$\forall x \in H$ $(x,Ax) = (x,Bx) \implies A=B$
122213
Proving that if $\langle Ax,x\rangle =0$ for every $x$, then $A$ is the zero operator
58113
Av = Bv for all v implies A = B?
150885
$v \otimes v' = v' \otimes v$ implies $v = av'$
146231
Let X be a set with an associative binary operation ◦ with identity e. Suppose every element of X satisﬁes x ◦ x = e. Prove that ◦ is commutative.
105769
Prove that $\exists a, b\in(0,1)$ such that $\int_0^{a} xf(x)dx=0\text{ and }\int_0^bxf(x)dx=\frac{b^2f(b)}{2}.$
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
49385
Proving $\forall x (A\to B) \to(A \to \forall x B):x\notin \mbox{free}(A)$ in a Hilbert system where it is not an axiom
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
68724
$||T-I|| < 1$ implies that $T$ is invertible.
67717
$A \oplus B = A \oplus C$ imply $B = C$?
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
64955
Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$
93165
A projection satisfying $\| Px \| \leq \|x\|$ for all $x$ is an orthogonal projection
142840
Open axioms of equality
145397
How to prove that for every $i$, $a_i = i$
35800
If $K \leq H \leq G$, show that $[G:K] = [G:H][H:K]$.
54430
For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$