One everyday example of a group is the set of whole numbers (integers) with the addition operation. It is easy to see that when adding two integers, the result is always an integer. So closure is true. The identity element for this group is zero. Because the order of additions does not matter (in other words, formula_1), associativity rule is also true. And the inverse of any integer is its opposite number (the inverse element of zero is zero). This group is also an abelian group. It is an infinite group (also called a group of "infinite order") because it has an infinite number of elements: all the integers.