query: Proving inequalities hold for all values
positive_passages.docid: 90218
positive_passages.text: Proving $\frac{x}{y} +\frac{y}{z} + \frac{z}{x} \ge 3$ for positive $x,y,z$
negative_passages.docid: 91871
negative_passages.text: Proving quadratic inequalities?
negative_passages.docid: 20816
negative_passages.text: Inequalities with assumptions and constraints
negative_passages.docid: 8007
negative_passages.text: Proof of Young's inequality
negative_passages.docid: 108704
negative_passages.text: Help with proof of $|x+y| \geq |x|-|y|$
negative_passages.docid: 108995
negative_passages.text: Prove $|e^{i\theta} -1| \leq |\theta|$
negative_passages.docid: 29679
negative_passages.text: Prove: $|x-y|\leq |x|+|y|$
negative_passages.docid: 20073
negative_passages.text: How to fill in inequality where all inequalities overlap
negative_passages.docid: 122691
negative_passages.text: Graphs of Linear Inequalities
negative_passages.docid: 91131
negative_passages.text: Question regarding an inequality
negative_passages.docid: 126032
negative_passages.text: Proving a certain inequality
negative_passages.docid: 136290
negative_passages.text: a mathematical problem on inequalities
negative_passages.docid: 106799
negative_passages.text: Proof Verification: Converse of Intermediate Value Theorem
negative_passages.docid: 32427
negative_passages.text: Basic mathematical induction regarding inequalities
negative_passages.docid: 147785
negative_passages.text: Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
negative_passages.docid: 116781
negative_passages.text: Could someone give a detailed (yet elementary) proof for Jensen's inequality?
negative_passages.docid: 95293
negative_passages.text: Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$