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Unter
     1. n-m. jack, knave (playing card)
     2. prep. under
     3. prep. below
     4. prep. among, between
     5. prep. (chiefly literary) with; along with; accompanied by an action (often concessive)
           Die englische Sprache überlebte die normannische Eroberung unter weitgehendem Verlust ihrer ursprünglichen Struktur. - The English language survived the Norman conquest, largely losing, however
     6. prep. (rare, or regional) during
dem
     1. art. dative singular of der: the
     2. pron. dative singular of der: to whom, to which
gängigsten
     1. adj. superlative of gängig
     2. adj. form of gängig
Begriff
     1. n. term, word
     2. n. idea, conception, perception, understanding
           Du hast keinen Begriff davon, was das bedeutet. - You have no idea what that means.
     3. n. concept
     4. v. first-person singular preterite of begreifen
     5. v. third-person singular preterite of begreifen
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
Dimension
     1. n-f. dimension
eines
     1. num. genitive singular of ein
     2. art. genitive singular of ein: a, an
     3. pron. singular of einer
     4. pron. genitive singular of einer
Raumes
     1. n. genitive singular of Raum
     Raum
          1. n. (physics) space
          2. n. capacity, volume, room
          3. n. room, chamber
          4. n. place, area, field, room, space
          5. n.          room, hold (of a vessel or vehicle)
          6. n. (figurative) scope, opportunity, field
          7. n. Alternative form of Rahm, t=ream
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
Hamel
Dimension
     1. n-f. dimension
eines
     1. num. genitive singular of ein
     2. art. genitive singular of ein: a, an
     3. pron. singular of einer
     4. pron. genitive singular of einer
Vektorraumes
versteht
     1. v. third-person singular present of verstehen
     2. v. second-person plural present of verstehen
     3. v. plural imperative of verstehen
     verstehen
          1. v. to understand
          2. v.          to hear and interpret (speech)
                        Ich verstehe dich nicht bei dem Lärm. - I can't understand you with this noise.
          3. v.          to comprehend, make sense of
                        Ich verstehe nicht, was du meinst. - I don't understand what you mean.
          4. v.          to take, see, gather (impute what is not explicitly stated)
                        Ich verstehe das so, dass Sie unzufrieden sind. - I understand this in such a way that you are dissatisfied.
          5. v.          to know, have knowledge or understanding of (through experience or study)
                        Er versteht viel von Autos. - He knows a lot about cars.
          6. v. to understand oneself, understand each other, be understood
          7. v.          (with als) to see oneself as, to think of oneself as
                        Wir verstehen uns als Dienstleister. - We see ourselves as a service provider.
          8. v.          to understand one another, be able to communicate
                        Ich hoffe, wir verstehen uns. - I hope we understand each other.
          9. v.          (with mit) to get along with
                        Die beiden verstehen sich gut. - The two get along well.
                        Wie verstehst du dich mit deinem Chef? - How do you get along with your boss?
          10. v.          (with auf) to be an expert (at something)
                        Sie versteht sich auf gut getarnte Beleidigungen. - She is an expert at making well disguised insults.
          11. v.          to be meant, to have to be interpreted (in some way)
                        Die angegebenen Preise verstehen sich ohne Mehrwertsteuer. - The indicated prices should be understood as without VAT.
          12. v.          (impersonal) to go without saying, to be obvious
                        Es versteht sich, dass ... - It goes without saying that ...
man
     1. pron. one, you (indefinite pronoun; construed as a third-person singular)
           Man kann nicht immer kriegen, was man will. - You can’t always get what you want.
           Manchmal muss man Kompromisse machen. - Sometimes one must compromise.
     2. pron. they, people (people in general)
           Zumindest sagt man das so... - At least that’s what they say...
     3. pron. someone, somebody (some unspecified person)
     4. pron. they (some unspecified group of people)
     5. adv. (colloquial regional northern Germany) just; only
           Komm man hier rüber! - Just come over here!
           Das sind man dreißig Stück oder so. - These are only thirty or so.
die
     1. art. feminine singular of der
           die Frau - the woman
     2. art. plural of der
           die Männer - the men
     3. pron. feminine singular of der
     4. pron. plural of der
     5. pron.          (in a subordinate clause as a relative pronoun) that; which; who; whom; whose
                   Ich kenne eine Frau, die das kann. - I know a woman who can do that.
     6. pron.          (as a demonstrative pronoun) this one; that one; these ones; those ones; she; her; it; they; them
                   die da - that one/she/they there
     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
Kardinalität
Einer
     1. n-m. (mathematics) unit
     2. n-m. (mathematics) units' place, ones' place (place value of a number)
     3. n-m. (sports) single scull
     4. n-m. (swimming) one-meter diving board
     5. num. feminine singular of ein
     6. art. feminine singular of ein
     7. pron. one
     8. pron. someone, somebody
     9. pron. feminine singular of einer
und
     1. conj. (co-ordinating) and
           Kaffee und Kuchen - coffee and cake
           Ich kam, sah und siegte. - I came, saw, and conquered.
     2. conj. (colloquial) links two nouns, often a person and an activity, in rhetoric questions to express an opposition between them
           Er und Abwaschen? Vielleicht einmal im Jahr! - Him doing the dishes? Maybe once per year!
     3. interj. so?, now?, and?
           Und? Wie ist es gelaufen? - So? How did it go?
dann
     1. adv. then, after that
           Ich ziehe mich erst an, dann frühstücke ich. - First I'm getting dressed, then I'll have breakfast.
     2. adv. then, in that case
           Wenn du dich anstrengst, dann schaffst du es. - If you make an effort, then you'll be able to do it.
jeder
     1. pron. each
           jedem das Seine - to each their own
     2. det. each, every
           jedes Mal - every time
diesen
     1. pron. masculine accusative singular of dieser; "this"
           Ich will diesen Apfel - I want this apple.
     2. pron. dative plural of dieser; "these"
           Ich half diesen Tieren - I helped these animals.
     dieser
          1. pron. this one, this
          2. pron. that one, that
Vektorraum
     1. n. (mathematics, linear algebra) vector space
aufspannenden
Basis
     1. n. basis (foundation, principle)
     2. n. (military) base
     3. n. (mathematics) basis
           Die Potenz a² hat die Basis a und den Exponenten 2 - The power a² has a base a and an exponent 2.
Dictionary entries from Wiktionary