For an infinite set $A$, does $|A| = |A \times A|$?
31318
Cardinality of cartesian square
66301
The cardinality of the set of countably infinite subsets of an infinite set
136835
ZF Set Theory - If $|A|^{|B|} = |B|$, then $|A| = 1 = |B|.$
145397
How to prove that for every $i$, $a_i = i$
66563
Is $ (A∪B)×(C∩D)=(A∪C)×(B∪D)$ true for all sets A,B,C and D?
89712
For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$
157513
How can I prove that these sets are countable infinite?
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
140103
If product of two sets $A\times B$ is closed, are $A$ and $B$ closed?
109219
How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?
149553
Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
83798
Does $A$ a UFD imply that  $A[T]$ is also a UFD?
77902
If $A,B,$ and $C$ are sets, then $A\times(B-C)$ = $(A \times B)$ $-$ $(A \times C)$.
146560
Is there any uncountably infinite set that does not generate the reals?
83714
$A \in B$ vs. $A \subset B$ for proofs
32929
Questions about proving $\lnot \lnot a = a$