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p. 172. Numbers and abstractionlocked

  • Timothy Gowers

Abstract

‘Numbers and abstraction’ explains the abstract method of mathematics, which can be encapsulated in the slogan: a mathematical object is what it does, using a graph model of chess. It then goes on to describes the natural numbers; the concept of a number, which is intimately connected with the arithmetical operations of addition and multiplication; and the commutative, associative, and distributive laws for addition and multiplication. The properties of the number zero, negative numbers and fractions, real and complex numbers, infinity, and raising numbers to negative and fractional powers are also described.

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