4/3 -- Intermediate: Mathematical Induction and Peano Axioms. (Oleg Gleizer)
At the beginning of this class we will (hopefully) finish the 1/31 handout, solving Problems 18 - 23. Then we will start a new topic, Mathematical Induction and Peano Axioms. The goal of the new mini-course is to show that a + b = b + a for any two non-negative integers a and b. To prove this seemingly obvious statement, we will need to teach an Artificial Intelligence (AI) some elementary arithmetic, proving that 1 + 1 = 2 as well as associativity and commutativity of addition along the way.