Why does $\mathbb{R}$ have the same cardinality as $\mathcal{P}(\mathbb{N})$?
41052
The set of real numbers and power set of the natural numbers
23837
Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
117478
Prove that $\mathbb{R}$ and the interval $(0, \infty)$ have the same cardinality.
102972
Cardinality of $\mathbb{R}^\mathbb{R}$ by diagonal argument
13398
Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
73927
Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
152382
Can an infinite set A be larger than an infinite set B but still have the same cardinality?
96845
Question: Compare the cardinality between the sets $\Bbb R$ and $\Bbb N^{\Bbb N}$
158671
Cardinality of a set that consists of all existing cardinalities
106325
Question about Cardinality
39880
Cardinality of Orderings of $\mathbb{R}$
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
22232
Proving that cardinality of the reals = cardinality of $[0,1]$
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
54496
Showing that $\mathbb{R}$ and $\mathbb{R}\backslash\mathbb{Q}$ are equinumerous using Cantor-Bernstein
59459
Binary sequences and ${2}^{\mathbb{N}}$ have the same cardinality
45216
Cardinality of $[0,1]$