query: How is the limit infimum of sets different from the limit infimum of a sequence of real numbers?
positive_passages.docid: 155999
positive_passages.text: How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$
negative_passages.docid: 156663
negative_passages.text: Interchanging limit with infimum/supremum
negative_passages.docid: 55826
negative_passages.text: Convergence of sequence of real numbers and (sub)subsequence
negative_passages.docid: 142045
negative_passages.text: What's the definition of limit of sets(esp. ordinals) in set theory?
negative_passages.docid: 9781
negative_passages.text: How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
negative_passages.docid: 55614
negative_passages.text: Prove that a set consisting of a sequence and its limit point is closed
negative_passages.docid: 48593
negative_passages.text: Proof that if $s_n \leq t_n$ for $n \geq N$, then $\liminf_{n \rightarrow \infty} s_n \leq \liminf_{n \rightarrow \infty} t_n$
negative_passages.docid: 43197
negative_passages.text: Showing that two definitions of $\limsup$ are equivalent
negative_passages.docid: 70590
negative_passages.text: limit of a sequence. might be related to Cesaro theorem
negative_passages.docid: 139356
negative_passages.text: How to find the limit of a sequence?
negative_passages.docid: 31836
negative_passages.text: Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$
negative_passages.docid: 32347
negative_passages.text: Limit of a decreasing sequence of measurable sets.
negative_passages.docid: 84969
negative_passages.text: When does $\lim_{n\rightarrow \infty} a_n = 0$ imply $\sum_{n = 0}^{\infty} a_n$ converges?
negative_passages.docid: 66198
negative_passages.text: Sufficient condition for convergence of a real sequence
negative_passages.docid: 149549
negative_passages.text: Infimum of $n$-th root of $n$
negative_passages.docid: 16826
negative_passages.text: prove that every infinite subset of compact set H has a limit point (Explanation)
negative_passages.docid: 114975
negative_passages.text: Limit of sequences $V(n)$ and $U(n)$