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p. 564. Limits and infinitylocked

  • Timothy Gowers

Abstract

In one way or another, the concept of infinity is indispensable to mathematics, and yet it is a very hard idea to make rigorous. ‘Limits and infinity’ discusses three statements that each look innocent enough at first, but turn out, on closer inspection, to involve the infinite. The first is to do with the square root of two, which concerns infinite decimals; the second involves the acceleration of a car; and the third considers the calculation of the area of a circle. How to deal with the difficulties that infinity creates is then explained.

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