Explore interval arithmetic in this 46-minute mathematics lecture from the MathFoundations series. Begin with a review of irrational numbers before delving into order relations for natural numbers and the construction of integers and rational numbers. Learn about interval representations for natural numbers, their interpretations, and how to perform arithmetic operations with them. Discover the challenges of extending this arithmetic to integral intervals. Gain insights into the foundations of mathematics, including discussions on logical difficulties in modern pure mathematics. Follow along with detailed explanations, examples, and challenges to deepen your understanding of this fundamental mathematical concept.