Tetra-trideca is equal to {10{10}10{10}10{10}10} using galaxy array notation.[1] The term was coined by Googology Wiki user Binary198. The creator insisted that it is the largest number coined by using dimensional galaxy array notation,[2], but the size does not make sense because galaxy array notation is ill-defined as we explain in galaxy array notation#Issue. Namely, Tetra-trideca is ill-defined.
Approximations in other notations[]
Since the number itself is ill-defined, we just give an approximation of the intended value.
| Notation | Approximation |
|---|---|
| Bowers' Exploding Array Function | \(\{10,\{10,10(10)2\}(0,1)2\}\) |
| Bird's array notation | \(\{10,\{10,10[11]2\}[1,2]2\}\) |
| Cascading-E notation | \(\textrm{E}10\textrm{#^#^#}10\textrm{#}2\) |
| Fast-growing hierarchy | \(f_{\omega^{\omega^{10}}}^3(10)\) |
| Hardy hierarchy | \(H_{\omega^{\omega^{\omega^{10}}}}^3(10)\) |
| Slow-growing hierarchy | \(g_{\vartheta(\Omega^{\Omega^9}\omega)}^3(10)\) |
Sources[]
- ↑ A mathematical journey. Retrieved 2021-10-31.
- ↑ The first version of this arctile