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For the next year I’ll be focused on the job hunt, but afterwards I’d quite like to work on a “motivated” course in real analysis. I’ve been working on my first paper, and I have realised that there is a lot of work that won’t be shown within it. The “discovery process” will not be…

There isn’t an immediately accessible proof of this that I am happy with, though it is not particularly hard. I will agonise every detail, strap in. Fix an explicitly known bijection \(\pi : \mathbb N \to \mathbb Q\), where \(\mathbb Q\) is represented by the equivalence classes of pairs \((p, q) \in \mathbb Z \times…

I’ve written this post before but looking back I don’t think it was particularly good. Too many symbols and not enough explanation maybe. In this post I’ll expand on the sense in which a failure of computability implies a failure in provability. Turing Machines Turing machines are a way to treat computer programs as a…