Remember: Let i be a non-empty interval I ⊆ ℝ. A function φ : I → ℝ is called monotonically increasing (or decreasing),
if
(or φ(x1) ≥ φ(x2)) holds true for all x1,x2∈ I where x1< x2. If equality
is excluded, the function is called strictly monotonically increasing (or decreasing)