Creating Numbers and Number Systems

In this book, we will be focusing very closely on numbers and their properties and ways to calculate with numbers that are not precise. We will create basically two different kinds of numbers, which I will call: precise numbers and imprecise numbers. The difference between these two kinds of numbers lies in their degree of precision. In the case of a precise number, there is no room for error, whereas in case of an imprecise number, there can be some room for error if its value is reasonably close to the stated value.

In Part I of this book, we create precise numbers and number systems, starting with a lighthearted fictional story of how the numbers were created. Followed by a step-by-step approach to creating many sets of numbers and number systems.

The second part of the book is devoted to numbers that are close to precise numbers, but themselves, are not precise, called imprecise numbers. An imprecise number can be a collection of precise numbers that describes this type of number. The collection that describes an imprecise number may be very large, so we need to develop techniques for summarizing their properties. The first method for working with imprecise numbers that we will explore involves simplifying them by finding the means and standard deviations of the collections representing them and how to calculate with them.

The second approach that we will explore involves determining the imprecise number's acceptable maximum and minimum end points values. Once we have found these values, we will discuss techniques for calculating the resultants after applying different functions and operations. Using this technique, we can calculate the worst-case scenario type of error analysis