- #1
Syrus
- 214
- 0
Homework Statement
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...
Homework Equations
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?
Last edited: