Thousalogue is a base googolism of the second order Hyper-L Notation invented by JTOnstead20. It is defined as \(L((3))\) in the notation.[1] This means the following:

Take the reverse Log function of 3 to get 1000. Then use the double parenthesis to build a power tower starting with \(10^{1000^{1000^{...}}}\) and going 1000 units high. This is roughly equivalent to \(1000\uparrow\uparrow 1000\) in arrow notation.


Notation Approximation
Up-arrow notation \(1000\uparrow\uparrow 1000\)
Hyper-E notation \(E1000\#1000\)
BEAF \(\{1000,1000,2\}\)
Chained arrow notation \(1000 \rightarrow 1000 \rightarrow 2\)
Notation Array Notation (1000{2,2}1000)
Hyperfactorial array notation \(1000!1\)
Nested Factorial Notation \(1000![2]\)
Fast-growing hierarchy \(f_3(1000)\)
Hardy hierarchy \(H_{\omega^3}(1000)\)
Slow-growing hierarchy \(g_{\varepsilon_0}(1000)\)


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