There are **9** NRICH Mathematical resources connected to **Infinity**, you may find related items under The Number System and Place Value.

Challenge Level

How much of the square is coloured blue? How will the pattern continue?

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Can you describe this route to infinity? Where will the arrows take you next?

Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses. . . .

This article is one parent's story describing his young son's exploration, and growing understanding, of infinity.

Challenge Level

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

This article gives a proof of the uncountability of the Cantor set.

Hilbert's Hotel has an infinite number of rooms, and yet, even when it's full, it can still fit more people in!

Challenge Level

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?

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Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?