Transfinite Recursion

Transfinite recursion is a method used in mathematics to define sequences or functions that extend beyond traditional finite processes. Instead of stopping at a specific number, it continues through an infinite hierarchy of sizes known as ordinals. Just as we can define functions for natural numbers (like adding 1 repeatedly), transfinite recursion allows us to create definitions for larger sets, ensuring consistency and completeness. This approach is particularly useful in set theory and computer science, enabling solutions to problems that require infinite steps in a logically coherent way.