Asougi in kanji. (Note that Chinese uses several graphical differences.)
An asougi (Hepburn: asōgi) or asengqi (阿僧祇 in Japanese and Chinese, Sanskrit for "uncountably large number") is \(10^{56}\)[1] in the Japanese counting system.The number was used in Buddhist sutras, and it was adopted in the traditional Japanese and Chinese numbering systems. This number used to have multiple different definitions caused by the incontinuity of Buddhist sutras (see Asankhyeya), but in the modern day traditional Japanese system, it now exclusively refers to \(10^{56}\).[2].
In English, it is one hundred septendecillion in short scale or one hundred nonillion in long scale.
Approximations in other notations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{56}\) | |
| Arrow notation | \(10\uparrow56\) | |
| Steinhaus-Moser Notation | 35[3] | 36[3] |
| Copy notation | 9[56] | 1[57] |
| Taro's multivariable Ackermann function | A(3,183) | A(3,184) |
| Pound-Star Notation | #*(7,4,5,4,1,3)*6 | #*(1,1,9,4)*11 |
| BEAF | {10,56} | |
| Hyper-E notation | E56 | |
| Bashicu matrix system | (0)(0)(0)(0)[3162] | (0)(0)(0)(0)[3163] |
| Hyperfactorial array notation | 44! | 45! |
| Strong array notation | s(10,56) | |
| Fast-growing hierarchy | \(f_2(178)\) | \(f_2(179)\) |
| Hardy hierarchy | \(H_{\omega^2}(178)\) | \(H_{\omega^2}(179)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega5+6}}(10)\) | |
Sources[]
See also[]
Indian counting system: Lakh · Crore · Padma · Tallakshana · Ogha · Ababa · Atata · Sogandhika · Uppala · Dvajagravati · Kumuda · Pundarika · Paduma · Kathana · Mahakathana · Asankhyeya · Dvajagranisamani · Vahanaprajnapti · Inga · Kuruta · Sarvanikshepa · Agrasara · Uttaraparamanurajahpravesa · Avatamsaka Sutra · Nirabhilapya nirabhilapya parivarta · Jaghanya Parīta Asaṃkhyāta
Chinese, Japanese and Korean counting system: Wan · Yi · Zhao · Jing · Gai · Zi · Rang · Gou · Jian · Zheng · Zai · Ji · Gougasha · Asougi · Nayuta · Fukashigi · Muryoutaisuu
See also: Template:Googology in Japan