Proving a set X is dense in [0,1] equivalence relation
50934
Let $x_n \in[0,1)$ s.t $x_n - \sqrt{n}\in \mathbb{Z}$. Prove that $X=\{x_n | n\in \mathbb{N}\}$ is dense in $[0,1]$.
24050
Characterization of the Closure of a Set
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
13550
For an irrational number $\alpha$, prove that the set $\{a+b\alpha: a,b\in \mathbb{Z}\}$ is dense in $\mathbb R$
61747
Proof of exchange principle in set theory
89167
Cardinality of equivalence relations in $\mathbb{N}$
28637
Proving continuous image of compact sets are compact
37924
Equivalence of norms proof
29965
Proving that $m+n\sqrt{2}$ is dense in $\mathbb R$
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
6523
Prove that the space has a countable dense subset
144362
The construction of a Vitali set
122463
How to show the that a set $A$ nowhere dense is equivalent to the complement of $A$ containing a dense open set?
95373
Additive set function on a semiring of sets
120252
Equivalences of bounded sets definitions
111032
Proof of Sets involving the Cartesian Product
39293
Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $