Prove for $x \in \mathbb{X}: x \in \bar{A} \Leftrightarrow d_A(x)=0$
123753
In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$
75002
show that $\det(A)=0$ in this case
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
85269
Proof that limit of (lnx)/x = 0 without LHopital
76292
Showing that $f$ is identically $0$ on $\mathbb{D}$
9957
Prove if $f:[a,b] \rightarrow \mathbb{R}$ is integrable, then so is $|f|$ and $\left|\int_{a}^{b}f(x)dx\right| \leq \int_{a}^{b}|f(x)|dx$
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
118873
Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
122149
How to prove that $\sum_{i<j}(X_i-X_j)^2=n\sum_{i=1}^{n}(X_i-\bar{X})^2$
34398
Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$
83337
If $A ∈M_n(C)$ is such that $(Ax,x) = 0$ for all $x ∈C^n$, then $A = 0$
59187
Proof, is $\forall x : (P(x) \lor Q(x)) \Leftrightarrow \forall x : P(x) \lor \forall x : Q(x)$?
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
106585
Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
18914
How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $