LND Function

LND function is a function defined by .Googology guy's site - LND Function. Retrieved 2023-08-05. It stands for Largest Number Definable and takes an input n and outputs the largest number definable using basic arithmetic, exponentiation of the form ab and up arrow notation, with no more than n symbols.
== Analysis ==
Here are the first few values from the source.
# \(\text{LND}(1)=9\)
# \(\text{LND}(2)=9^9\)
# \(\text{LND}(3)=9^{9^9}\)
# \(\text{LND}(4)=9\uparrow^9 9\)
By assuming that the basic arithmetic means the symbols of +, -, *, /, (), the calculation can continue as
* \(\text{LND}(5)=9\uparrow^{9^9} 9\)
* \(\text{LND}(6)=9\uparrow^{9^{9^9}} 9\)
* \(\text{LND}(7)=9\uparrow^{9\uparrow^9 9} 9\) = 9{{1}}3 (Expansion) = {9,3,1,2} (BEAF)
* \(\text{LND}(10)=9\uparrow^{9\uparrow^{9\uparrow^9 9} 9} 9\) = 9{{1}}4 = {9,4,1,2}
* LND(3n-2) = 9{{1}}n = {9,n,1,2} for n = 2,3,4,...
== Sources ==
Category:Functions
Category:Notations
Category:Numbers and functions by Googology guy