How do I disprove that $|\mathcal P([0,1]) \setminus \mathcal P((0,1))| > |\mathcal P(\mathbb{N})|$
71133
prove inequlity about cardinality power sets
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
76977
Prove that $f(n)$ is the nearest integer to $\frac12(1+\sqrt2)^{n+1}$?
2882
Limit points of the set $\{\frac {\varphi(n) }n : n\in \mathbb{N}\}$
155929
Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
72420
Is $\mathbb{N}$ impossible to pin down?
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
79734
Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets?
73221
How can I form a bijection between $\mathcal P(A)$ and $2^A$.
55023
if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$
21782
Is $\aleph_0 = \mathbb{N}$?
144819
Proving $P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}$
154076
How to show this property of $\mathbb{RP}^{n}$.
93606
Showing that $C[0,1]$ is not complete
50019
Prove $0$ is a partial limit of $a_n$