A while ago, I was playing a number game with my daughter. We took turns to think of bigger and bigger numbers. She started with a thousand; I said a million. But what, she wanted to know, is the biggest number?

We talked about the number line: whatever number you can think of, you can always add one (or more) to it, to make a bigger number. Counting never stops^{1}. So, in our game, we could have added one to a thousand or a million to make bigger numbers, like this:

1,000 + 1 = 1,001

1,000,000 + 1 = 1,000,001

You can also multiply a number by ten or a hundred (or more) to make it even bigger!

But there are some times when mathematicians and scientists find it helpful to think about things that go on and on forever and never stop. They describe this as ‘infinity‘. They use a special symbol for infinity, which looks like this: ∞

When you think about numbers, you can count and count and count but the the number line just keeps on going. There is always one more… and one more… and one more…

Sometimes in maths, we pretend that infinity is the biggest number. But it’s not a real number – you can’t count with it, or add to it, or multiply by it. Infinity is an idea of something that never ends, and you have to use your imagination to think about it.

- I would like to thank Professor Ian Stewart FRS for kindly helping us to think about the number line and why counting never stops. ↩

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