When defining closure property of the set $\{0,1,-1\}$ under addition? Can we say that this set is closed under addition?
My confusion is that if we take pairs like $(0,1),(0,-1),(1,-1)$ then the seems to be closed under addition. Can we take $1$ two times and say $1+1=2$ and as $2$ doesn't exist in the set, hence the given set is not closed under addition. Please help me in this.