proving $|\mathbb{N}|\leq|A|$ for any infinite set A
125411
Infinite set always has a countably infinite subset
67295
Please check my proof for $N$ is infinite
134071
If A is a finite set and B is an infinite set, then B\A is an infinite set
156006
Cardinality of set containing all infinite subsets of $\mathbb{Q}$
62208
If $A$ is a non-empty set, then $A \notin A$
73696
Given $(a_n)$ with $a_n \geq a_{n+1} \geq 0$ show that if $\sum \sqrt{a_n a_{n+1}} < \infty \implies \sum a_n < \infty$
48593
Proof that if $s_n \leq t_n$ for $n \geq N$, then $\liminf_{n \rightarrow \infty} s_n \leq \liminf_{n \rightarrow \infty} t_n$
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
145428
Set $A$ is countably infinite if and only if there exists a bijection $f: \mathbb{N} \rightarrow A$
107641
Show that an infinite set of families are linearly independent
151928
How to prove that $N\setminus A$ is finite?
157924
$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
77548
Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
132868
Bijection between an infinite set and its union of a countably infinite set
149673
Cardinality of an infinite union of finite sets
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$