Dedekind ordinal

A Dedekind ordinal is a type of ordinal number that embodies a comprehensive way of understanding order and size within infinite structures. In essence, it’s a way to classify well-ordered sets where each set is uniquely identified by its structure—specifically, if there's a one-to-one correspondence preserving order between two such sets, they share the same Dedekind ordinal. This concept helps mathematicians study infinite processes and sizes systematically, providing a foundation for understanding complex hierarchical infinities beyond the finite or simply countably infinite.