What is the identity of the irrational number

Summary

Not all numbers are the same before the Lord. The real numbers correspond to points on the number line and are similar in this sense, but there are still huge differences between them. Some of them were created by the early humans (1,2,3), others by the cultured Greeks (√2, π) and still others from the discoverers of differential and integral calculus (e). In addition to the elementary distinction between whole and non-whole numbers, there is a division into rational and irrational numbers or into algebraic and transcendent numbers. Other properties of certain - but not all - real numbers, such as normality and predictability in real time, are of more modern origin. In this chapter we present some unsolved problems about the properties of some famous numbers, and along the way we will encounter some interesting but lesser-known numbers, such as the Champernowne number (0.12345678910111213 ...) and the Liouville number (0.1100010000000000000001000 .. .).

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Authors and Affiliations

  1. 1. University of Washington USA
  2. 2.Macalester CollegeUSA