Let "x" be a real number in the interval (0,1). We know that in that interval x^2 is smaller than x. Now dx is smaller than 1. Then, dx^2 must be smaller than dx. But since dx is an infinitesimal number, the only number smaller than dx is zero.
1/inf = 0 = 2/inf. But we can't do this: (1/inf)*inf=(2/inf)*inf which leads to the contradiction 1=2. Is that the reason we say inf/inf is undefined?
2 apples - 2 apples = zero
2 apples - 2 apples = void?
"No single mathematical creation has been more potent for the general on-go of intelligence and power." G.B. Halsted, referring to zero