Googolon = {]1,1[}
BiGoogolon = {]1,2[}
TriGoogolon = {]1,3[}
TetraGoogolon = {]1,4[}
Googolplexolon = {]2,1[}
BiGoogoloplexolon = {]2,2[}
Nullimega ( 0.ω ) = 0.r0{ω}1 (0. followed by ω zeros and a 1)
Ξ0 = φ(φ(φ(..{ω}..),φ(..{ω}..),φ(..{ω}..)...{ω}),φ(φ(..{ω}..),φ(..{ω}..),φ(..{ω}..)...{ω}),φ(φ(..{ω}..),φ(..{ω}..),φ(..{ω}..)...{ω})...{ω})
Ξ(x) = φ(φ(φ(..{Ξ(x-1)}..),φ(..{Ξ(x-1)}..),φ(..{Ξ(x-1)}..)...{Ξ(x-1)}),φ(φ(..{Ξ(x-1)}..),φ(..{Ξ(x-1)}..),φ(..{Ξ(x-1)}..)...{Ξ(x-1)}),φ(φ(..{Ξ(x-1)}..),φ(..{Ξ(x-1)}..),φ(..{Ξ(x-1)}..)...{Ξ(x-1)})...{Ξ(x-1)})
A joke number
{](10^100)@(10^100)[} or {]10^100,10^100,10^100,10^100...10^100,10^100,10^100[} having 10^100 inputs