 In addition, if "L"/"K" is purely transcendental and "S" is a transcendence basis of the extension, it doesn't necessarily follow that "L" = "K"("S").For example, consider the extension formula_43 where "x" is transcendental over formula_9 The set formula_45 is algebraically independent since "x" is transcendental.Obviously, the extension formula_46 is algebraic, hence formula_45 is a transcendence basis.