Re: [math-fun] Volume-preserving vector field paradox: Spoiler

No. Surfaces (in 3-space) can have boundaries, and that's what they're talking about. --Dan Andy Latto wrote: -----

(*) div(V) == 0 implies that there exists a vector field W such that V == curl(W).

But their entry for Curl Theorem[2] states that the flux of a vector field of the form curl(W) through a surface S is equal to the line integral of W around its boundary bd(S).

Well, if we're working in 3 dimensions, it's a surface integral, not a line integral. -----