Notation

We use the following conventions.

$\mathbb{N}=\{1,2,3,\mathrm{\dots }\}$ is the set of natural numbers, or positive integers.

$\mathbb{Z}=\{\mathrm{\dots },-2,-1,0,1,2,\mathrm{\dots }\}$ is the set of integers.

$\mathbb{Q}=\{{\displaystyle \frac{p}{q}}|p,q\in \mathbb{Z},q\ne 0\}$ is the set of rational numbers, or fractions. This definition uses set notation; in words it says “the collection of all numbers of the form ${\displaystyle \frac{p}{q}}$ where $p,q$ are both integers and $q$ is not 0.”

$ℝ$ is the set of real numbers, including all the rational numbers and the irrational ones (as $\pi ,e,\sqrt{2}$, etc…).

The product of two numbers $a,b$ is written as $ab$, or $a\cdot b$. For instance