Proving that $|\{B\subseteq S: |B|<\infty \}|=|S|$
12436
The cardinality of the set of all finite subsets of an infinite set
55995
Why is the supremum of the empty set $-\infty$ and the infimum $\infty$?
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
134007
Borel-Cantelli-related exercise: Show that $\sum_{n=1}^{\infty} p_n < 1 \implies \prod_{n=1}^{\infty} (1-p_n) \geq 1- S$.
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
62077
Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
115411
if $A_n \longrightarrow \infty $ and $B_n \longrightarrow \infty $ then $(A_n+B_n) \longrightarrow \infty$
70746
Proving that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
11817
Proving that every set $A \subset \Bbb N$ of size $n$ contains a subset $B \subset A$ with $n | \sum_{b \in B} b$
145772
Proving $\liminf_{n\to\infty}(-a_n)=-\limsup_{n\to\infty}(a_n)$
83714
$A \in B$ vs. $A \subset B$ for proofs
28391
Prove the compactness of a set B
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
49143
Showing $A \subset B \iff A\cap B=A$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$