Explore measurement, approximation, and interval arithmetic in this 42-minute lecture from the MathFoundations series. Delve into the differences between arithmetic laws for natural numbers and integers, and briefly examine rational number intervals. Learn about multiplying intervals, analyze examples of interval arithmetic, and understand the sub-distributive law. Investigate the challenges associated with "real number" arithmetic and gain insights into the logical complexities of modern pure mathematics. Enhance your understanding of foundational mathematical concepts and their practical applications in this comprehensive exploration of interval arithmetic and its implications.