Prefixes can convey many different meanings. Here "be-" expresses that the action is or will be completed and it has or will have a result. In this case, the policeman certainly ends up in the building.
Jön by itself doesn't convey this. It doesn't suggest anything about the result. A rendőr jön, jön, but we don't know if he will make it to the building or not.
Other prefixes can add such a nuance as well, like in the case of ír -- megír:
- "Írtam a cikket." -- "I was writing the article." Who knows if I finished it or not?
- "Megírtam a cikket." -- "I wrote the article." I finished it, it's done, ready to be published.
Or tol -- eltol:
- "Tolja az autót." -- "He is pushing the car." He is in the process of pushing it. It's unclear where he's pushing it and for how long will he continue this action.
- "Eltolja az autót." -- "He is pushing the car away." The car will end up somewhere. We still don't know where, but we know that he will stop pushing it once it's in a certain place that's not here.
God, perfective/imperfective distinction is probably one of the worst features a language can have. Polish also has this but I think it's more complicated there (well, I hope it won't get more in Hungarian) and although my native language has this feature I had problems with it in Russian. I don't know how anybody can use it correctly and fluently (in a second language). Thanks for the explanation!
I will soon have to face that problem in Polish and I already fear that moment... I don't know if it's more or less difficult in Hungarian, but it's certainly not that important in the sense that you can get by with only a vague grasp of how it works until you just start feeling it.
I don't know much about it in Hungarian, is there more to it than this thing with the preverbs? Unfortunately, I think it's much more complicated and irregular in Polish (but maybe I'm wrong, I've never tried to analysed it). I've never learned a language that has this distinction developed (in this way), except from Russian but there I mainly relied on similarities with Polish, though I remember it was kind of confusing. At least you have the advantage of understanding this concept so you'll be able to better understand and use those forms.
Right now nothing other than preverbs comes to my mind, so probably there's nothing more to it (but as you said, I've never really analysed it either). It's definitely not as integrated part of the language as in Polish or Russian. This might be a very uneducated and naive analogy, but it seems to me that in Polish and Russian there's a whole system to this perfective/imperfective thing, while Hungarian only has the traces of it. We don't really make a difference between them, but we still do, just to confuse you. In regular grammar classes in Hungarian elementary or high schools this topic isn't even mentioned. It's only because of Duolingo I actually looked up how this even works in Hungarian.
And I hope I will be able to grasp it. I'm majoring in Polish, so there's no way out. :D
Good luck! When you learn a language more thoroughly you can get used to such things, so maybe it won't be that hard. I've only learned a bit of Russian, only done the tree, though I'm thinking of starting to learn it seriously (great language!) so maybe then I'll be able to say more.
So how do you say "I wrote an article?" To me, that's different from "I've written an article." The first is definitely in the past - I did it, it's done. The second also conveys that the article is written, but also that the action has immediate relevance in the present, such as that I've completed it and it can now be published. "I wrote an article" might be talking about an article that was published years ago. How do you make this distinction in Hungarian?
I am not Hungarian, therefore I reply as I see it. The only thing that matters is whether you have finished your work, achieved the goal. Írtam a könyvet is I wrote the book (but it may be finished years later), megírtam a könyvet - job's done. The same is about my native language, no matter if you talk about now or long ago. The latter is clear from the context.
I wrote an article - Írtam egy cikket.
I've written an article - Megírtam egy cikket.
On a second thought, I've written an article can also be Írtam egy cikket, but I wrote an article cannot be Megírtam egy cikket in the example that you give.
The barrier between the two isn't as clear in hungarian, but in the context you give here, I would say it this way.
This sentence repeats the "be" twice ... bejön and again with épületbe ... so, literally, it says "The policeman comes into into the building."
This double emphasis of "into", is this valid/normal? Does using "bejön" add meaning to the sentence, when "épületbe" already indicates that the policemen is entering the building?
Not if Hungarian uses aspect like Slavic languages. Let's use Polish because we both have it. In Polish, the sentence translates to Policjant wszedł do budynku, which implies that the officer entered the building because the perfective verb wejść is used instead of its imperfective counterpart wchodzić. The perfective aspect is for actions that have been, or will be, completed. That's why there is no present tense of a perfective verb.