How many subsets does a finite set with n elements have?

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Infinity — infinity Mathematical symbol representing the concept of infinity.

A finite set with $n$ elements has $2^{n}$ subsets.1

This collection of all subsets of a given set is known as its power set. According to Cantor’s theorem, the cardinality of a set is always strictly less than the cardinality of its power set. While this relationship is straightforward for finite sets, Georg Cantor demonstrated that this principle also applies to infinite sets, leading to an ever-increasing hierarchy of transfinite numbers.12