Among any $9$ real numbers, two satisfy $0 < \frac{x-y}{1+xy} < \sqrt{2} - 1$
87181
For any given set of 13 distinct real numbers, prove we can always find two numbers $x$ and $y$ that $0<\frac{x-y}{1+xy}\leq 2-\sqrt{3}$.
82085
Without solving the equation, show that all nine roots of $(𝑧 − 1)^{10} = 𝑧^{10}$ lie on the line $Re (𝑧) = \frac{1}{2}$
147892
Proving if $x<y$ then $\sqrt{x} < \sqrt{y}$
76568
$a,b,c$ are real numbers $>0$. If $a+b+c=1$, show that $(a+\frac{1}{a})^2+(b+\frac{1}{b})^2+(c+\frac{1}{c})^2\ge\frac{100}{3}$
90199
Prove that there exists a constant $c>0$ such that the following happens
123674
Show that $y = \frac{2x}{x^2 +1}$ lies between $-1$ and $1$ inclusive.
18530
Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
148585
Show that, for any $\epsilon>0$, there exist two rationals such that $q < x < q'$ and $|q-q'|<\epsilon$
114542
Can a number with $100$ $0$'s $100$ $1$'s and $100$ $2$'s ever be a perfect square?
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
112709
$\frac{1}{x-a} + \frac{1}{x-b} + \frac{1}{x-c} = 0 $ has precisely two real roots
91000
Prove that $\frac{1}{a+1}0$
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
122076
A one line proof that one is zero using Mathematica 10
154459
Constructing a HoTT proof term of 1≠0
140817
Real Analysis Inequality Proof Involving Reals and Rationals $0 < |r - q| < \varepsilon$