Chapter 1

Notes from the session.

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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