This unit is devoted to the real numbers and their properties. In particular, inequalities are discussed, which play a crucial role in analysis. The five sections of the unit cover revision of rational numbers and their decimal representations, real numbers as infinite decimals, their properties and the difficulties involved in doing arithmetic with such decimals, rules for manipulating inequalities, techniques for proving inequalities, and the concept of least upper bound.One subsection, of this unit, is intended to be studied in conjunction with an audio, available in the Analysis A Block Pack (order code M208/MMPAA). The general video programme, Coping with irrationality, is available on DVD00126 (order code M208/DVD02).