3 ms·
The article is dumb, but the paper is actually pretty interesting. Intuitively, I never treated differentials as "algebraic units" -- even though I can see why
by dvt 7y ago
The article is dumb, but the paper is actually pretty interesting.
Intuitively, I never treated differentials as "algebraic units" -- even though I can see why it might be tempting to do so. In other words, I never thought that dx^2/dy^2 = (dx/dy)^2. From my experience, most teachers and professors do hint that "something funky" is happening when you say "dBLAH."
Further, (and more to the root of the problem), as far as higher-order derivatives are concerned, I always held a firm belief that something like "d^nx" was not really a manipulatable statement and was just shorthand for "the nth derivative" and certainly not the "first derivative raised to the nth power."
- a1369209993 7y agoThe 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.