Cardinality of power set of $\mathbb N$ is equal to cardinality of $\mathbb R$
41052
The set of real numbers and power set of the natural numbers
70164
Proof exercise that the cardinal number of a set in $\mathbb R^2$ is $\frak c$
95747
Number of countable subsets of $\mathbb{R}$
117047
exponentiation of cardinal number
158671
Cardinality of a set that consists of all existing cardinalities
7785
Cardinality of sum-set
39880
Cardinality of Orderings of $\mathbb{R}$
145214
Showing the power set is equinumerous to ${}^X2$
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
44214
The number of subsets of a set of cardinality $n$
79974
The cardinality of Lebesgue sets
108922
Cardinality and infinite sets: naturals, integers, rationals, bijections
59459
Binary sequences and ${2}^{\mathbb{N}}$ have the same cardinality
86421
Proof of the definition of cardinal exponentiation
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
109054
Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?