Explore the successor-limit hierarchy and its connection to ordinal theory in set theory through this 22-minute mathematics video. Delve into the mysterious ladder of arithmetical operations on natural numbers, examining numbers so large they defy understanding. Learn how to write the hierarchy efficiently and list subscripts to extend the concept further. Compare the hierarchy to ordinals in set theory, while critically examining the foundations of modern set theory. Gain insights into these advanced mathematical concepts and their philosophical implications for number theory and the nature of infinity.