Nathan S Brown

SIMPLE INTRODUCTION TO MUNBER THEORY

zeroth edition

Acknowledgements

The investigation of munbers began during the first term of my frosh year at Caltech, when, in lecturing, one of the TAs [I think it was Tihomir] rightfully observed that two can't equal three, or something of the sort. This started me thinking. What if there was an object that could equal more than one number at a time? I jotted down in my notebook: MUNBER: multiple-value number. From then on, I spread my idea. Some found my idea strange, if not completely wacko. Others found it pointless: "Why can't you just use sets?" But there were a select few who believed.

Three people especially are owed a great debt for catalyzing the formation of this book. Whilst waiting for dessert, Clara Graham, Gray Rybka, Elizabeth Thomas, and I became engaged in a discussion about munbers, which had been sitting in the midst of my brain all this time. We began to formulate a few of their properties, until someone said, "You should write this down."

So here is the result. Endless thanks go out to the central members of the R&D team. Clara, Gray, and Liz have all provided various inputs, several of which went directly into this book. Brock Beauchamp, Jamal Rorie, and Sam Yeager are among the other contributors to this theory of munbers. Another influence has been Tom M Apostol, mathematics professor here at Caltech. Although I have yet to introduce him to munbers, his Calculus books provided some inspiration for this work.

Contents

• 1 Meet the Munbers! [added SUN 17 JAN 1999]
  • 1.1 Definition and properties of munbers
  • 1.2 Operations on munbers
  • 1.3 Field properties of munbers
  • 1.4 Exercises
  • 1.5 Geometric representation of munbers
  • 1.6 Using geometric representations
  • 1.7 Exercises
• 2 Other Sets of Munbers [added SUN 31 JAN 1999]
  • 2.1 Review of real munbers
  • 2.2 Integer munbers
  • 2.3 Rational munbers
  • 2.4 Complex munbers
  • 2.5 Exercises
• 3 Munbers as Numbers [added WED 17 MAR 1999]
  • 3.1 Introduction
  • 3.2 Binary operations on munbers
  • 3.3 Functions of munbers
  • 3.4 Muneric inverses of functions
  • 3.5 Zero and unit munbers
  • 3.6 Exercises
• 4 Munbers as Sets [added WED 17 MAR 1999]
  • 4.1 Introduction. Sets into munbers
  • 4.2 Review of basic set operations
  • 4.3 Supremum and infimum of munbers
  • 4.4 Exercises
  • 4.5 Maximum, minimum of munbers
  • 4.6 Statistical functions of munbers
  • 4.7 Exercises
• 5 Weighted Munbers [added SUN 26 MAR 2000]
  • 5.1 The need for weighted munbers
  • 5.2 Weighting a finite munber
  • 5.3 Redefining basic concepts
  • 5.4 Exercises
  • 5.5 Applications of weighted munbers
  • 5.6 Interpretations of weighted munbers
  • 5.7 Exercises