Peano arithmetic is a way of formulating arithmetic. It is based off of a set of basic axioms (the Peano axioms). We can construct all of the usual math-y stuff using second order logic (first order has variables that range over individuals; second order has variables that can range over sets), and get all sorts of mathematical wonderfulness.

Besides having a magnificant beard, Peano contributed greatly to mathematics. He produced a rigorous specification of induction. And, as we will soon find out, induction is SUPER important.

Mr. Peano, bearded italian extraordinare

Read the notes about it... but what is important to realze is how exactly we're using logic to talk about math. It's an interesting treatment that you should be familiar with, but don't get too hung up on it. It's just a preliminary stop on our VOYAGE THROUGH THE WORLD OF MATHEMATICS

Next stop: ADVENTURE Zermelo-Fraenkel set theory!!!

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