What is an N-tuple set? Why do n-ary sets have n subsets of 2, the n power of 2 minus a proper subset, the n power of 2 minus a nonempty set, and the n power of 2?

There are n elements in a set, and this set is called an n-tuple set.

A subset of n-tuples is classified according to the number of elements in the subset.

It can be 0 elements, 1 element, 2 elements ... n elements, a total of n classes.

The number of subsets in the combination number formula is c (n, 0)+c (n. 1)+...c (n, n) = 2 n.

So there are 2 n subsets in total.

As long as one of 2 n in all subsets is removed, the number of proper subset is (2 n)- 1.

As long as one empty set is removed from all subsets of 2 n, the number of non-empty sets is (2 n)- 1.

As long as one empty set and one self are removed from all subsets of 2 n, the number of non-empty proper subset is (2 n)-2.