Let $A = \{1,2,\ldots,n\}$. Show that there is a bijection from ${\cal P}(A)$ with the cartesian product $X^n$ where $X = \{0, 1\}$.
110464
Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
24107
Bijection $f:\mathcal{P}(A)\to(A\to \{0,1\})$
127365
Question on showing a bijection between $\pi_1(X,x_0)$ and $[S^1, X]$ when X is path connected.
31391
bijection between $\mathbb{N}$ and $\mathbb{N}\times\mathbb{N}$
107142
If $(x_n) \to x$ then $(\sqrt[n]{x_1x_2\cdots x_n}) \to x$
148731
Constructing a bijection between $[a,b)$ to $(0,1)$
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
134081
What is the Cartesian product of $n$ polygons?
380
Bijection from modular multiplication?
103769
The Cartesian product of a finite number of countable sets is countable
24561
$\mathbb S_n$ as semidirect product
13398
Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
8494
Proof Check: Number of elements of $\mathbb{F}_{p^{n}}$ of the form $a^{p}-a$ for some $a \in \mathbb{F}_{p^{n}}$.
113109
Showing that a map is bijective and finding its inverse
14403
If $n = p_1^{a_1} ... p_r^{a_r}$ the set of nilpotents of $\mathbb{Z}_n$ is $(p_1 p_2 ... p_{r-1} p_r)\Bbb Z_n$
111032
Proof of Sets involving the Cartesian Product
59644
Proof of Cartesian product intersection