Prove that for every $x,y\in R$ exist $z\in R$ such that $\langle x,y\rangle=\langle z\rangle$
65536
Finitely generated ideals in a Boolean ring are principal, why?
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
128710
Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
98352
If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
90345
If $\lVert x\rVert=\lVert y \rVert$, prove that exists a unitary transformation such as $Tx=y$
120766
Prove ${y_n}$ is a basis for a Hilbert space $H$.
128932
Is my expansion of the state $| x \rangle$ correct?
102871
$\langle r\rangle$ maximal $\iff r$ irreducible
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
143000
Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
20503
Meaning of inner product $\langle \vec{r} | \psi(t)\rangle $
7813
In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$
15354
Formal proof of $\exists x \forall y P(x,y) \implies \forall y \exists x P(x,y)$
118195
How does one prove that $e$ exists?