The main point seems to be that: / d\² d² D²ₓ = |−−| ≠ −−− \dx/ dx² because (1/dx)*d*(1/dx)*d ≠ (1/dx)*(1/dx)*d*d or just d*(1/dx

The main point seems to be that: / d\² d² D²ₓ = |−−| ≠ −−− \dx/ dx² because (1/dx)*d*(1/dx)*d ≠ (1/dx)*(1/dx)*d*d or just d*(1/dx) ≠ (1/dx)*d In other words, the "algebraic units" are fine, but multiplication on them is noncommutative.[0] 0: Like multiplication on damn near everything else that isn't really a number.