How big is infinity?

Infinity is bigger than you can ever imagine. But what if you want to imagine it? To do this, you need to rethink your intuitions about size.

It is easy to compare four chairs and five people. Five is bigger than four: There are more people than chairs. But if we want to compare two groups of infinite size, we cannot count to see which group is bigger.

Instead of counting people and chairs, we could ask everyone to sit down on one of the chairs. If there are any empty chairs left, then there are more chairs than people. If some people cannot find a seat, then there are more people.

We can use this trick for infinity too, but there is a twist: Leftover chairs do not equal that there are more chairs, because people could have seated themselves in the wrong way! Infinity is strange in this way. Together we will explore the limits of this strangeness and ultimately find how to decide which infinities are bigger than others.

In the end, you'll find that infinity is actually quite small.

(Illustration: Shutterstock)