I need clarification of what it means when they say Let $S = \mathbb{R} \setminus \{-1\}$. Does this mean all the real numbers except $-1$. Problem: Let $S = \mathbb{R} \setminus \{-1\}$ and define a binary operation on $S$ by $a*b = a + b + ab$. Prove that $(S,*)$ is an abelian group.
What I know: I know I need to show closure, identity, inverse, assoc, and comm.
For closure I want to prove using contrapositive. So I know I have to start with assuming that $a*b$ is not in S and show that $a$ is not in S or $b$ is not in $S$. But I'm really confused with $S = \mathbb{R} \setminus \{-1\}$. Because I know I can say $a*b = a+b+ab$ if it was in S but I'm assuming it is not.