Chapter 1: A classical beginning

Chapter 1: A classical beginning

We spent some time on variations of the proof of the fact that \(\sqrt{2}\) is irrational. Some things that came up:

• The least number principle vs axiom of choice: are these independent?
• While working through a critique of an incorrect proof showing that \(\sqrt{n}\) is irrational for all \(n\), we showed that \(\sqrt{n}\) is rational iff \(n = m^2\) for some \(m\).
• We went over a nice geometric proof of the irrationality of \(\sqrt{2}\) and translated it to algebraic terms.

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