 A function is called monotonically increasing (also increasing or non-decreasing), if for all formula_2 and formula_3 such that formula_4 one has formula_5, so formula_1 preserves the order (see Figure 1).Likewise, a function is called monotonically decreasing (also decreasing or non-increasing) if, whenever formula_4, then formula_8, so it "reverses" the order (see Figure 2).If the order formula_9 in the definition of monotonicity is replaced by the strict order formula_10, then one obtains a stronger requirement.