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Jun24-07, 06:27 AM
Gauss's law in differential forms
Firstly, they are equating volume integrals, not surface ones.
Yes, and the volume is bounded by a closed surface.
Secondly, I said why the argument was flawed in my previous post. Equality of n-dimensional integrals, even over all possible n-surfaces, does not rule out pointwise inequality over a set of measure zero (n-1-surfaces, for example).
I don't understand what you're trying to say. Maybe someone with more expertise in math can take a look?