Confused with the use of the word "smooth". [Multi-Variable Calc course] A couple weeks ago we went over the Fundamental Theorem of Line Integrals, which requires "smooth" simple connected curves. My professor's definition of smooth was a curve having "no corners". Now, with Green's Theorem, "smooth" curves are permitted to have corners. Are there multiple definitions for this word in mathematics? How am I supposed to justify what is smooth and what isn't?