$X$ and $X\times X$ has the same cardinal, if $X$ is inifinite.
41783
Cardinality of the Cartesian Product of Two Equinumerous Infinite Sets
21479
Why cofinality is a cardinal.
137203
Measurable cardinal existence condition
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
136835
ZF Set Theory - If $|A|^{|B|} = |B|$, then $|A| = 1 = |B|.$
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
41099
If $A \subseteq C$ and $B \subseteq D$ then $A \times B \subseteq C \times D$
62566
Does $X\times S^1\cong Y\times S^1$ imply that $X\times\mathbb R\cong Y\times\mathbb R$?
76432
$i^{-1} F$ a sheaf if and only if $\varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U) \to F_x \times F_y$ is an isomorphism.
120562
If A is an infinite set and B is at most countable set, prove that A and $A \cup B$ have the same cardinality
106325
Question about Cardinality
50939
If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
149382
Prove that $(0,1) \subseteq\mathbb R$ and $(4,10) \subseteq\mathbb R$ have the same cardinality.
5840
divides, not divides and cardinalities
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
80209
If $X,Y$ are equivalence relations, so is $X \times Y$