User blog comment:Dchew89/Basic Notation for Reaching FGH epsilon Level/@comment-35470197-20190301014624

\(\{2\}[2]^2\) is ill-defined because it is computed in the following way: \begin{eqnarray*} \{2\}[2]^2 & = & \{\ldots^2\{2\}[2]^1\ldots^2\}[2]^1\}[2]^1 \\ & = & \{\{\{2\}[2]^1\}[2]^1\}[2]^1 \end{eqnarray*} Here, you have no rule to compute \([2]\{2\}^1\), because you have only defined \(\{a\}[b]^0\) for the case \(a = b\) and \(\{a\}[b]^c\) for the case \(a = b = c\).