I have to study the limit of the following sequence:

{An}

^{∞}

_{n=1}, with {An} = { (x,y) € R^2 /[ -1+(1/n)] <= x <=[ 1 + (1/n)] , -1 <= y <= 1 }

Now, if I understand it well, the limit of a sequence of sets is a set which contains the sets of every term in the sequence.

In a non-formal way, I see that the y will always be between -1 and 1, and the x will move between -1 (which is the smallest posible value for [ 1 + (1/n)], and 2 (the largest possible value for [ 1 + (1/n)]).

So, intuitively, I'd say that the solution is -1 <= x <= 2, -1 <= y <= 1.

However, I'm not supposed to do that. Im supposed to find the superior limit, which according to the definition is

And that is when my problem comes, because I don't know how I should use that definition.

Any help?