Friday May 2

We talked about induction, and proved by induction that n² = 2n² for all naturals n. (Proof: n=0 is easy. Then for n>0, use the equation at step n to get the one at step n+1. No division by zero occurs.)

I talked about a curious induction proof in which the base case is at n=5. The cubic equation is solvable, and was solved by Tartaglia, but equations of degree 5 and higher are not.

Then we showed that gcds are unique. The case of gcd(a,b)=0 had to be made separately.

I stated the Euclidean algorithm to compute gcds, but didn't show that it terminates nor that it, in fact, computes gcds.