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Number Lines

Number Lines

Linear models of number are very important as they support the development of an informal internal representation of number magnitude, called the mental number line. Different models are best suited to the teaching of different skills and understandings at different levels. This book is designed to help teachers make the best use of number tracks, number grids, and both empty and calibrated number lines.

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Home > Student activities > National Maths Day > National Maths Day 2014 > Hilbert’s paradox of the Grand Hotel

Hilbert’s paradox of the Grand Hotel

The Grand Hotel has an infinite number of rooms, all of which are occupied. Can the hotel accommodate any more guests?

Move the person occupying room 1 to room 2, the person occupying room 2 to room 4, and, in general, the person occupying room n to room 2n. Then all the odd-numbered rooms will be free for the new guests.