query: If $x>y>0$ why is $\sqrt{x} > \sqrt {y}$?
positive_passages.docid: 147892
positive_passages.text: Proving if $x<y$ then $\sqrt{x} < \sqrt{y}$
negative_passages.docid: 125209
negative_passages.text: Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
negative_passages.docid: 16948
negative_passages.text: Need help with a proof that if $xy=0$ then $x=0$ or $y=0$
negative_passages.docid: 157847
negative_passages.text: If $x_n \to 0$, show that $\sqrt{x_n} \to 0$
negative_passages.docid: 49750
negative_passages.text: Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
negative_passages.docid: 111432
negative_passages.text: Square root of a number squared is equal to the absolute value of that number
negative_passages.docid: 81671
negative_passages.text: Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
negative_passages.docid: 142873
negative_passages.text: What does the function f: x ↦ y mean?
negative_passages.docid: 86567
negative_passages.text: Understanding $\sum_{x = 0}^y x = \frac{y(y + 1)}{2}$ in a step of a proof
negative_passages.docid: 42581
negative_passages.text: Simple algebra square root inequality
negative_passages.docid: 11707
negative_passages.text: If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$
negative_passages.docid: 41182
negative_passages.text: What does the construct x = x || y mean?
negative_passages.docid: 53583
negative_passages.text: Why $e^x$ is always greater than $x^e$?
negative_passages.docid: 49878
negative_passages.text: Why does `a == x or y or z` always evaluate to True?
negative_passages.docid: 108704
negative_passages.text: Help with proof of $|x+y| \geq |x|-|y|$
negative_passages.docid: 8027
negative_passages.text: How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?
negative_passages.docid: 33543
negative_passages.text: is "y1 < x < y2" an inequality or inequalities?