Adding infinitesimals

[Jehanne]

Why does adding two or more infinitesimals equal an infinitesimal?  What would happen if one added an infinite number of infinitesimals together?  How about multiplying an infinitesimal against any non-infinitesimal?  How about multiplying an infinitesimal by infinity?  Finally, consider the following:

dx = cos (theta) (dp)

Are 'dx' and 'dp' infinitesimals?  Trying to broaden my understanding of tensor calculus.

Can you give some context so we can tell what x and p are in this example? Where did you get this relation from?

It's from a book that I am trying to read, Tensor Calculus for Physics; it's on Amazon.