Imperative The imperative mood is used to express commands, just like in English. There are three different forms, according to the three types of "you" in German.
Du imperative The imperative for du is very similar to English: Du gehst nach Hause. (You go home.) Geh nach Hause! (Go home!) For most verbs, to come up with the correct verb form, just lose the -st ending: Du arbeitest nachts. (You work at night) Arbeite nachts! (Work at night!) Du nimmst das Taxi. (You take the taxi.) Nimm das Taxi! (Take the taxi!) You might have noticed that some common verbs have an extra umlaut in the 2nd/3rd person singular: fahren, du fährst schlafen, du schläfst In the imperative, these do not have an umlaut: Du fährst mit dem Taxi. Fahr mit dem Taxi!
Ihr imperative The second one is used to address more than one person informally. It uses the same conjugation as the regular ihr form of the present tense. This form of the imperative does not include a personal pronoun. Ihr fahrt nach Paris. (You go to Paris.) Fahrt nach Paris! (Go to Paris!)
Sie imperative The third one is used to address one or more people formally. It uses the same conjugation as the regular Sie form of the present tense. The formal imperative is the only form to include the personal pronoun (Sie). Note that the word order is reversed. The verb always precedes the pronoun. It essentially looks like a question. Sie lernen Deutsch. (You learn German.) Lernen Sie Deutsch! (Learn German!) Lernen Sie Deutsch? (Do you learn German?)
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Yeah, that's a perfectly fine answer, I'm not sure what to tell you. My best guess is you just had a typo or something, but it could be a glitch too. Next time you come across an issue like this, make a screenshot and link to it; that'll help to diagnose the problem.
It's either "Geh(e) nicht durch die Tür" (informal, addressing one person) or "Gehen Sie nicht durch die Tür" (formal, addressing one or more people).
How to understand the placement of nicht here?
I read somewhere else that when nicht is placed at the end of a sentence, it negates the entire expression. So to write this sentence in non-imperative form, it would be Du gehst durch die Tür nicht. Following this logic, is it correct to say Gehe durch die Tür nicht?
I agree with CallMeAnja. Yes, the construction "Go not through the door" sounds archaic, but it is perfectly correct and is also, I argue, in use. For example, I might address a humorous entreaty to a friend who was leaving my home by saying, "Go not through the door unless thou wilt have me perish with the pain of your leaving."
If we accept archaic grammar, then why not archaic spellings too, like "Love and Freindship"?
Duo's mission is to teach sensible modern usage (and spelling). What do you think about the sentence "He is at Berlin" instead of "He is in Berlin"? Believe it or not, that used to be the correct British English usage as late as the 19th century. But if someone wrote it today (or should I say "to-day", the way it used to be spelled), then it needs to be marked incorrect.