Math 3000 - Lecture 4

What is a proof?

Proofing as a social process, a communication art.

Rigor in proofs.

Methods of Proof

Direct
If n is an odd integer, then n2 is odd.
Contrapositive
Do converse of above.
If A and B are integers and B 0. Show that if A divides B then |A| |B|.
Contradiction
The sqrt(2) is irrational.

General Hints:

Some basic number theory: Divisibility, Congruence.