query: Which number is more near to $S$
positive_passages.docid: 1166
positive_passages.text: How to compute $\prod\limits^{\infty}_{n=2} \frac{n^3-1}{n^3+1}$
negative_passages.docid: 110383
negative_passages.text: How many numbers less than $m$ and relatively prime to $n$, where $m>n$?
negative_passages.docid: 123534
negative_passages.text: (k+1)th or (k+1)st?
negative_passages.docid: 81217
negative_passages.text: Fastest way to find out minimum of 3 numbers?
negative_passages.docid: 152838
negative_passages.text: Relation between Ramsey Numbers: $R(s, t) > (t-1)(s-1)$
negative_passages.docid: 72843
negative_passages.text: Parity of number of factors up to a bound?
negative_passages.docid: 106562
negative_passages.text: Is $3 \ge 1$ or is it just $3 > 1$?
negative_passages.docid: 13688
negative_passages.text: Why are these numbers not equal?
negative_passages.docid: 69833
negative_passages.text: Number of elements not equal to their inverses is even number
negative_passages.docid: 114321
negative_passages.text: Equation number too close to my equation
negative_passages.docid: 50781
negative_passages.text: $(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
negative_passages.docid: 76977
negative_passages.text: Prove that $f(n)$ is the nearest integer to $\frac12(1+\sqrt2)^{n+1}$?
negative_passages.docid: 57644
negative_passages.text: Lower bounds for ${{2n} \choose {n}}$
negative_passages.docid: 64470
negative_passages.text: Near, near to and nearby. What's the difference?
negative_passages.docid: 87536
negative_passages.text: Supremum of the infimum
negative_passages.docid: 148163
negative_passages.text: Show that if m/n is a good approximation of $\sqrt{2}$ then $(m+2n)/(m+n)$ is better
negative_passages.docid: 127102
negative_passages.text: Upper bound for $\sqrt[n]{n!}$