User blog:Vel!/Mega-Array Notation

Let \(U(x)\) be updog.

Rule 1: \(\{a\} = \{a, 1\} = U(a)\)

Rule 2: \(\{a, b\} = \{U(a), \{a, b - 1\}\}\)

Rule 3: \(\{a, b, 1\} = \{a, b\}\)

Rule 4: \(\{a, b, c\} = \{U(a), \{a, b - 1, c\}, U(c)\}\)

Growth rate is \(f_{\vartheta(\varepsilon_{\Omega_\omega + 1})}(n)\)