query: Cluster point of a sequence $\{x_n\}$ is the limit of some subsequence - Axiom of Choice?
positive_passages.docid: 18219
positive_passages.text: (ZF)subsequence convergent to a limit point of a sequence
negative_passages.docid: 56354
negative_passages.text: Uniformly Convergent Subsequence
negative_passages.docid: 80276
negative_passages.text: Metric Space & Cauchy Sequence
negative_passages.docid: 53005
negative_passages.text: Properties of $\liminf$ and $\limsup$ of sum of sequences: $\limsup s_n + \liminf t_n \leq \limsup (s_n + t_n) \leq \limsup s_n + \limsup t_n$
negative_passages.docid: 15319
negative_passages.text: Convergence of recurrence sequence
negative_passages.docid: 23335
negative_passages.text: A sequence converges if and only if every subsequence converges?
negative_passages.docid: 10933
negative_passages.text: Let $(x_n)$ be a bounded but not convergent sequence. Prove that $(x_n)$ has two subsequences converging to different limits.
negative_passages.docid: 55614
negative_passages.text: Prove that a set consisting of a sequence and its limit point is closed
negative_passages.docid: 139356
negative_passages.text: How to find the limit of a sequence?
negative_passages.docid: 102170
negative_passages.text: Showing a Sequence and its Limit are Closed
negative_passages.docid: 67420
negative_passages.text: Limit of quotient sequence
negative_passages.docid: 74542
negative_passages.text: Convergence of a sequence whose even and odd subsequences converge
negative_passages.docid: 46323
negative_passages.text: Criteria for convergent sequence (Baby Rudin Theorem 3.22)
negative_passages.docid: 97047
negative_passages.text: Limit for sequence $a_{m+n}\leq a_m+a_n$
negative_passages.docid: 3404
negative_passages.text: What are the convergent sequences in the cofinite topology
negative_passages.docid: 141484
negative_passages.text: Convergence of a sequence by convergence of sub-subsequence
negative_passages.docid: 109926
negative_passages.text: Axiom of Regularity and infinite sequences