I am unable to understand as to how the basis for the tangent space is
\frac{\partial}{\partial x_{i}}. Can this be proved ,atleast intuitively?
Bachman's Forms book says that if co-ordinates of a point "p" in plane P are (x,y), then
\frac{d(x+t,y)}{dt}=\left\langle 1,0\right\rangle...