In summary, we used associativity, identity elements, and inverses in a set of all integers to solve the given equation. This perhaps suggests that these would be useful traits for a binary structure ...In summary, we used associativity, identity elements, and inverses in a set of all integers to solve the given equation. This perhaps suggests that these would be useful traits for a binary structure and/or its operation to have. They are in fact so useful that a binary structure displaying these characteristics is given a special name. We note that these axioms are rather strong; “most” binary structures aren't groups.
