Japanese characters for muryoutaisuu
Muryoutaisuu (無量大数 written in Japanese, means "large number without measure") is \(10^{68}\) in Japanese counting system[1][2]. It was derived from Chinese counting system, which was derived from Buddism's sutra in India. There are several different versions of counting systems in Chinese, meaning different numbers for the same Chinese character but different pronunciation[3].
It first appeared in Jinkouki (Japanese: 塵劫記) by Mitsuyoshi Yoshida in 1631. In the first edition of Jinkouki published in 1627, numbers up to Fukashigi was defined, and muryoutaisuu did not appear. In the 1631 edition of Jinkouki, definition of Muryoutaisuu was \(10^{88}\), and later in the 1634 edition of Jinkouki, definition changed to \(10^{68}\). Therefore, the definition of Muryoutaisuu is now \(10^{68}\).
In English, it is one hundred unvigintillion in short scale and one hundred undecillion in long scale.
The total mass-energy of the observable universe is estimated to be about 130 muryoutaisuu joules.
Approximations
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{68}\) | |
| Arrow notation | \(10\uparrow68\) | |
| Steinhaus-Moser Notation | 41[3] | 42[3] |
| Copy notation | 9[68] | 1[69] |
| Taro's multivariable Ackermann function | A(3,222) | A(3,223) |
| Pound-Star Notation | #*(12,0,8,4,3)*10 | #*(7,0,8,6,3,1)*8 |
| BEAF | {10,68} | |
| Hyper-E notation | E68 | |
| Bashicu matrix system | (0)(0)(0)(0)[17782] | (0)(0)(0)(0)[17783] |
| Hyperfactorial array notation | 52! | 53! |
| Fast-growing hierarchy | \(f_2(218)\) | \(f_2(219)\) |
| Hardy hierarchy | \(H_{\omega^2}(218)\) | \(H_{\omega^2}(219)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega6+8}}(10)\) | |
Sources
See also
Indian counting system: Lakh · Crore · Tallakshana · Uppala · Dvajagravati · Paduma · 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