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 n^{2} 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:
 The importance of definitions.

 Working backwards.

 Iff proofs.

 Uniqueness proofs.

 Proof by cases.
Some basic number theory: Divisibility, Congruence.