Let $S = \{A : A \subseteq \mathbb{Z}^+, |A| < \infty\}$. Prove or disprove $|S| = |\mathbb{Z}|$.
41192
Neatest proof that set of finite subsets is countable?
31559
If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
135611
Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
32441
How to prove or disprove statements about sets
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 $[0,1]$.
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
34308
Given $|z|<1$ prove $\lim_{n \to \infty} z^n=0$.
13550
For an irrational number $\alpha$, prove that the set $\{a+b\alpha: a,b\in \mathbb{Z}\}$ is dense in $\mathbb R$
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
104855
Prove that $N \subset Z(G)$
73696
Given $(a_n)$ with $a_n \geq a_{n+1} \geq 0$ show that if $\sum \sqrt{a_n a_{n+1}} < \infty \implies \sum a_n < \infty$