If there are n elements in set a, then there are 2 ^ n-2 nonempty proper subsets of set A. why?

First of all, the number of all subsets of a is 2 ^ n (let B be the subset of a, then there are two cases in a whether or not the first element of a appears in a, and there are 2 * 2... * 2 = 2 ^ n in total), and then remove the empty set and a itself, there are 2 ^ n-2 non empty proper subsets

Does a proper subset include an empty set, excluding all subsets of the ability? What is the formula for all proper subsets when there is a subset of N in a set?

True subsets do not include themselves, but contain empty sets
If a set has n elements, the number of proper subsets is (2 ^ n) - 1

Why is an empty set a proper subset of any set that is not empty

Because an empty set is first a subset of any nonempty set
Then because a nonempty set has at least one element that an empty set does not have
When two points are added up, an empty set is the proper subset of any nonempty set

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