Examples of Groups The non-zero reals under multiplication G=R the group operator is"x>, ordinary multiplication If a, b are inR-109, then ab is inR-10) the identity the inverse of a is 1/a the reals are associative the reals are commutative(so the group is abelian)Examples of Groups The non-zero reals under multiplication G = R -{0} the group operator is “*”, ordinary multiplication • If a, b are in R-{0}, then ab is in R-{0} • the identity is 1 • the inverse of a is 1/a • the reals are associative • the reals are commutative (so the group is abelian)