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I heard that American English don't use the present perfect, is it true? I learned that if there's e.g. "just" I cannot use simple past. Do the Americans really say: I just arrived from school? instead of: I've just arrived?
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Yes, it true. But seldom they use it. If you ask me, it depends on many things - but I am not American so I can't be sure about it.
I sometimes watch American films, news (when I have got some free time) and I listen to them carefully... and yes, they often say sentences like this one: "Did you ever see such a..." It's another culture, another history and sometimes another language.
We do use present perfect. Few people know to CALL it that, but we USE it.

We CERTAINLY use past perfect - I had only just arrived when the movie began.

If there's any doubt, listen to the The Carpenters' song "We've only just begun..." Even your example "Did you ever see..." has a corresponding children's song with a refrain "Have you ever seen a ... [silly rhymes follow]."

But I don't think you'll find anyone here saying that "I've just now started on that project" is any different in meaning from "I started the project just now." Or "Did you see the movie Brokeback Mountain" as being different from "Have you seen the movie Brokeback Mountain?"
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No offense taken, I assure you. Americans, I think, tend to lead the trend at eliminating distinctions they find unnecessary and eventually making some "proper" usage archaic. Try to find people who use "whom" in speech, or who do differentiate between "will" and "shall." I think with so much communication now taking place in IM or text messaging, "proper grammar" is rapidly disappearing. But the odd part of the post, I thought, was not that it said "often do not" or "often disregard the difference" but that it said "they do not" as if somehow that kind of usage was wrong. I find the evolution of language interesting, but if you're just learning one, it can be hard to hit a moving target.
No offense taken, I assure you. Americans, I think, tend to lead the trend at eliminating distinctions they find unnecessary and eventually making some "proper" usage archaic. Try to find people who use "whom" in speech, or who do differentiate between "will" and "shall." I think with so much communication now taking place in IM or text messaging, "proper grammar" is rapidly disappearing. But the odd part of the post, I thought, was not that it said "often do not" or "often disregard the difference" but that it said "they do not" as if somehow that kind of usage was wrong. I find the evolution of language interesting, but if you're just learning one, it can be hard to hit a moving target.
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I heard that American English don't use the present perfect, is it true?
It is completely false. You have been grossly misled. You mustn't believe such nonsense!

Do the Americans really say: I just arrived ... instead of: I've just arrived?
Yes. This is partially true. We Americans use the adverb "just" with either tense, so it's not that we use one tense instead of the other.

CJ