The Dual Numbers#
Definition: Dual Number
A dual number is an expression of the form
\[ a + b\varepsilon, \]
where \(a, b \in \mathbb{R}\) are real numbers and \(\varepsilon\) is defined such that
\[ \varepsilon^2 = 0 \text{ and } \varepsilon \ne 0. \]
Notation
The set of all dual numbers is usually denoted by \(\mathbb{R}[\varepsilon]\).