Prove $|(0, 1]| = |\mathbb{R}|$
10458
How to define a bijection between $(0,1)$ and $(0,1]$?
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
16253
Proof that $|\sin(nx)| \le n|\sin(x)|$
138283
$|(a,b)| = |\Bbb R|$ ? Cardinality of any open interval
107765
Prove that there exists two roots in $[-1,1]$
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
66451
In a ring, how do we prove that a * 0 = 0?
153272
Basic question about $\sup_{x\neq 0}{} \frac{\|Ax\|}{\|x\|} = \sup_{\|x\| = 1}{\|Ax\|} $, $x \in\mathbb{R}^n$
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
152223
If $0<r<1$ show that $r^n$ goes to $0$ as $n$ goes to 1.
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
49240
$\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$