Explore the fascinating world of higher arithmetical operations in this 43-minute mathematics lecture. Delve into the successor-limit hierarchy, moving beyond basic addition, multiplication, and exponentiation. Examine detailed examples of advanced arithmetical computations, including the *_(n+1) operation and new types of limits. Discover how this hierarchy ascends to incredibly large numbers, pushing the boundaries of computational feasibility while still remaining within the realm of natural numbers. Follow along with a step-by-step analysis of a complex higher arithmetical calculation, gaining insight into the abstract yet intriguing nature of these advanced mathematical concepts.