Proof: $\kappa \cdot \kappa = \kappa$ for infinite cardinals
4912
Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$
48278
Inequality about infinite cardinals
9651
Cardinality of cartesian product of an infinite set with N
144372
How to Prove that if $A$ is bounded, then $A \cdot A$ is bounded?
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
23442
Cardinality of the union of infinite and countable sets
109054
Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
2044
Club filter of $\kappa$ is $\kappa$-complete
108957
Cardinality of a totally ordered union
73415
The reason why the existence of inaccessible cardinals cannot be proven in ZFC
122947
What is the cardinality of the set of infinite cardinalities?
75019
Infinite Cartesian product of countable sets is uncountable
25685
What is the product of all nonzero, finite cardinals?
25050
To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
97697
Countable union of sets of cardinality $c$ has cardinality $c$
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?