query: Proving $|V(a_0,...,a_{n-1})|=\Pi_{0\leq i<j<n-1}(a_j-a_i)$
positive_passages.docid: 142640
positive_passages.text: Prove determinant of a matrix $=\prod_{j<i}(a_i-a_j)$
negative_passages.docid: 94119
negative_passages.text: Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
negative_passages.docid: 108298
negative_passages.text: Prove $\sum_{i=1}^{i=n}\frac{a_i}{S-a_i}\geqslant \frac{n}{n-1}$ and $\sum_{i=1}^{i=n}\frac{S-a_i}{a_i}\geqslant n(n-1)$.
negative_passages.docid: 96133
negative_passages.text: Prove that $ m_{a} \geq m_{g} \geq m_{h} $ using strict inequalities unless $ a = b $.
negative_passages.docid: 129890
negative_passages.text: Proving inequality $|\sin(n\theta) |\le n\sin\theta$
negative_passages.docid: 126165
negative_passages.text: Prove $|\arctan x - \arctan y|\leq |x-y|$
negative_passages.docid: 82591
negative_passages.text: Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
negative_passages.docid: 88687
negative_passages.text: Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
negative_passages.docid: 3599
negative_passages.text: show that if ${a_n} \to a$, and $a>0$, then $\exists N$ such that $a_n>0$ for $n \ge N$.
negative_passages.docid: 63036
negative_passages.text: Proving that $\dim(\mathrm{span}({I_n,A,A^2,...})) \leq n$
negative_passages.docid: 157328
negative_passages.text: A complex analysis problem to prove an inequality
negative_passages.docid: 103536
negative_passages.text: How to prove $|e^{i\theta} - 1| \leq |\theta|$?
negative_passages.docid: 118471
negative_passages.text: Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
negative_passages.docid: 101286
negative_passages.text: How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
negative_passages.docid: 90343
negative_passages.text: Proving the inequality $|e^z-1|\leq e^{|z|}-1$
negative_passages.docid: 73987
negative_passages.text: Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
negative_passages.docid: 95293
negative_passages.text: Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$