I am reading a book named sets & groups, I would like to ask: What exactly is a finite set of order n? [itex]A_1\times A_2\times A_3...A_n[/itex] ? is pair [itex](x_1,x_2,x_3...x_m)[/itex] counted as a single element? or a set? or an order? also how should I prove that the number of subsets, including empty set, of a finite set of order n is [itex]2^n[/itex]? Thanks!