My textbook gives the definition of a reversible transformation as a transformation that can be inverted by effectuating only infinitesimal changes in the surroundings. I admit that I have no idea of what infinitesimal means in a rigourous mathematical language, therefore the definition is quite confusing to me. Then the book prove that the entropy of a Carnot cycle is zero and, since a reversible cycle can be approximated by sum of many Carnot cycles, the entropy of a reversible cycle is zero too. How can we see that a reversible cycle can be arbitrarily approximated by Carnot cycles? Thank you so much for any help in understanding!!!