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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.
Infinity
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problemOdds, evens and more evens
Age11 to 14Challenge level
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
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problemDiminishing returns
Age11 to 14Challenge level
How much of the square is coloured blue? How will the pattern continue?
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problemRoute to infinity
Age11 to 14Challenge level
Can you describe this route to infinity? Where will the arrows take you next?
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problemHow long is the Cantor set?
Age11 to 14Challenge 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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problemThe Cantor set
Age11 to 14Challenge 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?
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articleHow many elements are there in the Cantor set?
This article gives a proof of the uncountability of the Cantor set.
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articleHilbert'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! -
articleAll 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.