What is the exact definition of the tension of a rope?
Here http://web.mit.edu/8.01t/www/materials/modules/chapter08.pdf the following definition is given
The tension $T(x)$ in a rope at a distance $x$ from one end of the rope is the magnitude of the action -reaction pair of forces acting at the point $x$.
But I think that this is valid only in the case that the tension is the same, throughout all the rope. Is that definition still valid in that case?