SOWISO - UvA | Set Theory

Foreword

THEORY

T

1.

Naive vs axiomatic set theory

Elementary notions and notations

THEORY

T

1.

Specification of a set

PRACTICE

P

2.

Specification of sets

3

THEORY

T

3.

Equal set, subset, and power set

PRACTICE

P

4.

Equal set, subset, and power set

3

THEORY

T

5.

Operations on sets: intersection, union, difference, and complement

PRACTICE

P

6.

Operations on sets or relations between sets

4

THEORY

T

7.

Venn diagram

PRACTICE

P

8.

Venn diagram

3

THEORY

T

9.

Ordered pair & triple and Cartesian product of sets

PRACTICE

P

10.

Cartesian product of sets

2

Relations

THEORY

T

1.

Basic concepts

PRACTICE

P

2.

Basic concepts

3

THEORY

T

3.

Properties of relations on a set

PRACTICE

P

4.

Properties of relations on a set

1

THEORY

T

5.

Equivalence relation

PRACTICE

P

6.

Equivalentie relation

3

THEORY

T

7.

Partial ordering

PRACTICE

P

8.

Partial ordering

2

Functions

THEORY

T

1.

The concept of function

PRACTICE

P

2.

The concept of function

4

THEORY

T

3.

Properties of functions

PRACTICE

P

4.

Properties of functions

3

THEORY

T

5.

Dirichlet's box principle / pigeonhole principle

Size of a set

THEORY

T

1.

Equipotency and (in)finiteness

THEORY

T

2.

Countability

THEORY

T

3.

The Cantor-Schröder-Bernstein theorem

PRACTICE

P

4.

Equipotency

1