Week 7: Infinity
Introduction
The concept of infinity can seem difficult to grasp, whether you’re looking at the infinitely big or the infinitely small. Intuitively, the infinite can be thought of as something limitless in size. Mathematical progress on understanding the infinite was hindered by clashes with religious and establishment views, as infinity was felt to be God’s realm, not man’s. However, as you’ll see, working with infinity can simplify problems considerably. Sometimes it’s easier to work with the infinitely big than it is to work with the very big.
Here’s Marcus to introduce this week’s topic.
Download this video clip.Video player: Video 1
Transcript: Video 1 Introduction
MARCUS DU SAUTOY
This week returns to my own subject of mathematics, and the challenge of understanding the infinitely big and the infinitely small. You might think that the infinite by its very nature is something we cannot know. But that turns out not to be the case. Indeed, we’ve come up with amazing strategies to navigate infinity, and to understand that there are many different sorts of infinity – some bigger than others! We’ve also found intriguing ways to delve into the infinitely small, including the invention of calculus and the discovery of fractals. So I hope you enjoy this week, as we head off to infinity and beyond.
Video 1 Introduction
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By the end of this week, you should be able to:
- recognise that there are different sizes of infinity
- understand the idea of proof by induction
- describe how sequences (and their limits) help with understanding the infinitely small
- appreciate the paradoxical qualities of fractals.