title: Convergence - Journey to Nyorfias Book 1
author:  T. M. Roy 
description: <b>When the going gets tough...</b><br /> Sergeant Rett of the Nyorfian Special Forces is in the fight of her life, for herself and her worlds. She doesn't realize she's the key Player in a local battle of a Game of universal scope: the struggle of the Guardians of Balance to maintain a healthy equilibrium between evil and good, darkness and light.<br /><span></span><br /><b><span></span>...the tough deal with it...</b><br /> The neophyte Guardian for Nyorfias, Pheasyce, faces an ancient and powerful force of Dark, and must risk all in a dangerous and unique strategem, one that uses Rett as the focus. Arranging the convergence between the key Player and an imaginative dreamer from another world could be the best tactic ever.<br /><span></span><br /><b><span></span>...or maybe not.</b><br />That is, as long as Pam, who thinks this is all a dream, doesn't get Rett killed first. And as long as Rett can accept this dimwitted alien mindforce... from some planet called Earth.
zlib_text: Analysis
  
  Dr J.M.E. Hyland1
  
  Michælmas 1996
  
  1Comments and corrections to soc-archim-notes@lists.cam.ac.uk
  
  Revision: 1.5
  
  Date: 1998-10-27 15:54:56+00
  
  The following people have maintained these notes.
  
  initial typing
  
  Richard Cameron
  
  – date
  
  Paul Metcalfe
  
   **Contents**
  
   **Introduction**
  
   **v**
  
   **1**
  
   **Real Numbers**
  
   **1**
  
  1.1
  
  Ordered Fields
  
  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
  
  1
  
  1.2
  
  Convergence of Sequences . . . . . . . . . . . . . . . . . . . . . . .
  
  1
  
  1.3
  
  Completeness of R: Bounded monotonic sequences . . . . . . . . . .
  
  4
  
  1.4
  
  Completeness of R: Least Upper Bound Principle . . . . . . . . . . .
  
  5
  
  1.5
  
  Completeness of R: General Principle of Convergence . . . . . . . .
  
  7
  
   **2**
  
   **Euclidean Space**
  
   **9**
  
  2.1
  
  The Euclidean Metric . . . . . . . . . . . . . . . . . . . . . . . . . .
  
  9
  
  2.2
  
  Sequences in Euclidean Space . . . . . . . . . . . . . . . . . . . . .
  
  9
  
  2.3
  
  The Topology of Euclidean Space . . . . . . . . . . . . . . . . 