Prove that if $x$ and $y$ are rational numbers and $y\ne 0$, then $x/y$ is a rational number
44476
Can we ever get an irrational number by dividing two rational numbers?
108704
Help with proof of $|x+y| \geq |x|-|y|$
3820
Prove that $||x|-|y||\le |x-y|$
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
103744
Minimal $ab$ for Rational Number $a/b$ in an Interval
16774
If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
30478
How to prove that a number is irrational
118348
Let $x$ be transcendental over $F$. Let $y=f(x)/g(x)$ be a rational function. Prove $[F(x):F(y)]=\max(\deg f,\deg g)$
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
152495
Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
19973
If $X$ and $Y$ are independent $N(0,\sigma^2)$, then $X^2+Y^2$ and $X/Y$ are independent?