Explore the foundations of arithmetic with natural numbers in this 32-minute lecture. Delve into the subtle question of "What exactly is a natural number?" and examine the distinctions between primitive natural numbers, Hindu Arabic numerals, and arithmetical expressions. Challenge conventional notions about prime numbers and infinity, and discover a novel definition of primitive natural numbers using multiset theory. Learn why including zero as a natural number makes sense, departing from traditional views. Gain insights into the importance of careful examination of natural numbers and modern number theory for a deeper understanding of mathematical foundations.