Let $A$ a infinite set, prove $Card(A)+Card(A)=Card(A)$
53707
Prove that if $A$ is an infinite set then $A \times 2$ is equipotent to $A$
48278
Inequality about infinite cardinals
125683
Power set of a finite set is finite proof, no cardinality of power set
100726
Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
75966
Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
52614
(exercise from Tao's analysis book) Proof of a lemma relating to power set of X
157513
How can I prove that these sets are countable infinite?
44974
Infinite set and countable subsets
6478
Prove that for any infinite poset there is an infinite subset which is either linearly ordered or antichain.
123613
Double Complement of a set proof
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?
66301
The cardinality of the set of countably infinite subsets of an infinite set
23764
Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
37951
proof detail concerning bijection between a set and its power set
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.