1. The problem statement, all variables and given/known data I would define a group as follows: A group consists of a non-empty set G together with a binary operation (say, *) on G such that the following axioms hold: G1.....G2....G3... 2. Relevant equations 3. The attempt at a solution I know this is a trivial question, but doesn't a binary operation on a set (here G) necesserily imply that the set is closed under that binary operation? The only reason i ask is that many of the definitions of groups I have come across include both that * is a binary operation under which G is closed. Isn't this redundant?