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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?

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  • $\begingroup$ The definition is valid for all cases. $\endgroup$ – lucas Apr 16 '16 at 10:26
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The definition given by mit is perfectly correct. I don't see any problem with it.

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