An infinite-order group is simply a group that has an infinite number of elements. (Keep in mind that there
are different types of infinite.) Here are a few examples:
The set of all integers under the composition of addition.
The set of all displacements (translations) in a common direction with the composition of consecutive
displacement. The result of this transformation can be seen in patterns - imagine an infinite plane of
wallpaper. These infinite repetitions are also known as tesselations.
The set of all rotations about a point under composition of consecutive rotation. There are infinite
symmetry axes in this case (think of a sphere).
Page author: Sasie Sealy