Section 1 The Number Tree
Most numbers that we work with come from the set of numbers called the complex numbers. These numbers are of the form \(a + bi \) where \(a \) and \(b \) are real numbers and \(i =\sqrt{-1} \text{.}\) If \(b = 0 \) we are left with just the real number \(a \) and if \(a = 0 \) we are left with the number \(bi \text{,}\) what we will call a purely imaginary number.
From here the real numbers can be broken down into rational and irrational, and the rationals can be further divided into Integers, Natural Numbers, and then evens and odds. Further division can happen, but we will end here.
This general overview is nice, but starting with the complex stacks all the information at once. So instead of starting with the top (the complex numbers) we will start with at the bottom of the tree with the natural numbers.