Chapter 1 Prologue
¶What is number theory? Briefly, it is the study of the integers and questions arising from them.
Definition 1.0.1. The Integers.
The set of counting numbers is denoted
\begin{equation*}
\mathbb{N} = \{0,1,2,3,4,\cdots\}\text{.}
\end{equation*}
Note that in this text, this set begins at zero. The integers is the set of positive and negative counting numbers:
\begin{equation*}
\mathbb{Z} = \{ \cdots ,-3,-2,-1,0,1,2,3,\cdots \}\text{.}
\end{equation*}
This is a fairly dry definition, though. The best way to find out what this definition means is to try to answer some questions about integers!