query: Finding the length of a finite cover of a set of rationals
positive_passages.docid: 151544
positive_passages.text: Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$
negative_passages.docid: 73345
negative_passages.text: maximum size of a $k$-intersecting family of $[n]$
negative_passages.docid: 146098
negative_passages.text: Number of nonempty subsets of a set with $n$ elements
negative_passages.docid: 3801
negative_passages.text: Functions that take rationals to rationals
negative_passages.docid: 114442
negative_passages.text: Completion of rational numbers via Cauchy sequences
negative_passages.docid: 117132
negative_passages.text: Rationals of the form $\frac{p}{q}$ where $p,q$ are primes in $[a,b]$
negative_passages.docid: 96647
negative_passages.text: Number theory: Problem involving rational numbers
negative_passages.docid: 129476
negative_passages.text: The trace map in a finite field.
negative_passages.docid: 151928
negative_passages.text: How to prove that $N\setminus A$ is finite?
negative_passages.docid: 34998
negative_passages.text: How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
negative_passages.docid: 88283
negative_passages.text: Proving the length of angle bisector
negative_passages.docid: 142008
negative_passages.text: Find all natural numbers $n$ such that ${(n+1)}^{1/2}-{(n-1)}^{1/2}$ is rational
negative_passages.docid: 137610
negative_passages.text: Finding the field of fractions of a quotient of a polynomial ring.
negative_passages.docid: 19071
negative_passages.text: solution set for congruence $x^2 \equiv 1 \mod m$
negative_passages.docid: 75012
negative_passages.text: Additive group of rationals has no minimal generating set
negative_passages.docid: 117781
negative_passages.text: Proving that $S=\{\frac{1}{n}:n\in\mathbb{Z}\}\cup\{0\}$ is compact using the open cover definition
negative_passages.docid: 39642
negative_passages.text: Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$