" : ["Sierpinski’s constant"], "NSW-Primzahl " : ["NSW prime", "Newman-Shanks-Williams prime"], "Partialsummenfolge" : ["sequence of partial sums", "sequence of partial sums"], "subharmonische Reihe" : ["subharmonic series"], "Zeisel-Zahl" : ["Zeisel number"], "größte gemeinsame Teiler" : ["highest common factor", "greatest common factor", "greatest common divisor"], "einfach normale" : ["simply normal"], "Funktion" : ["function"], "Cassini-Identität" : ["Cassini identity"], "Plastic-Zahl" : ["plastic constant", "plastic number"], "Exponent" : ["exponent", "exponent", "exponent", "exponent"], "all-Niven-Zahl" : ["all-Niven number", "all-Harshad number"], "unendlich" : ["infinite"], "Eins" : ["one"], "Kantengraph" : ["line graph"], "Iban-Zahlen" : ["Iban number"], "Zentral-Polygonal-Zahl" : ["lazy caterer’s sequence", "central polygonal number"], "rechter Nullteiler" : ["right zero divisor"], "Beharrlichkeit" : ["multiplicative persistence"], "Durchschnittsgrad" : ["average degree"], "Ulam-Zahlen" : ["Ulam number"], "alpha-magisches Quadrat" : ["alphamagic square"], "Multiplikationsbereich" : ["range of multiplication", "range of multiplication"], "Feynman-Punkt" : ["Feynman point"], "Brunsche Konstante für Primzahlvierlinge" : ["Brun’s constant for prime quadruplets", "Brun’s constant for prime quadruplets", "Brun’s constant for prime quadruplets", "Brun’s constant for prime quadruplets"], "Möbiusfunktion" : ["Moebius function"], "Mersenne-Primzahl" : ["Mersenne prime"], "Quasigruppe" : ["quasigroup"], "leere Produkt" : ["empty product", "nullary product"], "wissenschaftlicher Notation" : ["scientific notation", "scientific notation"], "glatt" : ["infinitely differentiable", "smooth"], "Thabit-Zahl" : ["Thabit number"], "Primzahlsechsling" : ["prime sextuplet"], "Woodall-Primzahlen" : ["Woodall prime"], "konvex" : ["convex"], "Cabtaxi-Zahl" : ["cabtaxi number"], "Oban-Zahlen" : ["Oban number"], "ägyptischer Bruch" : ["Egyptian fraction"], "irrationale Zahl" : ["irrational number"], "Fibonacci Zahlen" : ["Fibonacci sequence", "Fibonacci series", "Fibonacci numbers"], "Hausdorffraum" : ["Hausdorff space"], "Summen-Produkt-Zahl" : ["sum-product number"], "assoziatives magisches Quadrat" : ["associative magic square"], "supersinguläre Primzahl" : ["supersingular prime"], "primitiv" : ["primitive Pythagorean triple"], "Hausdorff-Topologie" : ["Hausdorff topology"], "Antimagisches Quadrat" : ["antimagic square"], "Pell-Zahlen" : ["Pell number"], "Befreundete Zahlen" : ["Amicable number"], "Quadratzahl" : ["square number", "square"], "positiven natürlichen Zahlen" : ["positive natural number"], "Quotient" : ["quotient"], "absolut nicht-normal" : ["absolutely abnormal", "absolutely non-normal"], "normalisierten Gleitkommazahlen" : ["normalized", "normalized"], "1 -gleich" : ["alphabetic variant", "1 -equal"], "Startknoten" : ["start"], "hyperbolische Integralsinus" : ["hyperbolic sine integral"], "reflexiv" : ["reflexive"], "Bögen" : ["edge"], "Fibonacci-Wieferich-Primzahl" : ["Fibonacci-Wieferich prime", "Wall-Sun-Sun prime"], "Logarithmus" : ["logarithm"], "magische Konstante" : ["magic constant"], "Basis" : ["base", "base", "base", "base"], "Argumentbereich" : ["domain"], "Golomb-Dickman-Konstante" : ["Golomb-Dickman constant"], "Catalan-Identität" : ["Catalan identity"], "leeren Summe" : ["nullary sum", "empty sum"], "Catalan-Zahlen" : ["Catalan number"], "zusammenhängender" : ["connected graph"], "harmonische Reihe" : ["harmonic series"], "Verallgemeinerte harmonische Reihen" : ["general harmonic series"], "1 -rough-Zahl" : ["1 -rough number"], "Realteil" : ["real part"], "Blum-Zahl" : ["Blum integer"], "Tschebyschow-Funktion" : ["summatory von Mangoldt function", "Chebyshev function"], "Doppel-Mersenne-Primzahl" : ["double Mersenne prime"], "Integrallogarithmus" : ["logarithmic integral", "logarithmic integral", "integral logarithm", "logarithmic integral", "logarithmic integral", "integral logarithm"], "Limes superior" : ["limit superior", "supremum limit", "superior limit", "upper limit", "outer limit"], "Delannoy-Zahl" : ["Delannoy number"], "Fibonacci-Polynome" : ["Fibonacci polynomials"], "Kreis" : ["cycle"], "partielle Funktion" : ["partial function"], "freundliches 1 -Tupel" : ["friendly 1 -tuple"], "Repunit-Zahl" : ["repunit"], "glücklichen Zahlen" : ["lucky numbers", "lucky number"], "abc-Vermutung" : ["ABC Conjecture"], "Wieferich-Primzahl" : ["Wieferich prime"], "Pillai-Primzahl" : ["Pillai prime"], "negative ganze Zahlen" : ["negative integer"], "einfach normale Zahl zur Basis 1" : ["simply normal in base"], "Poulet-Zahlen" : ["Poulet number"], "Selbst-Zahl" : ["Devlali number", "Colombian number", "self number"], "Minimum" : ["minimum"], "transtiv-reflexiven Abschluss" : ["transitive-reflexive closure"], "Legendre-Symbol" : ["Legendre symbol"], "verallgemeinerte Cullen-Primzahl" : ["generalized Cullen prime"], "siebente Smarandache-Konstante" : ["seventh smarandache constant", "seventh Smarandache constant"], "Kronecker-Symbol" : ["Kronecker symbol"], "alphabetische Variante" : ["alphabetic variant", "1 -equal"], "kommutativ" : ["commutative"], "vollständig" : ["complete", "complete"], "kreuzungsfrei" : ["independent"], "Taxicab-Zahl" : ["taxicab number"], "Primzahlzwilling" : ["prime twin"], "gut" : ["good"], "Keith-Zahl" : ["Keith number"], "Multiplikationsindex" : ["index of multiplication"], "Halbring" : ["semiring"], "Artikulation" : ["cutvertex"], "Euler-Zahlen" : ["Euler number"], "Farey-Folge" : ["Farey sequence"], "sum of squares" : ["sum of squares function"], "Primzahlfünfling" : ["prime quintuplet"], "Pythagoras-Box" : ["Pythagorean box"], "Balance-Primzahl" : ["balanced prime"]}, "ro" : {"Obermenge" : ["super-mulţime"], "echte Teilmenge" : ["submulţime proprie"], "Potenzmenge" : ["mulţimea tuturor submulţimilor"], "Durchschnitt" : ["intersecţia"], "leere Menge" : ["Mulţimea vidă"], "Differenz" : ["diferenţa"], "disjunkt" : ["disjuncte"], "echte Obermenge" : ["submulţime proprie"], "Schnitt" : ["intersecţia"], "gleich" : ["egale"], "Paare" : ["perechi"], "Teilmenge" : ["submulţime"], "paarweise disjunkt" : ["familie de mulţimi disjuncte ", "familie de mulţimi disjuncte "], "Paar" : ["pereche"], "Vereinigung" : ["reuniunea", "reuniunea"]}}, "ru" : {"ro" : {"set difference" : ["diferenţa"], "empty set" : ["Mulţimea vidă"], "union" : ["reuniunea", "reuniunea"], "equal" : ["egale"]}, "tr" : {"set difference" : ["fark kümesi"], "empty set" : ["Boş küme"], "union" : ["birleşim", "birleşim"], "equal" : ["eşit"]}, "de" : {"set difference" : ["Differenz"], "empty set" : ["leere Menge"], "union" : ["Vereinigung", "Vereinigung"], "equal" : ["gleich"]}}, "tr" : {"bg" : {"ayrık" : ["disjoint"], "karşılıklı olarak ayrık" : ["pairwise disjoint", "mutually disjoint"], "çift olarak ayrık" : ["pairwise disjoint", "mutually disjoint"], "üssü küme" : ["power set"]}, "de" : {"ayrık" : ["disjunkt"], "üssü küme" : ["Potenzmenge"], "karşılıklı olarak ayrık" : ["paarweise disjunkt"], "birleşim" : ["Vereinigung", "Vereinigung"], "düzgün alt küme" : ["echte Teilmenge", "echte Obermenge"], "fark kümesi" : ["Differenz"], "çift" : ["Paare", "Paar"], "Boş küme" : ["leere Menge"], "alt" : ["Teilmenge"], "çift olarak ayrık" : ["paarweise disjunkt"], "üst küme" : ["Obermenge"], "eşit" : ["gleich"], "kesişim" : ["Durchschnitt", "Schnitt"]}, "ru" : {"eşit" : ["equal"], "fark kümesi" : ["set difference"], "birleşim" : ["union", "union"], "Boş küme" : ["empty set"]}, "en" : {"düzgün alt küme" : ["proper superset", "proper subset"], "çift" : ["pairs", "pair"], "alt" : ["subset"], "üst küme" : ["superset"], "kesişim" : ["intersection", "intersection"]}, "ro" : {"ayrık" : ["disjuncte"], "üssü küme" : ["mulţimea tuturor submulţimilor"], "karşılıklı olarak ayrık" : ["familie de mulţimi disjuncte ", "familie de mulţimi disjuncte "], "birleşim" : ["reuniunea", "reuniunea"], "düzgün alt küme" : ["super-mulţime proprie", "submulţime proprie"], "fark kümesi" : ["diferenţa"], "çift" : ["perechi", "pereche"], "Boş küme" : ["Mulţimea vidă"], "alt" : ["submulţime"], "çift olarak ayrık" : ["familie de mulţimi disjuncte ", "familie de mulţimi disjuncte "], "üst küme" : ["super-mulţime"], "eşit" : ["egale"], "kesişim" : ["intersecţia", "intersecţia"]}}, "en" : {"ro" : {"intersection" : ["intersecţia", "intersecţia"], "subset" : ["submulţime"], "pairs" : ["perechi"], "superset" : ["super-mulţime"], "pair" : ["pereche"], "proper subset" : ["submulţime proprie"], "proper superset" : ["super-mulţime proprie"]}, "tr" : {"intersection" : ["kesişim", "kesişim"], "subset" : ["alt"], "pairs" : ["çift"], "superset" : ["üst küme"], "pair" : ["çift"], "proper subset" : ["düzgün alt küme"], "proper superset" : ["düzgün alt küme"]}, "de" : {"quotient" : ["Quotienten", "Quotient"], "Additon" : ["Addition"], "endvertices" : ["Ende", "Endecken", "Endecke"], "Regular number" : ["Reguläre Zahlen"], "quasiperfect number" : ["quasiperfekte Zahl", "leicht abundant"], "1 -smooth" : ["glatte Zahl", "1 -glatt"], "Lobb number" : ["Lobb-Zahl"], "near Wilson prime" : ["Nah-Wilson-Primzahl"], "countable" : ["abzählbar"], "repdigit" : ["Schnapszahl"], "sixteenth smarandache constant" : ["sechzehnte Smarandache-Konstante"], "cosine integral" : ["Integralkosinus", "Integralkosinus", "Integralkosinus"], "Motzkin prime" : ["Motzkin-Primzahl"], "radical of an integer" : ["Radikal einer ganzen Zahl"], "repunit prime" : ["Repunit-Primzahl"], "continuous" : ["stetig"], "NSW prime" : ["NSW-Primzahl ", "Newman-Shanks-Williams-Primzahl"], "Cassini identity" : ["Cassini-Identität"], "pq number" : ["Fastprimzahl", "Halbprimzahl"], "divisor" : ["trivialen Teiler", "teilbar", "teilt", "Teiler"], "second Chebyshev" : ["zweite Tschebyschow-Funktion"], "inner limit" : ["Limes inferior"], "first derivative" : ["erste Ableitung"], "normal in base 1" : ["normale Zahl zur Basis 1"], "span" : ["aufspannt"], "parent" : ["Elternknoten"], "converges" : ["konvergiert", "konvergiert"], "primary pseudoperfect number" : ["Primär-Pseudoperfekte-Zahl"], "upper limit" : ["Limes superior"], "primitive root" : ["Primitivwurzel"], "quasiorder" : ["Quasiordnung "], "silver ratio" : ["Silberne Schnitt"], "Stern prime" : ["Stern-Primzahl"], "integral logarithm" : ["Integrallogarithmus", "Integrallogarithmus"], "sine integral" : ["Integralsinus", "Integralsinus"], "Ramanujan-Soldner constant" : ["Ramanujan-Soldner-Konstante"], "series" : ["Reihe"], "Brun’s constant" : ["Brunsche Konstante"], "Greco-Latin square" : ["Eulersches Quadrat", "griechisch-lateinisches Quadrat"], "cutvertex" : ["Artikulation"], "supremum limit" : ["Limes superior"], "Sexy primes" : ["Sexy-Primzahlen"], "seventh smarandache constant" : ["siebente Smarandache-Konstante"], "convex" : ["konvex"], "Woodall number" : ["Woodall-Zahl", "Woodall-Zahlen"], "Riesel number" : ["Riesel-Zahl"], "normal magic square" : ["normales magisches Quadrat"], "Achilles number" : ["Achilles Zahl"], "1 -closure" : ["1 -Abschluss"], "all-Niven number" : ["all-Niven-Zahl", "all-Harshad-Zahl"], "multiplication" : ["Multiplikation"], "first Chebyshev function" : ["erste Tschebyschow-Funktion"], "Keith number" : ["Keith-Zahl"], "complex number" : ["komplexen Zahlen b"], "leftsided limit" : ["linksseitige Grenzwert"], "Gelfond-Schneider constant" : ["Hilbert-Zahl", "Gelfond-Schneider Konstante"], "twelfth Smarandache constant" : ["zwölften Smarandache-Konstanten"], "aspiring number" : ["ehrgeizige Zahl"], "perfect number" : ["perfekte Zahl", "vollkommene Zahl"], "factorial" : ["Faktorielle", "Fakultät"], "panmagic square" : ["Panmagischen Quadrat"], "maximum length" : ["maximale Läenge"], "Smarandache-Wellin number" : ["Smarandache-Wellin-Zahl"], "induce" : ["induziert"], "cyclic number" : ["zyklische Zahl"], "generalized Cullen prime" : ["verallgemeinerte Cullen-Primzahl"], "point" : ["Knoten", "Punkte", "Ecken"], "Niven number" : ["Niven-Zahl", "Harshad-Zahl"], "defined piecewise" : ["stückweise definiert"], "source" : ["Quelle", "initial"], "Schröder number" : ["Schröder-Zahl"], "Kronecker symbol" : ["Kronecker-Symbol"], "loop" : ["Loop"], "Eban number" : ["Eban-Zahlen"], "Silver constant" : ["Silver-Konstante"], "partial function" : ["partielle Funktion"], "Lychrel number" : ["Lychrel-Zahl"], "alphabetic variant" : ["alphabetische Variante", "1 -gleich"], "right-truncatable prime" : ["Rechtstrunkierbare Primzahlen"], "Sociable number" : ["Soziale Zahlen"], "logarithmic integral" : ["Integrallogarithmus", "Integrallogarithmus", "Integrallogarithmus", "Integrallogarithmus"], "adjacent" : ["Nachbar", "adjazent"], "alternating harmonic series" : ["alternierende harmonische Serie"], "Mills prime" : ["Mills-Primzahl"], "path" : ["Pfad", "Weg"], "commutative" : ["kommutativ"], "independent" : ["unabhängig", "kreuzungsfrei"], "harmonic number" : ["harmonische Zahl"], "Aban number" : ["Aban-Zahlen"], "remainder" : ["Rest"], "nullary sum" : ["leeren Summe", "leere Summe"], "chord" : ["Sehne"], "1 th derivative" : ["1 te Ableitung", "1 te Ableitung"], "Pierpont prime" : ["Pierpont-Primzahl"], "size" : ["Kardinalität"], "prime sextuplet" : ["Primzahlsechsling"], "total function" : ["totale Funktion"], "relation" : ["Relation"], "Prime factorization" : ["Primfaktorzerlegung"], "safe prime" : ["sichere Primzahl"], "vector product" : ["Vektorprodukt"], "Hausdorff space" : ["Hausdorffraum"], "ideal" : ["Ideal", "beidseitiges Ideal"], "interprime" : ["Zwischenprimzahl"], "Newman-Shanks-Williams prime" : ["NSW-Primzahl ", "Newman-Shanks-Williams-Primzahl"], "Skewes number" : ["erste Skewes-Zahl", "Skewes-Zahl"], "field" : ["Körper"], "smooth" : ["unendlich differenzierbar", "glatt"], "Euler’s constant" : ["Eulersche Zahl"], "eighth Smarandache constant" : ["achte Smarandache-Konstante"], "Stoneham number" : ["Stoneham-Zahlen"], "totally ordered set" : ["total geordnete Menge"], "sixth Smarandache constant" : ["sechste Smarandache-Konstante"], "fifteenth Smarandache constant" : ["fünfzehnte Smarandache-Konstante"], "Carol number" : ["Carol-Zahl"], "cyclic" : ["zyklisch"], "divisor function" : ["Teilerfunktion"], "projection" : ["Projektion", "Projektion"], "lower limit" : ["Limes inferior"], "elite" : ["elitär"], "linear order" : ["lineare Ordnung"], "repunit" : ["Repunit-Zahl"], "root" : ["Wurzel", "Wurzel", "Wurzel"], "degree" : ["Grad"], "Poulet number" : ["Poulet-Zahlen"], "real part" : ["Imaginärteil", "Realteil"], "Hausdorff topology" : ["Hausdorff-Topologie"], "supersingular prime" : ["supersinguläre Primzahl"], "highest common factor" : ["größte gemeinsame Teiler"], "intersection" : ["Durchschnitt", "Schnitt"], "alphamagic square" : ["alpha-magisches Quadrat"], "decimal logarithm" : ["dekadische Logarithmus", "Zehnerlogarithmus"], "Ulam number" : ["Ulam-Zahlen"], "proper" : ["Teilung", "Ordnung", "echter Teiler", "echten", "nichttrivialen Teiler"], "natural density" : ["natürliche Dichte"], "image" : ["Bild", "Bild"], "thirteenth smarandache constant" : ["dreizehnte Smarandache-Konstante"], "lowest common multiple" : ["kleinste gemeinsame Vielfache", "kleinste gemeinsame Vielfache"], "summatory von Mangoldt function" : ["summierte Mangoldt-Funktion", "Tschebyschow-Funktion"], "closed" : ["geschlossen .", "abgeschlossen o"], "line" : ["Pfeile", "Linien", "Kanten"], "subtraction" : ["Subtraktion"], "all-Harshad number" : ["all-Niven-Zahl", "all-Harshad-Zahl"], "1 -additive" : ["1 -additiv"], "good" : ["gut"], "minimum degree" : ["Minimalgrad"], "Legendre symbol" : ["Legendre-Symbol"], "Fibonacci series" : ["Fibonacci Zahlen"], "Euclidean space" : ["Euclidische Raum"], "cubefree taxicab number" : ["kubikfreie Taxicab-Zahl"], "1 -ful number" : ["1 -potente Zahl"], "least common multiple" : ["kleinste gemeinsame Vielfache", "kleinste gemeinsame Vielfache"], "reverse Keith number" : ["reverse Keith-Zahl"], "Catalan identity" : ["Catalan-Identität"], "isomorphism" : ["Isomorphismus"], "zero" : ["Null", "Nullstelle"], "distance function" : ["Abstandsfunktion", "Metrik"], "outdegree" : ["Ausgangsgrad"], "Copeland-Erdös constant" : ["Copeland-Erdös-Zahl"], "normal" : ["normale"], "harmonic divisor number" : ["Ore-Zahl", "harmonische-Teiler-Zahl"], "friendly pair" : ["freundliches Paar"], "1 -Ulam number" : ["1 -Ulam-Zahlen"], "barrier" : ["Barriere"], "1 -simplex" : ["1 -Simplex"], "domain" : ["Argumentbereich"], "double Mersenne prime" : ["Doppel-Mersenne-Primzahl"], "asymptotic density" : ["asymptotische Dichte"], "closed ball" : ["geschlossene Kugel"], "Pythagorean box" : ["Pythagoras-Box"], "Lagrange’s notation" : ["Lagrange Notation"], "1 -dim Cartesian space" : ["1 -dimenionale Cartesische Raum"], "Euclid Mullin sequence" : ["Euklid-Mullin-Folge"], "neighbour" : ["Nachbar", "adjazent"], "proset" : ["quasigeordnete Menge"], "Sierpinski number" : ["Sierpinski-Zahl"], "multiplicative digital root" : ["iterierte Querprodukt"], "Riemann hypothesis" : ["Riemann’sche Vermutung"], "Pillai prime" : ["Pillai-Primzahl"], "uniformly convergent" : ["gleichmäßig konvergent"], "Padovan number" : ["Padovan-Zahlen"], "absolutely non-normal" : ["absolut unnormal", "absolut nicht-normal"], "Napier’s constant" : ["Eulersche Zahl"], "harmonic series" : ["harmonische Reihe"], "cardinality" : ["Kardinalität"], "anti-reflexive" : ["irreflexiv", "antireflexiv"], "cubic graph" : ["kubischer Graph"], "Riemann zeta function" : ["Riemannsche Zetafunction"], "integer interval" : ["ganzzahlige Intervall"], "Latin square" : ["lateinisches Quadrat"], "magma" : ["Magma", "Gruppoid", "Binar", "Operativ"], "multiplicative persistence" : ["Beharrlichkeit"], "infimum limit" : ["Limes inferior"], "Blum integer" : ["Blum-Zahl"], "vector" : ["Vektor"], "sparse totally antimagic square" : ["schwachbesetztes totales antimagisches Quadrat"], "ceiling" : ["Aufrundung"], "branch" : ["Pfeile", "Linien", "Kanten"], "googol" : ["Googol"], "interior" : ["Innere"], "ABC Conjecture" : ["abc-Vermutung"], "affinely independent" : ["affin unabhängig"], "separation" : ["Teilung", "Ordnung"], "lucky number" : ["glücklichen Zahlen", "glückliche Zahl"], "ninth Smarandache constant" : ["neunte Smarandache-Konstante"], "emirp" : ["Mirpzahlen"], "Cullen numbers of the second kind" : ["Woodall-Zahl", "Woodall-Zahlen"], "Lucas numbers" : ["Lucas-Zahlen"], "digital root" : ["iterierte Quersumme"], "ultramagic square" : ["Ultramagisches Quadrat"], "Woodall prime" : ["Woodall-Primzahlen"], "Gelfond’s constant" : ["Gelfond’s Konstante"], "unit fraction" : ["Stammbruch"], "generalized Cullen number" : ["verallgemeinerte Cullen-Zahl"], "automorphism" : ["Automorphismus"], "1 -equal" : ["alphabetische Variante", "1 -gleich"], "relation on" : ["Relation auf"], "seventh Smarandache constant" : ["siebente Smarandache-Konstante"], "Devlali number" : ["Devlali-Zahl", "Kolumbianische Zahl", "Selbst-Zahl"], "arithmetical" : ["arithmetische Funktion", "zahlentheoretische"], "greatest common divisor" : ["größte gemeinsame Teiler"], "prime quadruplet" : ["Primzahlvierling"], "prime factor" : ["Primfaktor"], "bridge" : ["Brücke"], "asymmetric" : ["asymmetrisch"], "orthogonal array representation" : ["orthogonal"], "tenth smarandache constants" : ["zehnten Smarandache-Konstanten"], "Wilson number" : ["Wilson-Zahl"], "fifth Smarandache constant" : ["fünfte Smarandache-Konstante"], "frugal number" : ["Frugal-Zahl"], "Primorial primes" : ["Primorial-Primzahlen"], "second Skewes number" : ["zweite Skewes-Zahl"], "Beraha constant" : ["Beraha-Konstante"], "small set" : ["small-set"], "googolplexplexplex" : ["Googolplexplexplex"], "Moufang loop" : ["Moufang Loop"], "regular" : ["regulär", "1 -regulär", "regulär"], "cube" : ["Kubikzahl"], "cross product" : ["Kreuzprodukt"], "Wall-Sun-Sun prime" : ["Fibonacci-Wieferich-Primzahl", "Wall-Sun-Sun-Primzahl"], "Taylor series" : ["Taylorreihe"], "Pell-Lucas number" : ["Pell-Lucas-Zahlen", "Pell-Zahlen 2. Art", "Companion Pell-Zahlen"], "Proth prime" : ["Prothsche Primzahl"], "squareful number" : ["potente Zahl"], "normalized sinc function" : ["normalisierte sinc-Funktion"], "Golomb-Dickman constant" : ["Golomb-Dickman-Konstante"], "super-Catalan number" : ["super-Catalan-Zahl", "Schröder-Hipparchus-Zahl", "super-Catalan-Zahl", "Schröder-Hipparchus-Zahl", "super-Catalan-Zahlen )", "Schröder-Hipparchus-Zahlen"], "1 -fold Cartesian product" : ["1 -fache Cartesische Product"], "Euclid number" : ["Euklid-Zahlen"], "central Delannoy number" : ["Zentrale Delannoy-Zahlen"], "lazy caterer’s sequence" : ["Zentral-Polygonal-Zahl"], "convex hull" : ["konvexe Hülle e"], "irrational number" : ["irrationale Zahl"], "Meertens number" : ["Meertens-Zahl"], "negative integer" : ["negative ganze Zahlen"], "von Mangoldt function" : ["Mangoldt-Funktion"], "lower" : ["Endwert", "Startwert", "untere"], "abundance" : ["Abundanz"], "nullary product" : ["leere Produkt"], "real function" : ["reellwertige Funktion", "reelle Funktion"], "linked" : ["verbunden"], "googolplexplex" : ["Googolplexplex"], "equivalence class" : ["Äquivalenzklasse"], "palindromic number" : ["Palindromzahlen", "Zahlenpalindrome"], "surjective" : ["surjektiv"], "divides" : ["trivialen Teiler", "teilbar", "teilt", "Teiler"], "ring" : ["Ring", "Ring"], "Keith cluster" : ["Keith-cluster i"], "empty product" : ["leere Produkt"], "arithmetic" : ["arithmetische Funktion", "zahlentheoretische"], "range of summation" : ["Summationsbereich"], "partial sum" : ["Partialsumme"], "real number" : ["reellen Zahlen reelle"], "superior limit" : ["Limes superior"], "limit superior" : ["Limes superior"], "Harshad number" : ["Niven-Zahl", "Harshad-Zahl"], "circular prime" : ["zirkulare Primzahl"], "distributive" : ["distributiv"], "induced subgraph" : ["induzierter Teilgraph"], "generalized taxicab number" : ["verallgemeinerte Taxicab-Zahl"], "multi-relation expression" : ["multirelationionaler Ausdruck"], "Giuga number" : ["Giuga-Zahl"], "positive natural number" : ["positiven natürlichen Zahlen"], "generalized Woodall number" : ["verallgemeinerte Woodall-Zahl"], "congruent modulo" : ["kongruent modulo"], "Ramanujan 6-10-8 identity" : ["Ramanujan-6-10-8-Identität"], "Liouville constant" : ["Liouville-Konstante"], "associative" : ["assoziativ"], "number-theoretic function" : ["arithmetische Funktion", "zahlentheoretische"], "exponent" : ["Exponent", "Exponent", "Exponent", "Exponent"], "Fischer–Griess monster" : ["Fischer–Griess Monster", "Monstergruppe"], "Brun’s constant for cousin primes" : ["Brunsche Konstante für Cousin-Primzahlen"], "index of summation" : ["Summationsindex", "Laufindex"], "open" : ["offene Menge"], "pronic number" : ["Rechteckszahl", "Rechteckzahl", "pronische Zahl"], "infinite sum" : ["unendliche Summe"], "pointwise convergent" : ["punktweise konvergent"], "limit inferior" : ["Limes inferior"], "injective" : ["injektiv"], "Integer division" : ["Ganzzahlige Division", "Ganzzahlige Division"], "simply normal in base" : ["einfach normale Zahl zur Basis 1"], "natural logarithm" : ["natürliche Logarithmus"], "1 -powersmooth" : ["1 -potenzglatt"], "connected graph" : ["zusammenhängender"], "subcover" : ["Teilüberdeckung"], "groupoid" : ["Magma", "Gruppoid", "Binar", "Operativ"], "Pythagorean quadruple" : ["Pythagoräisches Quadrupel"], "square" : ["Quadratzahl"], "chordless" : ["sehnenlos"], "division" : ["Division"], "Moufang Identity" : ["Moufang Eigenschaft"], "Sylvester sequence" : ["Sylvester-Folge"], "double Mersenne number" : ["Doppel-Mersenne-Zahl"], "valency" : ["Valenz"], "trivial divisor" : ["triviale divisor"], "monoid" : ["Monoid"], "Euler square" : ["Eulersches Quadrat", "griechisch-lateinisches Quadrat"], "deficient number" : ["defizient"], "cake number" : ["Kuchen-Zahl"], "extravagant number" : ["Extravagante-Zahl"], "prime number" : ["Primzahl"], "Hausdorff limit" : ["Hausdorff-Grenzwert"], "greatest integer function" : ["Gaussklammer", "ganze Teil", "Abrundung"], "negative real number" : ["negativen reellen Zahlen"], "polite number" : ["höfliche Zahl"], "sum-of-divisors function" : ["Teilersummenfunktion"], "subharmonic series" : ["subharmonische Reihe"], "Bailey-Borwein-Plouffe formula" : ["Bailey-Borwein-Plouffe-Formel", "BBP-Formel"], "friendly 1 -tuple" : ["freundliches 1 -Tupel"], "Proth number" : ["Proth-Zahl", "Proth-Zahlen"], "oriented graph" : ["gerichteter Graph"], "scientific notation" : ["wissenschaftlicher Notation", "wissenschaftlicher Notation"], "strong prime" : ["starke Primzahl"], "base" : ["Basis", "Basis", "Basis", "Basis"], "self prime" : ["Selbst-Primzahl"], "Motzkin number" : ["Motzkin Zahlen", "Motzkin-Zahl"], "closure" : ["Abschluss"], "Moebius function" : ["Möbiusfunktion"], "finite" : ["endlich"], "associative magic square" : ["symmetrisches magisches Quadrat", "assoziatives magisches Quadrat"], "pre-image" : ["Urbild"], "absolute value" : ["Absolutbetrag"], "maximum degree" : ["Maximalgrad"], "child" : ["Kind"], "practical number" : ["praktische Zahl"], "hyperbolic cosine integral" : ["hyperbolische Integralkosinus"], "rectangular number" : ["Rechteckszahl", "Rechteckzahl", "pronische Zahl"], "partial order" : ["partielle Ordnung"], "infinitely differentiable" : ["unendlich differenzierbar", "glatt"], "Mercator series" : ["Mercator-Reihe"], "arc" : ["Pfeile", "Linien", "Kanten"], "maximum" : ["Maximum"], "1 -perfect" : ["multiperfekte Zahl", "1 -perfekt"], "multiperfect" : ["multiperfekte Zahl", "1 -perfekt"], "non-trivial divisor" : ["echter Teiler", "echten", "nichttrivialen Teiler"], "sink" : ["Senke", "terminal"], "number of vertices" : ["Eckenanzahl"], "harmonic mean" : ["harmonische Mittel"], "Pythagorean prime" : ["pythagoräische Primzahl"], "permutable prime" : ["permutierbare Primzahl"], "zerofree" : ["nullfrei"], "maximal connected subgraph" : ["maximaler"], "normalized" : ["normalisiert", "normalisierten Gleitkommazahlen", "normalisierten Gleitkommazahlen"], "aliquot sum" : ["Teilersumme"], "Fermat number" : ["Fermatsche Zahl"], "Delannoy number" : ["Delannoy-Zahl"], "smallest common multiple" : ["kleinste gemeinsame Vielfache", "kleinste gemeinsame Vielfache"], "irreflexive" : ["irreflexiv", "antireflexiv"], "reduced" : ["reduziert"], "mutually prime" : ["relativ prim", "teilerfremd"], "first Skewes number" : ["erste Skewes-Zahl", "Skewes-Zahl"], "Abelian" : ["Abelsch"], "Catalan-Mersenne number" : ["Catalan-Mersenne-Zahlen"], "primorial" : ["Primorial"], "unnormalized sinc function" : ["nicht-normalisierte sinc-Funktion"], "significand" : ["Mantisse"], "happy number" : ["fröhlich"], "1" : ["Eulersche Zahl"], "cover" : ["Überdeckung"], "convex polytope" : ["konvexes Polytop"], "Zeisel number" : ["Zeisel-Zahl"], "composite number" : ["zusammengesetzte Zahl"], "Cahen’s constant" : ["Cahen-Konstante", "Cahen-Konstante i"], "Jacobi symbol" : ["Jacobi-Symbol"], "fourth Smarandache constant" : ["vierten Smarandache-Konstanten"], "structure" : ["Struktur"], "additive structure" : ["additive Struktur"], "1 -regular" : ["regulär", "1 -regulär"], "binomial coefficient" : ["Binomialkoeffizient"], "third derivative" : ["dritte Ableitung"], "DAG" : ["azyklisch"], "Pythagorean triple" : ["pythagoreisches Zahlentripel"], "restriction" : ["Beschränkung"], "equal" : ["gleich"], "common logarithm" : ["dekadische Logarithmus", "Zehnerlogarithmus"], "converse relation" : ["konverse Relation"], "natural number" : ["natürlichen Zahlen"], "empty sum" : ["leeren Summe", "leere Summe"], "happy" : ["fröhlich"], "cyclic group" : ["zyklische Gruppe"], "definitional equation" : ["definitionale Gleichung"], "Wagstaff prime" : ["Wagstaff-Primzahl"], "complete" : ["vollständig", "vollständig"], "topological space" : ["topologischer Raum"], "definiens" : ["Definiens"], "1 – 2  path" : ["1 – 2 -Weg"], "heterosquare" : ["Hetero-Quadrat"], "subring generated" : ["generierten Subring"], "reflexive" : ["reflexiv"], "clopen" : ["abgeschloffen"], "panarithmic number" : ["praktische Zahl"], "Carmichael number" : ["Carmichael-Zahl"], "reversal" : ["Umkehrung"], "multiplicative structure" : ["multiplikative Struktur"], "Newton’s" : ["Newton"], "highly composite number" : ["hochzusammengesetzte Zahl"], "inner vertices" : ["inneren Ecken"], "range of multiplication" : ["Multiplikationsbereich", "Multiplikationsbereich"], "balanced prime" : ["Balance-Primzahl"], "Catalan number" : ["Catalan-Zahlen"], "subset" : ["Teilmenge"], "cycle" : ["Schleife", "Zykel", "Kreis"], "zero divisor" : ["Nullteiler"], "equidigital number" : ["Äquidigital-Zahl"], "central polygonal number" : ["Zentral-Polygonal-Zahl"], "nonhypotenuse number" : ["Nicht-Hypotenuse-Zahl"], "Thabit number" : ["Thabit-Zahl"], "sum of squares function" : ["sum of squares"], "special linear group" : ["spezielle lineare Gruppe"], "exponentiation" : ["Exponentiation"], "Farey sequence" : ["Farey-Folge"], "limit point" : ["Häufungspunkt"], "binary logarithm" : ["binäre Logarithmus"], "Perrin pseudoprime" : ["Perrin-Pseudoprimzahl"], "complete graph" : ["vollständiger Graph"], "indegree" : ["Eingangsgrad"], "Gregory number" : ["Gregory-Zahl"], "total ordering" : ["totale Ordnung", "einfache Ordnung"], "sum-product number" : ["Summen-Produkt-Zahl"], "1 -tuple" : ["1 -Tupel"], "floor" : ["Gaussklammer", "ganze Teil", "Abrundung"], "Semimagic square" : ["Semi-magische Quadrate"], "googolplexian" : ["Googolplexian"], "stable set" : ["stabile Mengen"], "Liouville number" : ["Liouvillesche Zahl"], "primitive Pythagorean triple" : ["primitiv"], "order" : ["Teilung", "Ordnung", "Ordnung"], "Mersenne number" : ["Mersenne-Zahl"], "simple" : ["einfach", "einfach"], "directed graph" : ["gerichteter Graph"], "Nivenmorphic number" : ["Harshadmorphic-Zahl f", "Nivenmorphic-Zahl"], "aliquot sequence" : ["Aliquot-Folge"], "lucky numbers" : ["glücklichen Zahlen", "glückliche Zahl"], "Multiplication" : ["Multiplikation", "Multiplikation"], "cabtaxi number" : ["Cabtaxi-Zahl"], "decadic logarithm" : ["dekadische Logarithmus", "Zehnerlogarithmus"], "Oban number" : ["Oban-Zahlen"], "left ideal" : ["linkes Ideal"], "thirteenth Smarandache constant" : ["dreizehnte Smarandache-Konstante"], "metric" : ["Abstandsfunktion", "Metrik"], "Higgs prime" : ["Higgs-Primzahl"], "partial ordering" : ["partielle Ordnung"], "function" : ["Funktion"], "plastic number" : ["Plastic-Konstante", "Plastic-Zahl"], "quasigroup" : ["Quasigruppe"], "Ore number" : ["Ore-Zahl", "harmonische-Teiler-Zahl"], "powerful number" : ["potente Zahl"], "Euclid-Mullin sequence" : ["Euklid-Mullin-Folge"], "generalized Woodall prime" : ["verallgemeinerte Woodall-Primzahl"], "pairs" : ["Paare"], "magic square" : ["magisches Quadrat"], "Chebyshev function" : ["summierte Mangoldt-Funktion", "Tschebyschow-Funktion"], "function space" : ["Raum der Funktionen"], "topology" : ["Topologie"], "preordered set" : ["quasigeordnete Menge"], "superset" : ["Obermenge"], "geometric mean" : ["geometrische Mittel"], "sequence of partial sums" : ["Partialsummenfolge", "Partialsummenfolge"], "generated" : ["generiert"], "1 -full number" : ["1 -potente Zahl"], "Hardy-Ramanujan number" : ["Hardy-Ramanujan-Zahl"], "Leibniz’s notation" : ["Leibniz Notation"], "Newton-Mercator series" : ["Mercator-Reihe"], "prime gap" : ["Primzahllücke"], "Lebesgue identity" : ["Lebesgue-Identität"], "two-sided ideal" : ["Ideal", "beidseitiges Ideal"], "equivalence relation" : ["Äquivalenzrelation"], "circumference" : ["Umfang"], "Briggsian logarithm" : ["dekadische Logarithmus", "Zehnerlogarithmus"], "disconnected" : ["nicht", "unzusammenhängend"], "Franel number" : ["Franel-Zahlen", "Franel-Zahlen"], "separate" : ["trennt"], "lucky prime" : ["glückliche Primzahlen"], "companion Pell number" : ["Pell-Lucas-Zahlen", "Pell-Zahlen 2. Art", "Companion Pell-Zahlen"], "leaf" : ["Blatt"], "Lucas polynomials" : ["Lucas-Polynome"], "plastic constant" : ["Plastic-Konstante", "Plastic-Zahl"], "weakly prime" : ["Schwache Primzahlen"], "Jacobsthal numbers" : ["Jacobsthal-Zahlen"], "acyclic" : ["azyklisch"], "googolplex" : ["Googolplex"], "modulus" : ["Modulus", "Modulus", "Modulus", "Modul"], "1 -Ulam sequence" : ["1 -Ulam-Folge"], "Kynea number" : ["Kynea-Zahl"], "ordered set" : ["geordnete Menge"], "Narayana number" : ["Narayana-Zahlen"], "Euler’s notation" : ["Eulers Notation"], "codomain" : ["Wertebereich"], "Friendly Giant" : ["Fischer–Griess Monster", "Monstergruppe"], "2-full numbers" : ["potente Zahl"], "Friendly number" : ["Freundliche Zahlen"], "mantissa" : ["Mantisse"], "Sierpinski’s constant" : ["Sierpinski-Konstante w"], "Brun’s constant for prime quadruplets" : ["Brunsche Konstante für Primzahlvierlinge", "Brunsche Konstante für Primzahlvierlinge", "Brunsche Konstante für Primzahlvierlinge", "Brunsche Konstante für Primzahlvierlinge"], "second smarandache constant" : ["zweite Smarandache-Konstante"], "end" : ["Ende", "Ende", "Endecken", "Endknoten"], "upper bound" : ["obere", "obere"], "Knoedel number" : ["Knödel-Zahl", "Knödel-Zahlen"], "transitive" : ["transitiv"], "Amicable number" : ["Befreundete Zahlen"], "proper subgroup" : ["echte Untergruppe"], "Wilson quotient" : ["Wilson-Quotient"], "tree" : ["Baum"], "approximately equal" : ["annährend gleich"], "square-full number" : ["potente Zahl"], "magic sum" : ["magische Summe"], "golden ratio" : ["goldene Schnitt"], "Pell number" : ["Pell-Zahlen"], "magic series" : ["magische Serie"], "Number theory" : ["Zahlentheorie"], "isomorphic" : ["isomorph"], "length" : ["Länge", "Länge", "Länge"], "Sarrus number" : ["Sarrus-Zahlen"], "Hilbert number" : ["Hilbert-Zahl", "Gelfond-Schneider Konstante", "Hilbert-Zahl"], "graph" : ["Graph", "Graph"], "node" : ["Knoten", "Knoten", "Punkte", "Ecken"], "abundancy" : ["Abundancy"], "empty graph" : ["leere"], "Baxter-Hickerson function" : ["Baxter-Hickerson-Funktion"], "Fibonacci polynomials" : ["Fibonacci-Polynome"], "least integer function" : ["Aufrundung"], "sixteenth Smarandache constant" : ["sechzehnte Smarandache-Konstante"], "lucky numbers of Euler" : ["glücklichen Zahlen von Euler"], "Hilbert prime" : ["Hilbert-Primzahl"], "digraph" : ["gerichteter Graph"], "positive real number" : ["positiven reellen Zahlen", "positiven reellen Zahlen"], "imaginary unit" : ["imaginäre Einheit"], "Cullen number" : ["Cullen-Zahl"], "inferior limit" : ["Limes inferior"], "pair" : ["Paar"], "not connected" : ["nicht", "unzusammenhängend"], "Schröder-Hipparchus number" : ["super-Catalan-Zahl", "Schröder-Hipparchus-Zahl", "super-Catalan-Zahl", "Schröder-Hipparchus-Zahl", "super-Catalan-Zahlen )", "Schröder-Hipparchus-Zahlen"], "lower bound" : ["Endwert", "Startwert", "untere Grenze"], "real-valued function" : ["reellwertige Funktion", "reelle Funktion"], "integer quotient" : ["ganzzahligen Quotienten", "ganzzahligen Quotienten"], "standard Ulam sequence" : ["Standard-Ulam-Folge"], "left zero divisor" : ["linker Nullteiler"], "line graph" : ["Kantengraph"], "1  times differentiable" : ["1 mal differenzierbar", "1 mal differeinzierbar", "1  mal differeinzierbar", "1  mal differenzierbar"], "Euler number" : ["Euler-Zahlen"], "edge" : ["Pfeile", "Linien", "Kanten", "Bögen", "Kanten"], "index of multiplication" : ["Multiplikationsindex", "Laufindex"], "multiple" : ["Vielfaches"], "second derivative" : ["zweite Ableitung"], "googolminex" : ["Googolminex"], "digit product" : ["Querprodukt"], "power" : ["Potenz", "Potenz", "Potenz", "Potenz"], "minimum" : ["Minimum"], "Egyptian fraction" : ["ägyptischer Bruch"], "Fibonacci-Wieferich prime" : ["Fibonacci-Wieferich-Primzahl", "Wall-Sun-Sun-Primzahl"], "antisymmetric" : ["antisymmetrisch"], "co-prime" : ["relativ prim", "teilerfremd"], "countably infinite" : ["abzählbar unendlich"], "Feynman point" : ["Feynman-Punkt"], "number of edges" : ["Kantenanzahl"], "logarithm" : ["Logarithmus"], "semiprime" : ["Fastprimzahl", "Halbprimzahl"], "derivative function" : ["Ableitungsfunktion"], "Colombian number" : ["Devlali-Zahl", "Kolumbianische Zahl", "Selbst-Zahl"], "Hurwitz zeta function" : ["Hurwitzsche Zetafunction"], "left-truncatable prime" : ["Linkstrunkierbare Primzahlen"], "good prime" : ["gute Primzahl"], "tenth Smarandache constants" : ["zehnten Smarandache-Konstanten"], "right ideal" : ["rechtes Ideal"], "Fermat pseudoprime" : ["Fermatsche Pseudoprimzahl"], "abundant number" : ["abundant"], "Fibonacci numbers" : ["Fibonacci Zahlen"], "sphenic number" : ["Sphenische Zahlen"], "Uban number" : ["Uban-Zahlen"], "1 -rough number" : ["1 -rough-Zahl"], "magic square of prime" : ["magisches Quadrat aus Primzahlen"], "start" : ["Startknoten"], "Cousin prime" : ["Cousin-Primzahlen"], "second Smarandache constant" : ["zweite Smarandache-Konstante"], "prime quadruple" : ["Primzahlvierling"], "hyperbolic sine integral" : ["hyperbolische Integralsinus"], "definiendum" : ["Definiendum"], "1 – 2 path" : ["1 – 2 -Weg"], "arithmetic mean" : ["arithmetische Mittel"], "strict ordering" : ["strikte Ordnung"], "1 -powerful number" : ["1 -potente Zahl"], "magic constant" : ["magische Konstante"], "digit sum" : ["Quersumme"], "undefined at" : ["undefiniert auf", "undefiniert auf"], "symmetric" : ["symmetrisch"], "prime twin" : ["Primzahlzwilling"], "minimum length" : ["minimale Länge"], "quadratic nonresidue" : ["quadratischer Nichtrest"], "Infinity" : ["Unendlichkeit"], "Leyland number" : ["Leyland-Zahl"], "Perrin number" : ["Perrin-Zahlen"], "Erdös-Borwein constant" : ["Erdös-Borwein-Konstante"], "Cauchy sequence" : ["Cauchyfolge"], "self number" : ["Devlali-Zahl", "Kolumbianische Zahl", "Selbst-Zahl"], "square number" : ["Quadratzahl"], "proper subgraph" : ["echter Teilgraph"], "biprime" : ["Fastprimzahl", "Halbprimzahl"], "idoneal number" : ["Idoneal-Zahl"], "bijective" : ["bijektiv"], "difference" : ["Differenz", "Differenz", "Differenz", "Differenz"], "fourteenth Smarandache constant" : ["vierzehnte Smarandache-Konstante"], "Wieferich prime" : ["Wieferich-Primzahl"], "girth" : ["Taillenweite"], "BBP formula" : ["Bailey-Borwein-Plouffe-Formel", "BBP-Formel"], "root mean square" : ["quadratische Mittel"], "proper subset" : ["echte Teilmenge", "echte Obermenge"], "relatively prime" : ["relativ prim", "teilerfremd"], "open set topology" : ["Topologie"], "component" : ["Komponenten", "Komponente"], "Mills’ constant" : ["Mills-Konstante"], "third Smarandache constant" : ["dritte Smarandache-Konstante"], "Wilson prime" : ["Wilson-Primzahl"], "Wolstenholme prime" : ["Wolstenholme-Primzahl"], "phi function" : ["Eulersche Phi-Funktion", "eulersche Funktion", "Eulersche 1 -Funktion"], "Factorial primes" : ["Fakultäts-Primzahlen"], "ringoid" : ["Ringoid"], "composition" : ["Verkettung"], "Fortunate number" : ["Fortunate-Zahl"], "group" : ["Gruppe", "Gruppe"], "2-almost prime" : ["Fastprimzahl", "Halbprimzahl", "Fastprimzahl", "Halbprimzahl"], "absolutely abnormal" : ["absolut unnormal", "absolut nicht-normal"], "identity function" : ["Identitätsfunktion"], "Diophantine equation" : ["Diophantische Gleichung"], "outer limit" : ["Limes superior"], "Fibonacci sequence" : ["Fibonacci Zahlen"], "differentiable" : ["differenzierbar"], "trivial subgroup" : ["triviale Untergruppe"], "junction" : ["Knoten", "Punkte", "Ecken"], "quadratic residue" : ["quadratischer Rest"], "multiple Harshad number" : ["vielfache Harshad-Zahl"], "Iban number" : ["Iban-Zahlen"], "coprime" : ["relativ prim", "teilerfremd"], "prime quintuplet" : ["Primzahlfünfling"], "sum" : ["Summe", "Summe", "Summe", "Summe"], "sparse antimagic square" : ["schwachbesetztes Antimagisches Quadrat"], "average degree" : ["Durchschnittsgrad"], "factorion" : ["Factorion"], "Subtraction" : ["Subtraktion", "Suptraktion", "Subtraktion"], "simply normal" : ["einfach normale"], "Smarandache function" : ["Smarandache-Funktion"], "right zero divisor" : ["rechter Nullteiler"], "oblong number" : ["Rechteckszahl", "Rechteckzahl", "pronische Zahl"], "taxicab number" : ["Taxicab-Zahl"], "one" : ["Eins"], "two-sided prime" : ["Beidseitig trunkierbare Primzahlen"], "Fortunate prime" : ["Fortunate-Primzahl"], "simple order" : ["totale Ordnung", "einfache Ordnung"], "happy prime" : ["fröhliche Primzahlen"], "preorder" : ["Quasiordnung "], "almost prime" : ["Fastprimzahl n-ter Ordnung", "n-Fastprimzahl"], "twelfth Smarandache constants" : ["zwölften Smarandache-Konstanten"], "quotient space" : ["Quotientenmenge"], "semiring" : ["Halbring"], "convergent" : ["konvergent"], "open ball" : ["offene Kugel"], "Mersenne prime" : ["Mersenne-Primzahl"], "Ramanujan’s constant" : ["Ramanujan-Konstante"], "vertices" : ["Knoten", "Knoten", "Punkte", "Ecken"], "standard form" : ["Standardform"], "complete space" : ["vollständiger Raum"], "sublime number" : ["sublime Zahl", "erhabene Zahl"], "compact" : ["kompakt"], "infinite" : ["unendlich"], "Fermat prime" : ["Fermatsche Primzahl"], "product" : ["Produkt", "Produkt", "Produkt"], "transitive-reflexive closure" : ["transtiv-reflexiven Abschluss"], "general harmonic series" : ["Verallgemeinerte harmonische Reihen"], "greatest common factor" : ["größte gemeinsame Teiler"], "Sophie Germain prime" : ["Sophie-Germain-Primzahl"], "repeated digital sum" : ["iterierte Quersumme"], "inverse function" : ["inverse Function"], "1 times differentiable" : ["1 mal differenzierbar", "1 mal differeinzierbar", "1  mal differeinzierbar", "1  mal differenzierbar"], "monster group" : ["Fischer–Griess Monster", "Monstergruppe"], "square-free" : ["quadratfrei"], "Wilbraham-Gibbs constant" : ["Wilbraham-Gibbs-Konstante"], "Mclaurin series" : ["Taylorreihe"], "subgroup" : ["Untergruppe"], "antimagic square" : ["Antimagisches Quadrat"]}}, "ro" : {"bg" : {"familie de mulţimi disjuncte " : ["pairwise disjoint", "mutually disjoint", "pairwise disjoint", "mutually disjoint"], "mulţimea tuturor submulţimilor" : ["power set"], "disjuncte" : ["disjoint"]}, "de" : {"pereche" : ["Paar"], "submulţime" : ["Teilmenge"], "egale" : ["gleich"], "submulţime proprie" : ["echte Teilmenge", "echte Obermenge"], "perechi" : ["Paare"], "mulţimea tuturor submulţimilor" : ["Potenzmenge"], "diferenţa" : ["Differenz"], "super-mulţime" : ["Obermenge"], "disjuncte" : ["disjunkt"], "intersecţia" : ["Durchschnitt", "Schnitt"], "reuniunea" : ["Vereinigung", "Vereinigung"], "Mulţimea vidă" : ["leere Menge"], "familie de mulţimi disjuncte " : ["paarweise disjunkt", "paarweise disjunkt"]}, "ru" : {"egale" : ["equal"], "diferenţa" : ["set difference"], "reuniunea" : ["union", "union"], "Mulţimea vidă" : ["empty set"]}, "tr" : {"pereche" : ["çift"], "submulţime" : ["alt"], "egale" : ["eşit"], "submulţime proprie" : ["düzgün alt küme"], "perechi" : ["çift"], "mulţimea tuturor submulţimilor" : ["üssü küme"], "diferenţa" : ["fark kümesi"], "super-mulţime" : ["üst küme"], "disjuncte" : ["ayrık"], "intersecţia" : ["kesişim", "kesişim"], "super-mulţime proprie" : ["düzgün alt küme"], "reuniunea" : ["birleşim", "birleşim"], "Mulţimea vidă" : ["Boş küme"], "familie de mulţimi disjuncte " : ["çift olarak ayrık", "karşılıklı olarak ayrık", "çift olarak ayrık", "karşılıklı olarak ayrık"]}, "en" : {"pereche" : ["pair"], "submulţime" : ["subset"], "submulţime proprie" : ["proper subset"], "perechi" : ["pairs"], "super-mulţime" : ["superset"], "intersecţia" : ["intersection", "intersection"], "super-mulţime proprie" : ["proper superset"]}}}