The gorgegolplex is equal to E(E100#100#100#100#100) using Hyper-E notation.[1] It is equal to 1 followed by gorgegol zeroes or 10gorgegol. The term was coined by Sbiis Saibian to show how negligible the effect the -plex prefix gives to heptational level numbers. It is gorgegol+1 digits long.
Etymology[]
The 2 parts of the name, "gorgegol" and "-plex" means E100#100#100#100#100 and 10n which basically means 1 followed by n zeroes, which formed 10(E100#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 | Lower bound | Upper bound |
|---|---|---|
| Arrow notation | \(10^{100 \uparrow^{5} 101}\) | \(10^{100 \uparrow^{5} 101 + 1}\) |
| Chained arrow notation | \(10→(100 \rightarrow 101 \rightarrow 5)\) | \(10→((100 \rightarrow 101 \rightarrow 5)+1)\) |
| BEAF & Bird's array notation | \(\{10,\{100,101,5\}\}\) | \(\{10,\{100,101,5\}+1\}\) |
| Hyperfactorial array notation | \(\text{gorgegol}!\) | \(\text{gorgegol} + 1!\) |
| Fast-growing hierarchy | \(f_2(f_6(100))\) | \(f_2^2(f_6(100))\) |
| Hardy hierarchy | \(H_{\omega^6}(100)\) | \(H_{\omega^6}(101)\) |
| Slow-growing hierarchy | \(g_{\omega^{\varphi(4,0) + 1}}(100)\) | \(g_{\omega^{\varphi(4,0) + 2}}(100)\) |
Sources[]
- ↑ Sbiis Saibian, Hyper-E Numbers - Large Numbers