Cantor's Dedekind Infinite Set

A Dedekind-infinite set, named after mathematician Georg Cantor, is a set that can be put into a one-to-one correspondence with a proper subset of itself—meaning it has the same size as some part of itself but not all. For example, the set of natural numbers (1, 2, 3, ...) is Dedekind-infinite because you can match each number to its successor, creating a perfect pairing between the whole set and its tail. This idea helps distinguish infinite sets from finite ones, emphasizing that some infinities have structures that mirror themselves, allowing endless self-similarity.