Tobias Holck Colding opens MIT's 18.100B Real Analysis course by laying the groundwork for mathematical analysis, starting with the real numbers themselves. He builds up the properties that distinguish the reals from the rationals, including completeness and the least upper bound property, setting the stage for the rigorous proof-writing the course demands. Running 66 minutes, the lecture moves at a chalkboard pace typical of MIT OpenCourseWare, with Colding working through definitions and basic theorems while explaining the logical structure a proof needs to hold together. This is the first lecture in the Spring 2025 offering of 18.100B, aimed at students who already know calculus and are moving into the more abstract, definition-driven territory of analysis. The focus throughout is on precision: what a real number actually is, why the axioms matter, and how to argue from them rather than from intuition.