Gar-

Gar- is a prefix invented by the then-six year old Kieran Cockburn, to indicate the number multiplied by itself that many times. Alistair pointed out that the gar- prefix on a number simply indicates its square: gar-n = n2. 
It is a backformation of gargoogolplex, which Kieran explicitly stated it to be the square of a googolplex, without using the term "square".
== Examples ==
*gar(1) = 1 = 1×1
*gar(2) = 4 = 2×2
*gar(3) = 9 = 3×3
*gar(4) = 16 = 4×4
*gar(5) = 25 = 5×5
*gar(6) = 36 = 6×6
*gar(7) = 49 = 7×7
*gar(8) = 64 = 8×8
*gar(9) = 81 = 9×9
*gar(10) = 100 = 10×10
*gar(100) = 10,000 = 100×100
*gar(1,000) = 1,000,000 = 1,000×1,000
*gar(googol) = 10200
*gar(googolplex) = 102×10100
*gar(gar(n)) = (n2)2 = n4
== In googological notations ==
Notation 	Expression
Fast-growing hierarchy	less than \(f_2(n)\)
Hardy hierarchy 	less than \(H_{\omega^2}(n)\)
Slow-growing hierarchy	\(g_{\omega^2}(n)\) (exact)
The Q-supersystem 	\(Q_2(n)\) (exact)
== Sources ==
== See also ==
Category:Fuga- family
Category:Numbers discussed by Alistair Cockburn
Category:Prefixes
Category:Functions