My textbook ("Mathematical Methods for Physicists", George B. Arfken) says the following when talking about SO(2):
The dimension of this vector space (over the complex numbers) is the order of G, that is, the number of linearly independent generators of the group. (page 247)
However, I cannot seem to find such a definition anywhere else. For finite groups, I know that order is equal to the number of elements, so continuous (Lie) groups must have infinite cardinals for their order. Could someone please elucidate on the different definitions?