# Resources tagged with: Infinity

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

Broad Topics > The Number System and Place Value > Infinity

### Diminishing Returns

##### Age 11 to 14Challenge Level

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

### Route to Infinity

##### Age 11 to 14Challenge Level

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

##### Age 11 to 18

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. . . .

### Odds, Evens and More Evens

##### Age 11 to 14Challenge Level

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

### How Many Elements Are There in the Cantor Set?

##### Age 14 to 18

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

### Hilbert's Hotel

##### Age 14 to 18

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

### How Long Is the Cantor Set?

##### Age 11 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?

### The Cantor Set

##### Age 11 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?