@MartinSleziak Like amWhy, I like people who ask for hints rather than full solutions, as it indicates that they are not just trying to get rid of their homework; they're just stuck. However, I still expect effort shown. The first link is a bit lacking; the author thinks "induction is not a very helpful way", but didn't try. I think it does work, but didn't try. Therefore I tend to close one eye to such questions unlike PSQs. =P
That said, it's still a duplicate and if it's an old post we might as well close it as such since future readers will overall benefit from seeing the whole list of approaches.
@MartinSleziak Two of those four questions about continuity of metric have been closed as duplicates. i flagged for merging - we will see whether the mods agree with the suggestion.
@user21820 I wonder whether it is a bug that you are listed among users who marked those questions as duplicates. You voted there off-topic/missing context, didn't you?
@user21820 I mean here: "This question appears to be off-topic. The users who voted to close gave this specific reason: "This question is missing context or other details: ... Henrik, JonMark Perry, Shailesh, M. Winter"
I am not listed among users who chose the specific reason. I am still listed among users who voted to close: "closed as off-topic by Henrik, JonMark Perry, Shailesh, M. Winter, Martin Sleziak Jun 1 at 13:49".
So only now I realized that duplicate close votes are different in that aspect.
I think maybe it's because no detailed reason was provided, so neither was the list of those who gave that specific reason. The final consensus reason just has all the close-voters' names.
Since they were deleted by the OP, I guess he can undelete them at any time. So I leave it for you whether the message can be already removed from the starboard or whether we should wait to see what the OP does.
The most frequent reason is adding new answer, editing question on answer.
But there are many others (reopening, undeleting answer, etc.)
In the links give above you can find far more detailed information than I would be able to give you from the top of my head.
Personally, I use active tab with 50q per page, but I usually look at second page. And sometimes I look at the post in my favorite tags instead.
Some time ago I made a poll on meta about how various users access the site and display the posts: Exposure of new questions (poll on browsing habits). But since it was a few years ago, the information given there is probably mostly obsolete.
If you look here math.stackexchange.com/questions/tagged/… (the same collection of tags as in your link) you can choose from these tabs: newest/frequent/votes/active/unanswered.