\begin{definition}[Definition:Hyperoperation/Sequence]
The '''hyperoperation sequence''' is the sequence $\left\langle{H_n}\right\rangle$ of binary operations $H_n : \Z_{\ge 0} \times \Z_{\ge 0} \to \Z_{\ge 0}$, defined as:
$\forall n, x, y \in \Z_{\ge 0}: H_n \left({x, y}\right) = \begin{cases}
y + 1 & : n = 0 \\
x & : n = 1, y = 0 \\
0 & : n = 2, y = 0 \\
1 & : n > 2, y = 0 \\
H_{n - 1} \left({x, H_n \left({x, y - 1}\right)}\right) & : n > 0, y > 0 \end{cases}$
\end{definition}