How to prove that the set of natural numbers $\mathbb{N}$ has the same size as $\mathbb{N\times N}$?
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
151553
Big-O proof showing that t(n) is O(1)
45788
$n$-th digit in the sequence of natural numbers
28223
Prove/Disprove that if two sets have the same power set then they are the same set
85099
How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
35692
The set of all finite subsets of the natural numbers is countable
73174
Prove $KN\cong K\times N$ if $K\cap N=\{e\}$
46967
What is wrong with this proof that the power set of natural numbers is countable?
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
42603
How can I prove that the cadinality of a set minus a finite number of elements of it is still the same as the original set?
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
86263
How do we show there are the same number of elements in each of the sets?
109219
How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?
59535
Prove that there exists such a set of $n$ positive integers
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
154754
Is $O_n$ isomorphic to $SO_n \times \{\pm I\}$?
76823
Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?