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# 2 Numbers

This chapter is about numbers. A pertinent question to ask is: ``What is a number?''. Rather than answering such a philosophically contentious question I will answer a simpler question: ``What are numbers used for?''. Numbers are used to quantitatively describe things. For a description to be quantitative it must be possible to mechanistically compare and combine descriptions in a meaningful way.

In this chapter I will very briefly describe some common number systems before introducing a novel system of numbers. This chapter is intended to be pragmatic. Extraneous philosophical debate will be omitted. Readers are encouraged to consult [25, 67] for a deeper discussion of the nature of numbers.

A note, for the mathematically mature reader: the first four sections of this chapter define , , , and along with some standard notation. Please begin reading with section , and use the initial sections for reference, as necessary.

Next: 2.1 Integers Up: Generalized Interval Arithmetic M.Sc. Thesis Previous: 1.7 Outline
 Jeff Tupper March 1996