If "Y" is a subset of "X", we write "GY" for the set {"g" · "y" : "y" formula_8 "Y" and "g" formula_8 "G"}. We call the subset "Y" "invariant under G" if "GY" = "Y" (which is equivalent to "GY" ⊆ "Y"). In that case, "G" also operates on "Y". The subset "Y" is called "fixed under G" if "g" · "y" = "y"for all "g" in "G" and all "y" in "Y". In the example of the orbit {−8,−6,2,4,12,14,22,24..}, {−9,−8,−6,−5,1,2,4,5,11,12,14,15,21,22,24,25..} is invariant under "G", but not fixed.