###### Learning Outcomes:

On successful completion of this module, the student is expected to be able to understand the definitions, theorems and examples covered in all of the topics listed above. These include, but are not limited to, reviewing injections, surjections and bijections; demonstrating that there is no 'largest infinite set'; Russell's Paradox; the axioms of Set Theory; the Axiom of Infinity and the Principle of Mathematical Induction; constructing and ordering the natural numbers; finite, infinite and uncountable sets; building the arithmetic of natural numbers; partially ordered sets and the Schroeder-Bernstein Theorem via Tarski's Fixed Point Theorem; the Axiom of Choice and Zorn's Lemma; `good' and `bad' consequences of Choice; building a more complete theory of equinumerosity and dominance; and (time allowing) metamathematics and undecidability in Set Theory (e.g the Continuum Hypothesis) and Computer Science (Turing's Halting Function).