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Broad Topics > Numbers and the Number System > Countability

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All about Infinity

Stage: 3, 4 and 5

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. . . .

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How Many Elements Are There in the Cantor Set?

Stage: 4 and 5

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

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Hilbert's Hotel

Stage: 4 and 5

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