Power Set

A power set is a specially defined set using the elements of another set. The power set contains all possible combinations of elements from the original set. So, the power set contains all the proper subsets of a given set, the set itself and the empty set as its elements. The word power refers to the mathematical power function. The number of elements in the power set is always equal to the number of elements in the original set to the power of two. The power set determines all possible set combinations of a given set. Every set has a power set, but a set with an infinite number of elements will have a power set with an infinite number of elements. In other words, the power set of an infinite set is infinite.

Using the set of numbers (1, 2, 3, 4) the elements of this power set are all the proper subsets (1, 2, 3, 4), (1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4), (1), (2), (3), (4) and (the empty set). There are sixteen elements in this power set. This is equal to four squared, which is four to the power of two.