Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
70552
Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$.
90055
Show that $\mathcal P(x)\notin x$
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
133266
If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
113391
Prove that if $A$ is transitive, then $\mathcal{P}(A)$ is transitive too.
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
102042
If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$
31559
If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
76689
How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
30630
Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$