# Power sets

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## Power sets

The cardinality of a set is the number of elements of the set. For example, the set A = {1, 4, 6} contains 3 elements, and therefore A has a cardinality of 3. There are two approaches to cardinality, one which compares sets directly using bijections and injections, and another which uses cardinal numbers.The cardinality of a set is also known as its "size", when there is no possibility to make confusion with other concepts. The cardinality of a set A is usually denoted | A |, with a vertical bar on each side; this is the same notation as absolute value and the meaning depends on context. Alternatively, the cardinality of a set A may be denoted by n(A), A, card(A), # A, or \(P(x)\) N.B. The power set of the empty set is not the empty set, it is a set which contains one element, the empty set, and as a consequence the power set of that set is a set with two elements: the empty set, and a set which contains the empty set.

**Power set**

A power set is the total of possibles subsets that a set has.

- If a set A contain the numbers 1 to 3, then the posibles subsets ( its power set) that A can has is 2 cube.

2 to the third power is equal to 8, so they are 8 possibles subsets for this set.

A= { {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} }

it include the empty set and the original set itself.