email@example.com wrote: > What is the difference between a vector and a point? > Why are there two concepts? > > Wessel described complex numbers as "vectors" in some space like R^2. > Argand described complex numbers are "points" in some space like R^2. > > What's the difference? > > What's wrong with me saying "a vector is a point, and a point is a vector" ?
If your universe is a vector space you can say it all you like. But there are perfectly good metric spaces consisting of a set of points that are not vectors. For example, the set [0,1], with the metric it inherits from either R or R^2.