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**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?