title: "Rational Number"

Rational Number

Definition. A real number $x$ is rational if $x = a/b$ for some integers $a$ and $b$ with $b \neq 0$. Every rational number has a lowest-terms form in which $a$ and $b$ share no common factor greater than 1.

A real number that is not rational is irrational. Defined in Lecture 1; the positive rationals are countable (Lecture 2, Example 3).