Showing that there exists a bijection from $\{0,1\}^X$ to $\mathcal{P}(X)$
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
125008
Define a bijection between $Z^{X \cup Y}$ and $Z^X \times Z^Y$, where $X, Y \in \mathcal{P}(\Omega) $ and $X \cap Y = \emptyset$
124374
A bijective function between a square and its side
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
147047
Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
93964
Proving that $f$ is a bijection from $N$x$N$ to $N$.
2907
How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$?
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
21152
Exactly half of the elements of $\mathcal{P}(A)$ are odd-sized
125707
A simple proof (hopefully) for $2^x \neq 0$
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
38257
Continuous bijection from $(0,1)$ to $[0,1]$
33014
Bijection between an open and a closed interval
30630
Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
148458
$x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.