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This is a book about interesting and entertaining numbers, but not just any numbers. We will restrict our attention to the integersIntegers, numbers which can be written without a fractional component, e.g. 3, \(-5\) and 89. Of course, numbers like 3.75, 22/7, \(\sqrt{2}\) are not integers. Because counting is fundamental to almost all human activity, the integers were the only category of numbers of which our early ancestors were aware. Indeed, today we distinguish those integers used in counting, the positive integers, as the natural numbersNatural numbers. What makes the integers special is that while the sum, difference or product of any two integers is also an integer, their quotient is in general not an integer. We learned this in elementary school when performing long division. Consider 315/29: we can divide 315 by 29 and find that \(315=10\times 29+25\) .

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Introduction

  • 章节

  • 发表日期：

    2025年

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  • Eric L. F. Roettger,
  • Hugh C. Williams

摘要

This is a book about interesting and entertaining numbers, but not just any numbers. We will restrict our attention to the integersIntegers, numbers which can be written without a fractional component, e.g. 3, \(-5\) and 89. Of course, numbers like 3.75, 22/7, \(\sqrt{2}\) are not integers. Because counting is fundamental to almost all human activity, the integers were the only category of numbers of which our early ancestors were aware. Indeed, today we distinguish those integers used in counting, the positive integers, as the natural numbersNatural numbers. What makes the integers special is that while the sum, difference or product of any two integers is also an integer, their quotient is in general not an integer. We learned this in elementary school when performing long division. Consider 315/29: we can divide 315 by 29 and find that \(315=10\times 29+25\) .