## Florence Nightingale Day: Dona Strauss

**Professor Dona Strauss**, University of Leeds

**Wednesday 17 April 2013, 1330-1400
Management School Building**

**Infinite numbers**

Infinite numbers were developed in the nineteenth century, to measure the size of infinite sets. They have some surprising properties. For example, a proper subset of a set can have the same size as the set itself. The set of whole numbers has the same size as the set of rational numbers. But it is far from being the case that all infinite sets have the same size - there are an infinite number of different infinite numbers. Handling infinite sets gave rise to some of the paradoxes which challenged mathematicians a century ago; and some statements about infinite numbers are undecideable - they cannot be proved or disproved. A statement which is easy to formulate, but which is undecideable, is that any infinite set of real numbers has the same size as the set of real numbers or the same size as the set of whole numbers.