2.1.1 - Introduction

2.1.1

Introduction

In Section I we learned how we could express and manipulate the integers. We saw that it wasn't difficult to develop numerical notations that could express huge numbers, much larger than we would encounter in day to day life. In Chapter 2.1 we will be putting those numbers to some good use, counting objects in the known universe. Then we'll see that even larger numbers than those in cosmology can be put to practical use when we count configurations in combinatorics.

The "Cosmic Horizon" refers to the limit of our ability to look into the cosmos. In a sense there are many "Cosmic Horizons". These are the boundaries of our ability to know the full size and extent of existence. These cosmic horizons put definite limits on the largest kinds of numbers which can serve a purpose in science. We will be taking science to the absolute limit to find out what the largest finite numbers in science actually are! We'll discover that for some of these numbers, even our decimal notation is inadequate!

For that reason we'll begin Chapter 2.1 by learning about scientific notation. This notation allows us to express, in general terms, a vaster range of values than decimal notation, and with far greater ease. Even scientific notation however, is unable to handle some of the numbers occurring in combinatorics. For this purpose we'll have to learn about stacked exponential notation.

When we are finished with this chapter you'll have a far greater appreciation of just how large numbers can get even in mainstream science, and yet as we'll discover through subsequent chapters ... even these numbers pale in comparison to what mathematics is capable of...

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