MIT's 18.100B Real Analysis course, taught by Tobias Holck Colding, dedicates this session to the mechanics of mathematical proof-writing. Colding returns to the Archimedean property, examined in an earlier lecture, and uses it as a case study in how to structure a rigorous argument, what assumptions can be taken for granted, and what must be justified step by step. He then works through the classic proof that the square root of 2 is irrational, using it to illustrate proof by contradiction and the kind of precision expected in real analysis. At eighty minutes, the lecture moves at the pace of a full class session, with Colding working through the logic on the board rather than rushing to results. It is aimed at students already in the course, building directly on prior material rather than standing alone as a general introduction.