The gulgolplex is equal to E(E100#100#100#100#100#100) using Hyper-E notation.[1] It is equal to 1 followed by gulgol zeroes or 10gulgol. The term was coined by Sbiis Saibian to show how negligible the effect the -plex prefix gives to octational level numbers. It is gulgol+1 digits long.
Etymology[]
The 2 parts of the name, "gulgol" and "-plex" means E100#100#100#100#100#100 and 10n which basically means 1 followed by n zeroes, which formed 10(E100#100#100#100#100#100) (1 followed by gulgol zeroes) when concentrated from left to right. So the full name indicates how the number is constructed.
Approximations in other notations[]
| Notation | Approximation |
|---|---|
| Up-arrow notation | \(10^{100 \uparrow^{6} 101}\) |
| Chained arrow notation | \(10→(100 \rightarrow 101 \rightarrow 6)\) |
| BEAF | \(\{10,\{100,101,6\}\}\) |
| Hyperfactorial array notation | \(\text{gulgol}!\) |
| Fast-growing hierarchy | \(f_2(f_7(100))\) |
| Hardy hierarchy | \(H_{\omega^2+\omega^7}(100)\) |
| Slow-growing hierarchy | \(g_{\omega^{\varphi(5,0) + 1}}(100)\) |
Sources[]
- ↑ Sbiis Saibian, Hyper-E Numbers - Large Numbers