Power Sets and the Cardinality of the Continuum

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In this video we will learn about the power set, which is the set of all subsets of a given set. The cardinality of the power set of size n is given by 2^n. Finally, we will see a really interesting function that maps surjectively from the power set of the natural numbers using binary numbers to the interval [0,1] which is a continuum and we have previously seen by Cantor's diagonalization that [0,1] is uncountably infinite. In general, the power set of a set has a higher cardinality than the original set.

0:00 Definition of Power Sets
2:18 Example with 3 elements
3:10 Power Set of the Empty Set
4:33 Cardinality of a (finite) power set
5:52 Power Set of the Natural Numbers
10:22 Cardinality and uncountably infinite

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