What does a negative superscript mean on a positive Integer number

Question

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.

Answer 1

Ummm.... $m^{-1} = \frac{1}{m}$ ........

Answer 2

We have $$ m^{-1} + n^{-1}= \frac{1}{m}+\frac{1}{n}=\frac{m+n}{mn}. $$ So we can take an integer to a negative power, namely as $n^{-k}=\frac{1}{n^k}$. And can we use the complex number $i$ as an exponent? We sure can. See here.