For $n$ sets with intersection of size at most $1$ sets we have $\frac{1}{n}\sum\limits_{i=1}^{n}|S_i|=O(\sqrt n)$
132541
Showing ${1\over n}\sum|S_i|=O(\sqrt n)$ for $S_i\subset [n]$, $|S_i\cap S_i|\le 1$ for $i\ne j$
17461
Show that a set is dense in $[-1,1]$
3392
Sum of products of elements of nonempty subsets of A set
55659
Sum of closed and compact set in a TVS
55648
Intersection of finite number of compact sets is compact?
37012
The number of summands $\phi(n)$
5215
Can the principle of inclusion/exclusion be used to count elements in the intersection of a sequence of sets?
130156
Image of the union and intersection of sets.
152342
$x_1+x_2+\cdots+x_n\leq M$: Cardinality of Solution Set is $C(M+n, n)$
86902
Consider the smallest number in each of the $n\choose r$ subsets (of size $r$) of $S=\{1,2,\ldots,n\}$...
25338
Sum of $n$ integers from set of size $2n-1$ divides $n$
134770
For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
121685
Is there a bijection of the natural numbers which swaps $\frac{1}{n}$-summable subsets with $\frac{1}{\sqrt{n}}$-summable subsets?
112084
Proof of a formula for the power set of a union of two sets
107010
How many elements of order $k$ are in $S_n$?
568
Consider a set $A$ of $10$ integers, $A = \{a_1,a_2, \ldots ,a_{10}\}$. Prove that there is at least one subset of $A$ whose sum is divisible by $10$.
11817
Proving that every set $A \subset \Bbb N$ of size $n$ contains a subset $B \subset A$ with $n | \sum_{b \in B} b$