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der
     1. art. the
     2. art. feminine singular of der
     3. art. genitive plural of der
     4. pron. who; that; which
           Ich kenne einen Mann, der das kann. - I know a man who can do that.
     5. pron. feminine dative singular of der: (to) whom, which, that
     6. pron. (attributive, stressed) that
           Der Mann war es! - It was that man!
     7. pron. (indicative) him, he
           Der hat es getan! - It was him who did it!
     8. pron. (differential) the one, him
           Der mit dem Mantel - The one with the coat
     9. pron. feminine dative singular of der: (to) that, (to) her
Körper
     1. n-m. body (of a person, animal, etc.)
     2. n-m. (physics) body
     3. n-m. (geometry) body, solid (three-dimensional object)
     4. n-m. (algebra) field (algebraic structure with addition and multiplication)
der
     1. art. the
     2. art. feminine singular of der
     3. art. genitive plural of der
     4. pron. who; that; which
           Ich kenne einen Mann, der das kann. - I know a man who can do that.
     5. pron. feminine dative singular of der: (to) whom, which, that
     6. pron. (attributive, stressed) that
           Der Mann war es! - It was that man!
     7. pron. (indicative) him, he
           Der hat es getan! - It was him who did it!
     8. pron. (differential) the one, him
           Der mit dem Mantel - The one with the coat
     9. pron. feminine dative singular of der: (to) that, (to) her
reellen
     1. adj. form of reell
     reell
          1. adj. decent, solid, fair (of a company or person)
                reeller Marktpreis - fair market price
          2. adj. real
                reelle Chancen
          3. adj. (mathematics) the property of being an element of the set of real numbers
                reelle Zahlen - real numbers
Zahlen
     1. n. gerund of zahlen
     2. n. plural of Zahl
     3. v. to pay (money)
           Ich muss meine Steuern zahlen. - I have to pay my taxes.
           Er muss noch die Gebühr an die Verwaltung zahlen. - He still has to pay the fee to the administration.
     4. v. to pay for, to atone for
           Ich will keinen Fehler machen, für den ich später zahlen muss. - I don't want to make a mistake that I'll have to pay for later.
     Zahl
          1. n-f. number, numeral, figure
          2. n-f. tails (side of a coin)
ist
     1. v. third-person singular present of sein
     sein
          1. v. (copulative, with a predicate adjective or predicate nominative) to be
                Das ist schön. - That is beautiful.
                Das ist ein Auto. - That is a car.
          2. v. (with a dative object and certain adjectives) to feel, (to experience a condition)
                Usage: In this sense sein is always conjugated in the third person singular and takes a Dative noun. The impersonal subject es may be present, but is often taken as implied. For example: "Mir i
                Ist dir kalt? - Are you cold?
                Mir ist schlecht. - I'm sick.
                Dem Mann ist schwindelig. - The man feels dizzy.
                Den Kindern ist langweilig. - The children are bored.
          3. v. (with a dative object and nach or danach, sometimes with zumute) to feel like, to be in the mood for
                Usage: As in the previous sense sein takes a Dative noun and is always conjugated according to the impersonal subject es, although it is usually omitted.
                Uns ist nach einem Film zumute. - We feel like watching a movie.
                Mir ist nicht danach. - I don't feel like it.
          4. v. (auxiliary) forms the present perfect and past perfect tenses of certain intransitive verbs
                Er ist alt geworden. - He has become old.
          5. v. to exist; there to be; to be alive
                Was nicht ist, kann noch werden. (a common proverb) - That which does not exist now, may come into existence.
                Wenn ich nicht mehr bin, erbst du das Haus. - When I am no more, you'll inherit the house.
          6. v. to have the next turn (in a game, in a queue, etc.)
                Du bist. - It’s your turn.
                Du bist nach mir. - Your turn is after mine.
          7. v. to be "it"; to be the tagger in a game of tag
                Du bist! - You're it!
                Ich bin nicht mehr. - I'm not it anymore.
          8. det. his
                Daniel schickt seiner Schwester eine SMS. - Daniel is sending a text to his sister.
                Der Kater spielt oft mit seinen Spielsachen. - The cat often plays with his toys.
          9. det. its (agreeing with a masculine or neuter noun)
                der Mond und sein Licht - the moon and its light
                das Schaf und seine Lämmer - the sheep and its lambs
          10. det.          (informal) Used to express an approximate number, often with so.
                        Der kostet so seine zweihundert Euro. - That one costs around two hundred euros.
          11. det. one's
                Man muss seinem Herzen folgen. - One must follow one’s heart.
der
     1. art. the
     2. art. feminine singular of der
     3. art. genitive plural of der
     4. pron. who; that; which
           Ich kenne einen Mann, der das kann. - I know a man who can do that.
     5. pron. feminine dative singular of der: (to) whom, which, that
     6. pron. (attributive, stressed) that
           Der Mann war es! - It was that man!
     7. pron. (indicative) him, he
           Der hat es getan! - It was him who did it!
     8. pron. (differential) the one, him
           Der mit dem Mantel - The one with the coat
     9. pron. feminine dative singular of der: (to) that, (to) her
Bis
     1. n. (music) B-sharp
     2. conj. (subordinating, temporal) until
           Wir warten hier, bis das Gewitter vorbei ist. - We'll wait here until the thunderstorm is over.
     3. conj. (coordinating) to
           Ich arbeite 40 bis 50 Stunden in der Woche. - I work 40 to 50 hours a week.
           Ihre Haare sind braun bis dunkelbraun. - Her hair is brown to dark brown.
     4. prep. (temporal) until, to, (US) through
           Meine Tochter ist bis zwei Uhr in der Schule. - My daughter is at school until two o'clock.
           Ich war von Montag bis Freitag krank. - I was sick from Monday to Friday.
     5. prep. (temporal) by
           Die Aufgabe muss bis Donnerstag fertig sein. - The task must be complete by Thursday.
     6. prep. (local) to; all the way to
           Der Zug fährt bis Köln. - The train goes to Cologne.
auf
     1. prep. (with dative) on, upon (positioned at the top of)
           Das Buch liegt auf dem Tisch. - The book is lying on the table.
     2. prep. (with accusative) on, onto, up (moving to the top of)
           Ich lege das Buch auf den Tisch. - I’m putting the book on the table.
     3. prep. (with accusative) on (indicating responsibility)
           Das erste Getränk geht aufs Haus. - The first drink is on the house.
           Das fällt nicht auf dich zurück, sondern auf mich. Ich hab's vermasselt. - That's not on you but on me. I messed up.
     4. prep. (with dative) in, at; used with certain nouns instead of bei or in
           Niemand auf der Welt hätte das voraussehen können. - No one in the world could have predicted that.
           auf dem Stadtplatz - in the town square
           Das Schiff ist auf See - The ship is at sea.
           auf der Kirmes - at the fun fair
           auf der Post - at the post office (also: bei der Post)
     5. prep. (with accusative) to; used with certain nouns instead of zu or in
           auf die Kirmes - to the fun fair
           auf die Post - to the post office (also: zur Post)
     6. prep. (with a language name) in (see usage note below)
           Was heißt das auf Deutsch? - What’s this in German?
     7. prep. (linguistics) in (of a word: ending with some sound or syllable)
           Wörter auf -heit sind weiblich. - Words in -heit are feminine.
           Du kannst doch auf (’n) Sonntag nich’ den Rasen mähen! - You can’t mow the lawn on a Sunday!
     8. prep. (with accusative) for (during the continuation of)
           auf Jahre hinaus - for years to come
     9. prep. (with accusative) to, for (indicating purpose, goal or wish)
           Lasst uns auf deine Gesundheit drinken! - Let's drink to your health!
           Sie spielen auf Zeit. - They are playing for time.
     10. prep. (with accusative) by (used to separate dimensions when describing the size of something)
           X auf Y Meter groß
     11. adv. (somewhat, informal) open
           Die Tür ist auf. - The door is open.
     12. adv. (colloquial) finished; gone (food)
           Hast du deine Suppe auf? - Have you finished your soup?
           Die Milch is’ auf. - The milk is gone. (consumed)
     13. adv. (colloquial) up; awake; out of bed
           Ich war um sechs Uhr auf. - I was up at six o'clock.
     14. interj. carry on (continue or proceed as before)
     15. interj. have a go
Isomorphie
eindeutig
     1. adj. unambiguous, unequivocal, explicit, unique
     2. adj. clear, definite
     3. adv. unambiguously
     4. adv. clearly, obviously
bestimmte
     1. Participle. form of bestimmt
     2. adj. form of bestimmt
     3. v. first-person singular preterite of bestimmen
     4. v. third-person singular preterite of bestimmen
     5. v. first-person singular subjunctive of bestimmen
     6. v. third-person singular subjunctive of bestimmen
     bestimmen
          1. v. to determine
vollständig
     1. adj. (also math) complete
     2. adj. entire
     3. adv. completely, fully
geordnete
     1. adj. form of geordnet
     geordnet
          1. Participle. past participle of ordnen
          2. adj. orderly
          3. adj. well-ordered
archimedische
     1. adj. form of archimedisch
     archimedisch
          1. adj. (relational) of Archimedes; Archimedean
Erweiterungskörper
der
     1. art. the
     2. art. feminine singular of der
     3. art. genitive plural of der
     4. pron. who; that; which
           Ich kenne einen Mann, der das kann. - I know a man who can do that.
     5. pron. feminine dative singular of der: (to) whom, which, that
     6. pron. (attributive, stressed) that
           Der Mann war es! - It was that man!
     7. pron. (indicative) him, he
           Der hat es getan! - It was him who did it!
     8. pron. (differential) the one, him
           Der mit dem Mantel - The one with the coat
     9. pron. feminine dative singular of der: (to) that, (to) her
rationalen
Zahlen
     1. n. gerund of zahlen
     2. n. plural of Zahl
     3. v. to pay (money)
           Ich muss meine Steuern zahlen. - I have to pay my taxes.
           Er muss noch die Gebühr an die Verwaltung zahlen. - He still has to pay the fee to the administration.
     4. v. to pay for, to atone for
           Ich will keinen Fehler machen, für den ich später zahlen muss. - I don't want to make a mistake that I'll have to pay for later.
     Zahl
          1. n-f. number, numeral, figure
          2. n-f. tails (side of a coin)
Brüche
     1. n. plural of Bruch
Dictionary entries from Wiktionary