## U Can: Basic Math and Pre-Algebra For Dummies

Chapter 1
Playing the Numbers Game
In This Chapter
Finding out how numbers were invented
Looking at a few familiar number sequences
Examining the number line
Understanding four important sets of numbers
One useful characteristic about numbers is that they're conceptual, which means that, in an important sense, they're all in your head. (This fact probably won't get you out of having to know about them, though - nice try!)
For example, you can picture three of anything: three cats, three baseballs, three cannibals, three planets. But just try to picture the concept of three all by itself, and you find it's impossible. Oh, sure, you can picture the numeral 3, but threeness itself - much like love or beauty or honor - is beyond direct understanding. But when you understand the concept of three (or four, or a million), you have access to an incredibly powerful system for understanding the world: mathematics.
In this chapter, I give you a brief history of how numbers came into being. I discuss a few common number sequences and show you how these connect with simple math operations like addition, subtraction, multiplication, and division.
After that, I describe how some of these ideas come together with a simple yet powerful tool: the number line. I discuss how numbers are arranged on the number line, and I also show you how to use the number line as a calculator for simple arithmetic. Finally, I describe how the counting numbers (1, 2, 3, ...) sparked the invention of more unusual types of numbers, such as negative numbers, fractions, and irrational numbers. I also show you how these sets of numbers are nested - that is, how one set of numbers fits inside another, which fits inside another.
Inventing Numbers
Historians believe that the first number systems came into being at the same time as agriculture and commerce. Before that, people in prehistoric, hunter-gatherer societies were pretty much content to identify bunches of things as "a lot" or "a little."
But as farming developed and trade between communities began, more precision was needed. So people began using stones, clay tokens, and similar objects to keep track of their goats, sheep, oil, grain, or whatever commodity they had. They exchanged these tokens for the objects they represented in a one-to-one exchange.
Eventually, traders realized that they could draw pictures instead of using tokens. Those pictures evolved into tally marks and, in time, into more complex systems. Whether they realized it or not, their attempts to keep track of commodities led these early humans to invent something entirely new: numbers .
Throughout the ages, the Babylonians, Egyptians, Greeks, Romans, Mayans, Arabs, and Chinese (to name just a few) all developed their own systems of writing numbers.
Although Roman numerals gained wide currency as the Roman Empire expanded throughout Europe and parts of Asia and Africa, the more advanced system that the Arabs invented turned out to be more useful. Our own number system, the Hindu-Arabic numbers (also called decimal numbers), is closely derived from these early Arabic numbers.
Understanding Number Sequences
Although humans invented numbers for counting commodities, as I explain in the preceding section, they soon put them to use in a wide range of applications. Numbers were useful for measuring distances, counting money, amassing an army, levying taxes, building pyramids, and lots more.
But beyond their many uses for understanding the external world, numbers have an internal order all their own. So numbers are not only an invention, but equally a discovery: a landscape that seems to exist independently, with its own structure, mysteries, and even perils.
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