There are a few very popular sets that we will be using in our study of Linear Algebra. These sets show up in many fields of mathematics and as such have standard names. We will define each of these for future reference:

• $\mathbb{N}=\{1,2,3,4,5,\dots \}$, the set of natural numbers or positive integers.
• $\mathbb{Z}=\{\dots ,-3,-2,-1,0,1,2,3,\dots \}$, the set of integers.
• $\mathbb{Q}=\{x:x=\frac{p}{q}\text{ for some }p,q\in \mathbb{Z},q\ne 0\}$, the set of rational numbers.
• $\mathbb{R}=\{x:x\text{ is a real number }\}$, the set of real numbers.
• $\mathbb{C}=\{x:x=a+bi\text{ for some }a,b\in \mathbb{R},i=\sqrt{-1}\}$, the set of complex numbers.