Treexillion is equal to \(10^{9\times 10^{3\times 10^{18}}+3}\).[1] It is defined using Sbiis Saibian's generalization of Jonathan Bowers' -illion system.
Etymology[]
"\( n \)-illion" means \( 10^{3n+3} \), "ex(o)-" means \( n=10^{3\times10^{18}} \). (6th entry in the 3rd tier), and "tre" means "three times", referring "ex". Therefore, "treexillion" means \(10^{3\times(3\times 10^{3\times 10^{18}})+3}\).
(note: Even though the name starts with "tree", it has nothing to do with TREE sequence.)
Approximations in other notations[]
| Notation | Approximation or exact value |
|---|---|
| Up-arrow notation | \(10 \uparrow\uparrow 4\) |
| Hyperfactorial array notation | \(6!1\) |
| Fast-growing hierarchy | \(f_3(6)\) |
| Hardy hierarchy | \(H_{\omega^3}(6)\) |
| Slow-growing hierarchy | \(g_{\omega^ {\omega^ {\omega^ {\omega+8}} } }(10)\) |
Sources[]
- ↑ Sbiis Saibian, Jonathan Bowers' 4 Tiered -illion Series - Large Numbers