E xamples o of Groups The integers under addition G=Z= the integers={….-3,-2,-1,0,1,2….} the group operator is "+ ordinary addition the integers are closed under addition the identity is 0 the inverse of x is-x the integers are associative the integers are commutative(so the group is abelianExamples of Groups The integers under addition G = Z = the integers = { … -3, -2, -1, 0 , 1 , 2 …} the group operator is “+”, ordinary addition • the integers are closed under addition • the identity is 0 • the inverse of x is -x • the integers are associative • the integers are commutative (so the group is abelian)