## Numbers: A Very Short IntroductionNumbers are integral to our everyday lives and feature in everything we do. In this Very Short Introduction Peter M. Higgins, the renowned mathematics writer, unravels the world of numbers; demonstrating its richness, and providing a comprehensive view of the idea of the number. Higgins paints a picture of the number world, considering how the modern number system matured over centuries. Explaining the various number types and showing how they behave, he introduces key concepts such as integers, fractions, real numbers, and imaginary numbers. By approaching the topic in a non-technical way and emphasising the basic principles and interactions of numbers with mathematics and science, Higgins also demonstrates the practical interactions and modern applications, such as encryption of confidential data on the internet. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. |

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### Contents

1 How not to think about numbers | 1 |

2 The unending sequence of primes | 16 |

3 Perfect and not so perfect numbers | 27 |

the secret life of primes | 36 |

5 Numbers that count | 52 |

6 Below the waterline of the number iceberg | 69 |

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### Common terms and phrases

abundant numbers algebraic Alice and Bob aliquot sequence argument arise arithmetic series Arithmetic Triangle base binomial coefficients calculate Cantor’s Catalan numbers Chapter cipher collection complex numbers composite number continued fraction coprime corresponding counting numbers cryptography cube decimal expansion denominator diagonal divided division divisor enciphering equal Euclid Euclidean Algorithm example Fibonacci numbers formula geometric given number gives Golden Ratio imaginary integers irrational number known mathematical mathematician matrix Mersenne number Mersenne primes multiplication n-set negative numbers number line number system odd numbers one-time pad pair partition Pell equation perfect numbers plaintext polar coordinates powers prime factors prime numbers problem Pythagorean triple quaternions rational numbers real numbers represent representation secret simple solution square root Stirling numbers subsets subtract symbols ternary expansion Theorem transcendental triangular number unit fraction whole number zero