For a fixed x in X, consider the map from G to X given by g ∣ ∣ → → g ⋅ ⋅ x . The image of this map is the orbit of x and the coimage is the set of all left cosets of G x. The standard quotient theorem of set theory then gives a natural bijection between G / G x and G x . Specifically, the bijection is given by h G x ∣ ∣ → → h ⋅ ⋅ x . This result is known as the orbit-stabilizer theorem. If, in the example, we take x = 3 , the orbit is {−7,3,13,23,..}, and the two groups are isomorphic with Z.