In this video we show a quick and easy way to establish the linear space of Vector Differentials, DL, as a companion to any given linear space, L. We introduced the Euclidean norm on L and obtain a Euclidean norm on DL. The norms allow us to calculate the length of vectors and recover the "smallness" of vector differentials compared to vectors in the original space L. We find an interesting "Arbitrariness Dilemma." That is, we find that the range of functions on DL such as norm and inner product are sets whose bounds are products of arbitrarily small and arbitrarily large numbers. Seems like too much arbitrariness. Not to worry, there is a way to reduce the amount of arbitrariness in the theory.
