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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!