Show that for all $u,v \in \mathbb{R}, u>v$ if and only if $u^3 > v^3$.
96153
$ x^3<y^3 \iff x<y $ proof issue.
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
30583
If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
108837
How to show that $\vdash (\forall x \beta \to \alpha) \leftrightarrow \exists x (\beta \to \alpha)$?
83449
Proof with 3D vectors
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
6547
Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$
9854
If $U$ is a neighborhood of $e$, there exists $V$ neighborhood of $e$ such that $V^{-1}V \subseteq U$
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
27147
Proving $n! > n^3$ for all $n > a$
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
40930
Prove that $ex \leq e^x$ for all $x \in \mathbb{R}$
60684
Determine whether the set $W$ is a subspace in $\mathbb{R}^{3}$
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
99821
Show that $u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$.