For a fixed "x" in "X", consider the map from "G" to "X" given by formula_11. The image of this map is the orbit of "x" and the coimage is the set of all left cosets of "Gx". The standard quotient theorem of set theory then gives a natural bijection between formula_12 and formula_13. Specifically, the bijection is given by formula_14. This result is known as the orbit-stabilizer theorem. If, in the example, we take formula_15, the orbit is {−7,3,13,23..}, and the two groups are isomorphic with Z.