For each $x,y∈\mathbb N$, if $x≤y$ and $y≤x$, then $x=y$
30003
Proving that Order for N is Anti-symmetric
28266
For $n\geq 3$ there exist $x,y\in S_n$ such that $x$ and $y$ have order $2$ and $xy$ has order $n$.
96153
$ x^3<y^3 \iff x<y $ proof issue.
15733
Show that the cardinality of $\mathbb N$ is the same as the cardinality of $\mathbb N \times \mathbb N$
77412
Product of $\min$ and $\max$ of $n$ i.i.d. random variables.
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
108429
Show that if $x_n \to x$ then $\sqrt{x_n} \to \sqrt{x}$
52565
Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.
140988
Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
15491
Prove that $f:\mathbb R^n\to\mathbb R$ is affine if and only if it is convex and concave
110495
$X_n \to X, Y_n \to c$ in distribution implies $X_n Y_n \to Xc$ in distribution
93771
Prove that for any set $A$ there is some $x \notin A$
59724
Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
74835
how to prove that $ \lim x_n^{y_n}=\lim x_n^{\lim y_n}$?