query: Why is the lim inf the union of intersections
positive_passages.docid: 22804
positive_passages.text: Interpretation of limsup-liminf of sets
negative_passages.docid: 18907
negative_passages.text: Is this proof of $\liminf E_k \subset \limsup E_k $ correct?
negative_passages.docid: 21070
negative_passages.text: Lim inf with norm and weak convergence
negative_passages.docid: 67637
negative_passages.text: How come $\lambda(\mathbb{Q})= \inf\left\{\sum_{n \ge 1} \lambda([a_n,b_n)) : \mathbb{Q} \subset \bigcup_{n \ge 1} [a_n,b_n)\right\} = 0$?
negative_passages.docid: 38807
negative_passages.text: Does set difference distribute over set intersection?
negative_passages.docid: 33310
negative_passages.text: Proving that the set of limit points of a set is closed
negative_passages.docid: 39034
negative_passages.text: How would you evaluate $\liminf\limits_{n\to\infty} \ n \,|\mathopen{}\sin n|$
negative_passages.docid: 45988
negative_passages.text: limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$
negative_passages.docid: 105107
negative_passages.text: How to explain the following definition of $\lim\sup s_n$ intuitively?
negative_passages.docid: 132264
negative_passages.text: Is there a (basic) way to understand why a limit cannot be brought inside of a sum, in certain situations?
negative_passages.docid: 36881
negative_passages.text: Empty intersection and empty union
negative_passages.docid: 139988
negative_passages.text: Counter example for a result of intersection of subspaces
negative_passages.docid: 50966
negative_passages.text: In a topological space, why the intersection only has to be finite?
negative_passages.docid: 54304
negative_passages.text: How to make sense out of the $\epsilon-\delta$ definition of a limit?
negative_passages.docid: 78082
negative_passages.text: Dense subset of two Banach spaces also dense in the intersection
negative_passages.docid: 38692
negative_passages.text: Please clear up this misunderstanding I have involving limits.
negative_passages.docid: 30231
negative_passages.text: The boundary of union is the union of boundaries when the sets have disjoint closures