Infinity

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All about infinity

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 the different types of infinity.
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Hilbert's hotel

Hilbert's Hotel has an infinite number of rooms, and yet, even when it's full, it can still fit more people in!
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How many elements are there in the Cantor set?

This article gives a proof of the uncountability of the Cantor set.
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Early encounters with infinity

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

Age

11 to 14

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 picture it?
problem
How long is the Cantor set?

Age

11 to 14

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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Diminishing returns

Age

11 to 14

Challenge level

How much of the square is coloured blue? How will the pattern continue?
problem
Odds, evens and more evens

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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