In This Chapter
Identifying counting numbers, integers, rational numbers, and real numbers
Discovering imaginary and complex numbers
Looking at how transfinite numbers represent higher levels of infinity
The more you find out about numbers, the stranger they become. When you're working with just the counting numbers and a few simple operations, numbers seem to develop a landscape all their own. The terrain of this landscape starts out uneventful, but as you introduce other sets, it soon turns surprising, shocking, and even mind blowing. In this chapter, I take you on a mind-expanding tour of ten sets of numbers.
I start with the familiar and comfy counting numbers. I continue with the integers (positive and negative counting numbers and 0), the rational numbers (integers and fractions), and real numbers (all numbers on the number line). I also take you on a few side routes along the way. The tour ends with the bizarre and almost unbelievable transfinite numbers. And in a way, the transfinite numbers bring you back to where you started: the counting numbers.
Each of these sets of numbers serves a different purpose, some familiar (such ...