I am reading Foundations of Constructive Analysis by Errett Bishop. In the first chapter he describes a particular construction of the real numbers. There is a intermediate definition before his primary introduction of the Real numbers:
A sequence ${\{x_n\}}$ of rational numbers is regular if
$|x_m – x_n | \le m^{-1} + n^{-1}\;\;\;\;\;(m, n\in \Bbb Z^+)$
Chapter 1 (2.1)
What does the negative superscript mean in this definition? Since clearly you cannot take an integer to a negative power. Am I correct in interpreting $m$ and $n$ on the right hand side of the equation as the actual elements of the sequence? I am fairly sure the definition seems to parallel the Cauchy Sequence.
Best Answer
Ummm.... $m^{-1} = \frac{1}{m}$ ........