Z,(1/2) Define Z={[0],[1],[2],,[n-l]}. Or,more conveniently,Z=0,1,2,...n-1). (Z,+)forms a commutative additive group -Associavitivity:for Va,b,c eZn,[a]+([b]+[c])= [a]+[b+c]=[a+b+c]=[a+b]+[c]=([a]+[b])+[c] -Existence of identity:0 is the identity element. -Existence of inverse:the inverse of a,denoted by-a,is n-a. -Communitivity:for Va,be Zn,[a]+[b][b]+[a] When doing addition/subtraction in Zn just do the regular addition/subtraction and then compute the result modulo n. -InZ10,5+9=4 99 Zn (1/2)  Define Zn={[0], [1], [2], …, [n-1]}.  Or, more conveniently, Zn={0, 1, 2, …, n-1}.  (Zn,+) forms a commutative additive group ─ Associavitivity: for ∀a, b, c ∈ Zn, [a]+([b]+[c]) = [a]+[b+c]=[a+b+c]=[a+b]+[c]=([a]+[b])+[c] ─ Existence of identity: 0 is the identity element. ─ Existence of inverse: the inverse of a, denoted by –a, is n-a. ─ Communitivity: for ∀a, b∈ Zn, [a]+[b] = [b]+[a]  When doing addition/subtraction in Zn, just do the regular addition/subtraction and then compute the result modulo n. ─ In Z10, 5+9=4