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Zero to Infinity

This is a Teachers’ TV programme from the series Painting with Numbers. In this episode Professor Marcus du Sautoy explains how humans have developed numbers for their mathematical needs. We learn that humans first began counting with whole numbers only, but then needed to invent others as their mathematical skills increased.

Exponential growth is explained by placing one grain of rice on the first square of a chessboard, two grains on the second square, four grains on the third and so on which leads to an explanation of the role the digit zero played using place value to represent larger numbers. He then explains the problems encountered when attempting to divide by zero and takes us to Hilbert's Hotel to demonstrate the mind-boggling concept of infinity and looks at the difference between countable and non-countable infinities.

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