@ benquo: “Incidentally, that “illegal operation” is essential to the symbolization of the differential Calculus, as I’m sure you’re aware. dy = K dx, ergo dy/dx = k (i.e. 0 = K 0, therefore 0 / 0 = K)”
Benquo, you should go and look up mathematical real analysis—see for example
This will give you the rigorous basis upon which calculus is founded. dy/dx is not dividing zero by zero, it is just notation for the following limit:
lim_c --> 0 { [ y(x+c) - y(x)] / c }
the above is a limit of well-defined quotients, since c is never equal to zero. If the limit exists, we say that y(x) is a differentiable function.
@ benquo: “Incidentally, that “illegal operation” is essential to the symbolization of the differential Calculus, as I’m sure you’re aware. dy = K dx, ergo dy/dx = k (i.e. 0 = K 0, therefore 0 / 0 = K)”
Benquo, you should go and look up mathematical real analysis—see for example
http://en.wikipedia.org/wiki/Real_analysis
This will give you the rigorous basis upon which calculus is founded. dy/dx is not dividing zero by zero, it is just notation for the following limit:
lim_c --> 0 { [ y(x+c) - y(x)] / c }
the above is a limit of well-defined quotients, since c is never equal to zero. If the limit exists, we say that y(x) is a differentiable function.