Explore the foundational issues surrounding the definition and arithmetic of real numbers in calculus and analysis. Examine popular textbooks to uncover how they address the concept of real numbers, revealing potential weaknesses in standard mathematical thinking. Gain insights into the challenges of defining real numbers and their arithmetic, and consider the implications for the field of mathematics. Compare treatments from various calculus and analysis texts, including works by Stewart, Spivak, Apostol, and Rudin. Challenge conventional wisdom and open your mind to new possibilities in mathematical foundations.