Prove that the set of all finite sequences of real numbers has the same cardinality as the set $\mathbb{R}$ of reals.
12436
The cardinality of the set of all finite subsets of an infinite set
94363
Prove: Any open interval has the same cardinality of $\Bbb R$ (without using trigonometric functions)
45792
Rigorous proof that surjectivity implies injectivity for finite sets
144246
Subset of $\mathbb{R}^n$ homeomorphic to $\mathbb{R}^n$
132778
All distances are rational prove the set is countable
156783
$\mathbb R$ has the same cardinality of any interval
23608
Prove the set of all infinite binary sequences is uncountable by using Cantor's theorem.
116009
Proving that if a set is both open and closed then it is equal to the real numbers
135315
Proving whether a function on the set of real sequences is a metric
155168
Is the collection of finite subsets of $\mathbb{Z}$ countable?
95747
Number of countable subsets of $\mathbb{R}$
35692
The set of all finite subsets of the natural numbers is countable
70164
Proof exercise that the cardinal number of a set in $\mathbb R^2$ is $\frak c$
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
93330
Cardinality of all cardinalities
149382
Prove that $(0,1) \subseteq\mathbb R$ and $(4,10) \subseteq\mathbb R$ have the same cardinality.
59459
Binary sequences and ${2}^{\mathbb{N}}$ have the same cardinality