How is the cardinality of a finite set determined?

In set theory, the cardinality of a finite set is determined by establishing a one-to-one correspondence between its elements and the elements of a standard set of natural numbers, specifically the set {1, 2, 3, ..., n}.1

If such a pairing exists, the set is considered finite, and its cardinality is defined as the natural number n. For the empty set, which contains no elements, the cardinality is defined as 0. More broadly, the cardinality of any set is the property it shares with all other sets that can be put into a one-to-one correspondence with it. While this process uses natural numbers for finite sets, the concept of cardinality extends to infinite sets through the use of transfinite numbers.1234