Aarex function
Based onXi function
Growth rate\(f_{\omega_\alpha^\text{CK}+\omega^2}(n)\)
The Aarex function is a googological function invented by Aarex Tiaokhiao.[1] It is defined as follows:
  • \(\text{Arx}(1,m) = 10^6 = 1{,}000{,}000\)
  • \(\text{Arx}(n,1) = \Xi(\text{Arx}(n-1,1))\)
  • \(\text{Arx}(n,m) = \text{Arx}(\text{Arx}(n-1,m),m-1)\)

where \(\Xi\)(n) is the xi function, which was used due to Adam Goucher's mistaken claim that it outgrew Rayo's function. The function is a naive extension of the xi function and is easily beaten by functions such as the Rayo/FOST function and its stronger cousin the FOOT function

He later upgraded the function, adding the rules:

  • \(\text{Arx}(a,b,c,\cdots,y,1) = \text{Arx}(a,b,c,\cdots,y)\)
  • \(\text{Arx}(a,b,c,\cdots,x,y,z)\)
    \(= \text{Arx}(\text{Arx}(a,b,c,\cdots,x,y,z-1),\cdots,\text{Arx}(a,b,c,\cdots,x,y,z-1),1)\)

He further extended his function to multidimensional arrays, and then, instead of the xi function, started using \(\phi^\text{CK}(\omega,0)\). The current version combines Bird's array notation with this function.


  1. Aarex Tiaokhiao's large numbers site[dead link]