Examines the logical foundations of concepts used throughout mathematics, such as order and equivalence relations, number and continuity. The use of infinity in mathematical arguments is investigated and implicit assumptions about infinite sets are exposed. Notions of infinity are formulated precisely and it is shown how infinite sets may be counted and compared in size. It is seen that, even in something as basic as set theory, 'truth' is not absolute.
Not currently offered.
This Course was last offered in Semester 2 - 2015.
On successful completion of the course students will be able to:
1. Learn about the logical foundations of such mathematical concepts as number, continuity and set
2. Gain an appreciation of the usefulness and limitations of the development of theories from axioms
3. Understand the concept of infinity and its role in mathematics.
- The need for a rigorous treatment of the infinite in mathematics
- The Zermelo-Fraenkel Axioms
- Ordinal and cardinal numbers
- Transfinite induction
- The Axiom of Choice
- The Continuum Hypothesis.
MATH2320 or MATH2330
Written Assignment: Assignments
In Term Test: Mid Semester Test
Formal Examination: Examination