# Math Help - Finite set of integers closed under addition

1. ## Finite set of integers closed under addition

I kind of have an understanding of what this means but don't know how to prove this?

2. Originally Posted by acevipa

I kind of have an understanding of what this means but don't know how to prove this?
{0}

3. Hello, acevipa!

Suppose the set is: . $S \:=\:\{a,\:b,\:c,\:\hdots\:n\}$ . . . in increasing order.

. . $\text{If }n\text{ is positive: }\:n+n\;\notin S$

. . $\text{If }a\text{ is negative: }\:a+a\;\notin S$

The set is not closed under addition.

The only such set is a trivial one: . $\{0\}$

Edit: too slow . . . again !