THESE ARE THE WRONG TYPE OF PIANOS!!!!
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!!!