The trenanillion is equal to 109,000,000,003 in short scale.[1] It is equal to 1018,000,000,000 in the long scale. It is defined using Sbiis Saibian's generalization of Jonathan Bowers' -illion system.
Approximations[]
For short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{9000000003}\) | |
| Arrow notation | \(10\uparrow9000000003\) | |
| Down-arrow notation | \(42\downarrow\downarrow7\) | \(248\downarrow\downarrow5\) |
| Steinhaus-Moser Notation | 9[3][3] | 10[3][3] |
| Copy notation | 8[8[10]] | 9[9[10]] |
| H* function | H(3H(2)) | |
| Taro's multivariable Ackermann function | A(3,A(3,31)) | A(3,A(3,32)) |
| Pound-Star Notation | #*((1))*31075 | #*((1))*31076 |
| BEAF | {10,9000000003} | |
| Hyper-E notation | E9000000003 | |
| Bashicu matrix system | (0)(1)[5] | (0)(1)[6] |
| Hyperfactorial array notation | (12!)! | (13!)! |
| Fast-growing hierarchy | \(f_2(f_2(29))\) | \(f_2(f_2(30))\) |
| Hardy hierarchy | \(H_{\omega^22}(29)\) | \(H_{\omega^22}(30)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^99+3}}(10)\) | |
For long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{18000000000}\) | |
| Arrow notation | \(10\uparrow18000000000\) | |
| Down-arrow notation | \(98\downarrow\downarrow6\) | \(47\downarrow\downarrow7\) |
| Steinhaus-Moser Notation | 9[3][3] | 10[3][3] |
| Copy notation | 1[1[11]] | 2[2[11]] |
| H* function | H(5H(2)) | H(6H(2)) |
| Taro's multivariable Ackermann function | A(3,A(3,32)) | A(3,A(3,33)) |
| Pound-Star Notation | #*((1))*43283 | #*((1))*43284 |
| BEAF | {10,18000000000} | |
| Hyper-E notation | E(18E9) | |
| Bashicu matrix system | (0)(1)[5] | (0)(1)[6] |
| Hyperfactorial array notation | (12!)! | (13!)! |
| Fast-growing hierarchy | \(f_2(f_2(30))\) | \(f_2(f_2(31))\) |
| Hardy hierarchy | \(H_{\omega^22}(30)\) | \(H_{\omega^22}(31)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^\omega+\omega^98}}(10)\) | |