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.
Approximations
| 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 | \(g_{\varepsilon_0}(1000)\) |