Gauss's law for magnetism is stated as followed with the beautiful closed surface double integral (by wikipidia):
$$ \mathop{\vcenter{ \huge\unicode{x222F}\, }}_{S} \mathbf{B} \cdot \text d\mathbf{A} = 0 $$
As I understand, the idea is to say that if we sum (continuous sum since integral) all the scalar products between the vector field $\mathbf{B}$ (i.e., magnetic field) and surface elements $\text d\mathbf{A}$ defined by their surface normals, we get $0$?
Given the above is correct, why using the double integral (I assume the circle is for ''closed surface'') ? But why use a double integral, whereas in other fomulas like for the magnetic flux, they use a simple integral although it is still a continuous summation over a surface - unless I'm mistaken - ?
i.e., :
$\Phi_B = \oint_S \mathbf{B} \cdot \text d\mathbf{S}$