Given a function f :S→S, a subset A of S is invariant if f(A) ⊆ A. Note that this is a much weaker condition than requiring that f(a) = a for all a ∈ A. For example, if f reflects ℝ2 in the x-axis, then the x-axis is invariant in the latter sense—every point is fixed—but any line parallel to the y-axis is an invariant set.