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There is a notification area (small red dot) that lists questions on which a user has made a recent remark. Once you click outside of it, it disappears. Is it possible to get a full list (in last item first) order?

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You can find your "inbox" for tex.sx at https://tex.stackexchange.com/users/10827/maesumi?tab=responses&sort=comments (everybody can just see it for themselves). In order to get there manually, go to your profile, "responses", and "comments".

There's also a global inbox, showing comments from all Stack Exchange sites that you're a member of: http://stackexchange.com/users/1174715/maesumi?tab=inbox. Manual way: Go to your profile, "network profile", "inbox".

As for the terminology: Since the recent notification system revamp, the inbox (red circle) tells you when another user wrote something for you (comment, answer, chat message), the notifications (gray circle) are reserved for badges, which are considered less important.

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