Welcome to Week 10. This is a short week, we have just one lecture. The theme of this lecture is to give a precise meaning to the very important concept of convergence of a sequence of real numbers. We will also discuss some other properties of sequences, such as boundedness and monotonicity. We will prove the Monotone Convergence Theorem, which states that the properties of boundedness and montonicity in combination are enough to guarantee that a sequence is convergent – along with the Axiom of Completeness in the real numbers.