Additive group of integers

The additive group of integers consists of all whole numbers (positive, negative, and zero) with the operation of addition. In this system, adding any two integers results in another integer within the group. The group has an identity element, which is zero, since adding zero to any integer leaves it unchanged. Each integer has an inverse, which is its negative. This structure follows the rules of a mathematical group: closure (sum of any two integers is an integer), associativity, identity (zero), and invertibility. It provides a fundamental framework for understanding how integers combine under addition.