Math 4200

Introduction to Set Theory

2 &

1. Sets

a) { } , { 1, 2, 3, 4 } , { x : p(x) }

b)

c) Power sets, interval notation

d) Set operations

Definitions

e) DeMorgan’s Laws

,

f) Addition and multiplication of whole numbers

2. Definitions and Theorems

Functions

Definition of a function

3. George Cantor

Z is the same size as  J

4. Are There Really That Many Real Numbers?

5. Power Set: To Infinity and Beyond!

6. Bertrand Russell

a) Russell’s Paradox: In the town of Seville, the barber shaves those and only those men who do not shave themselves. Who shaves the barber?

b) Axioms of Set Theory

7. Function: A Set of Ordered Pairs