Let $X$ be an infinite subset of $\mathbb{N}$. Prove that $|X| = |\mathbb{N}|$
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
145397
How to prove that for every $i$, $a_i = i$
34154
Prove the statement $\forall x\in\mathbb N (x > 1\to\exists k\in\mathbb N\exists m \in\mathbb N (m \equiv 1 (\text{mod }2) \wedge x = 2^km))$.
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
109968
Let $X= \{ A \subset \mathbb{N} : \mathbb{N} \backslash A \text{ is finite}\}$. What is the cardinality of $X$? Prove it.
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
36281
A set is infinite iff it is equivalent to a proper subset of itself
64320
Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
50880
Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
53707
Prove that if $A$ is an infinite set then $A \times 2$ is equipotent to $A$
32155
Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
23442
Cardinality of the union of infinite and countable sets
32965
Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
117561
A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
151852
How to prove $A \subset B \iff A \cup B = B$