Infinity

The paradoxes of Zeno in antiquity might seem like sophisms, but, as it has turned out, they shed light on mathematical infinity and have led to many derivative ideas in mathematics and science. Zeno’s paradoxes portray movement in terms of discrete points on a number line, where a move from A to B is done in separate (discrete) steps. But the gap in between is continuous. So, to resolve the paradoxes a basic distinction between discrete and continuous is required—a gap that was filled with the calculus much later. The infinity concept became in the nineteenth century the basis for the discovery of new numbers—by the German mathematician Georg Cantor—which seemed at the time to be counterintuitive. This chapter looks at the paradox of infinity and at Cantor’s ingenious discoveries.