query: Can the closed interval [0, 1] be expressed as the union of a sequence of disjoint closed subintervals each of length smaller than 1?
positive_passages.docid: 143586
positive_passages.text: Is $[0,1]$ a union of family of disjoint closed intervals?
negative_passages.docid: 22077
negative_passages.text: Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$
negative_passages.docid: 128987
negative_passages.text: A collection of pairwise disjoint open intervals must be countable
negative_passages.docid: 128844
negative_passages.text: An empty intersection of decreasing sequence of closed sets
negative_passages.docid: 84359
negative_passages.text: On Lebesgue Outer Measure of an interval
negative_passages.docid: 88028
negative_passages.text: Topology - closures of intervals with the order topology
negative_passages.docid: 82628
negative_passages.text: Cardinality of a set of closed intervals
negative_passages.docid: 47903
negative_passages.text: How to prove every closed interval in R is compact?
negative_passages.docid: 107842
negative_passages.text: Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
negative_passages.docid: 66951
negative_passages.text: Proving the existence of a sequence of functions converging to 0 with an added property
negative_passages.docid: 74792
negative_passages.text: $(X,\tau)$ needs to be $T_1$ in order to guarantee that $A'$ is closed?
negative_passages.docid: 55826
negative_passages.text: Convergence of sequence of real numbers and (sub)subsequence
negative_passages.docid: 102163
negative_passages.text: Find the sub-sequential limits of a recursive sequence
negative_passages.docid: 140379
negative_passages.text: Cauchy sequence in a discrete space
negative_passages.docid: 53363
negative_passages.text: Ultralimit of an eventually constant generalized sequence
negative_passages.docid: 149317
negative_passages.text: An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
negative_passages.docid: 3023
negative_passages.text: Construction of a Borel set with positive but not full measure in each interval