Not getting edit's +2 rep after reaching 2k rep
The FAQ didn't describe it.
If yes, How Stack Overflow encourage users (with 2000+ rep) to improve Q&A?
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Yes that is true. From 2000 onwards there is no reputation gain through edits.
People that are dedicated enough will edit posts anyway because they want to improve the overall quality. I have never edited because of the reputation, in fact that didn't even exist until I got to 2000.
It is just about the dedication to maintain the site and make it the best place it can be.