If Y is a subset of X, we write GY for the set { g · y : y ∈ ∈ Y and g ∈ ∈ 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.